Study on Support-Free Printing of Large-Flow Material Extrusion Process

Support-free printing is one of the research hotspots of material extrusion process-based 3D printing. When printing bridge or suspended structures, the sagging of large-flow extruded material probably causes printing failure due to its big mass and fusion state. If the support is added, it is hard to remove because of its large adhesion with the matrix. Therefore, large extrusion flow printing process is more willing to print structures without support; the large and complex structures are often difficult to print. In order to realize support-free printing of bridge structure, this paper defines a concept of quantitative fusing segment and analyzes its dynamic balance characteristics during the pellet extrusion printing process. Then the printing speed reduction and air cooling scheme according to the analysis conclusion are put forward, and the experimental verification is carried out. The results show that the sag deformation of bridge structure can be reduced effectively, and it proves that support-free printing is feasible by the rapid cooling method.


Introduction
In the trial production stage of automobiles and aviation, there are many thin-walled part manufacturing needs with large size, small quantity, and complex structure requirements. The traditional mold manufacturing method can easily cost millions, making the innovation verification cycle long and cost high. Material extrusion process-based 3D printing is becoming increasingly popular due to its low-cost and simple operation and maintenance. Pellet additive manufacturing (PAM) can cover the same applications as fused filament fabrication (FFF), and in addition, can lead to scale toward larger workspaces that cannot be covered by FFF, due to the limited diameters of standard filaments [1]. The width of a single bead of PAM based large-flow material extrusion process can meet the thickness requirements of thin-walled parts, and they can be manufactured efficiently and used directly after post-treatment. But it suffers from an inherent printing limitation where it cannot produce overhanging surfaces of non-trivial size. This limitation can be handled by constructing temporary support structures; however, this solution involves additional material costs, longer print time, and often a fair amount of labor in removing it [2]. These support structures have more serious impact on PAM. Support-free printing is a research hotspot in additive manufacturing.
Object partitioning is a common way to realize supportfree 3D printing [2,3], and multi-axis printing reinforces this approach [4]. The high degree of freedom of the robotic systems allows the fabrication of complex objects without support structures [5][6][7]; the model is decomposed into support-free parts that can be printed one by one in a collisionfree sequence [8,9]. Multiple model decomposition methods and multi-degrees of freedom 3D printers have been researched a lot. A model can be partitioned into several sub-parts using a gravity effect partition method simulating the material-falling process when the model is stacked along the Z direction [10]. Equidistant iso-polylines are obtained as gas metal arc welding path by using geodesic distance on triangular mesh to generate a geodesic scalar field [11]. A lattice infill structure generation method is researched by considering both the self-supporting condition for the infill and the support-free requirement at the boundary surface of the part [12]. There are some model decomposition methods for multidirectional 3D printing: a global-optimal decomposition method for minimizing the surface area to be supported [13,14], an accelerated decomposition algorithm based on neutral network [15], wire and arc additive manufacturing method with surface/interior separation and surface segmentation [16], etc. The methods mentioned above are mainly aimed at FFF, on one hand, the extrusion material is thin and light and its cooling is faster; on the other hand, part decomposition or printing path algorithms are not universal, different parts may have different algorithms.
In addition to multi-axis motion printing, there are some other methods for support-free printing. Some methods focus on printing materials. Self-healing materials can also realize free-standing seamless large-scale 3D printing [17]. Self-healing materials can be printed with modular designs capable of healing together to form highly complex and large parts [18]. Some methods focus on structural avoidance at the beginning of model design. A vertically arranged long ellipsoids can be used to realize support-free hollowing 3D printing [19]. An overhang angle constrained algorithm is used in model design to avoid the possible support demand risk [20]. There is also a support-free printing method that replaces the physical object of the supporting structure with ultrasonic levitation force [21].
The large-scale additive manufacturing (LSAM) of 3D printing of polymers is a commercial production field emerging from its infancy [22]. It has a large extrusion flow per unit of time. LSAM of thermoplastic material requires some new design ideas compared to small-scale additive manufacturing (SSAM) to create large-scale parts. For large-scale printing, the research contents are generally in thermal analysis [23], mechanical properties [24], characterizing material transitions [25], process simulation [26], fiber orientation analysis [27], extrusion control [28], layer time control [29], etc. LSAM stays hotter than SSAM for a longer period of time. This facilitates interlayer diffusion and weld formation, but can also lead to slumping or sagging [30]. To avoid slumping of overhanging features, the thermal profiles of large printed parts have been experimentally measured and mathematically modeled [31]. In large-scale PAM, the temperature of the substrate just before the deposition of a new subsequent layer affects the overall structure of the part [32]. So the temperature is one of the key parameters. As hot plastic is extruded over a large gap, small printers can bridge gaps of several inches; however, on the LSAM system, it will sag and break off due to the increased weight and temperature [33]. At present, the bridge or overhanging structures are avoided as far as possible in the printing process of LSAM system, and how to solve their sagging problem is rarely mentioned. This severely limits the printing of large and complex parts.
If the first layer of the bridge structure of a part can be printed without support, the subsequent layers can continue to print with this layer as a support. Based on this idea, in order to realize support-free printing of parts, the most important thing is to finish support-free printing of the first layer of the bridge structure. The main purpose of this paper is to verify the feasibility of support-free printing with rapid cooling method for large-scale PAM.

Printing problems of large-scale thin-walled parts in PAM
Most of the thin-walled parts contain features as suspended structure, bridge structure, etc., such as a car dashboard (see Fig. 1a and b). No matter how it is placed, according to the process characteristics, it needs a lot of support structures before it can be 3D printed (see Fig. 1c). Apparently, support-free PAM with one single bead will have less material and high efficiency for composite thin-walled parts (see Fig. 1d). Object partitioning and reassembling had been researched to manufacture a large thin-walled part, as shown in Fig. 2. An additional assembly datum was designed, the product was printed in two parts, and then they were bonded. The material was saved, but a lot of assembly time was consumed and the assembly accuracy was hard to guarantee. So one-time printing is the quality assurance for large-size thin-walled parts, and support-free printing is the guarantee of one-time successful printing.
Compared to small-scale 3D printing, the support structures in PAM will cause more serious problems. These unique problems mainly include the following three aspects: 1) With the increase of single bead width, the joint surface is enlarged and the supporting structure is more difficult to be removed. 2) The support structures will increase the number of discontinuous print paths, and in the switch positions, because of the viscous flow characteristics of the material and the delayed reaction of screw rotation, the defects of drawing fiber (see \* MERGEFORMAT Fig. 3a), too much or insufficient material will be formed (see \* MERGEFORMAT Fig. 3b). 3) Support structures will add more cross paths and printing time, thus may lead to greater thermal deformation, cause the collision risk between the print head and the printed layer.
In this paper, a novel low-cost large-scale support-free PAM method is proposed, and its feasibility is verified. This will provide a different idea from the existing research for support-free printing.

Fused deposition analysis model
The large flow printing process is described in \* MERGEFORMAT Fig. 4. First, the material is extruded out from the print head in direction y. Second, the material is deposited on the former layer along x direction. The material shape will change from section A to section B (see Fig. 4a), and they are equal in volume. The printing process can be described as the dynamic continuous transformation of section A to section B material. If external conditions remain unchanged, this stable transformation will continue. So section A is defined as quantitative fusing segment (QFS). In order to ensure the quality of the printed parts, it is better to extrude the same amount of material at the same print distance theoretically. Therefore, with the print head moves from position 1 to position 1′, the geometry of A′ material should be the same as that of QFS-A. The moving speed of the print head is analyzed by the average speed v.
The QFS-A and QFS-B are taken out separately for force analysis (see \* MERGEFORMAT Fig. 4b and c). QFS-A segment is under the action of gravity G A , the supporting force F A from the former fused deposition layer, the pulling force f AB (internal bonding force of the material between QFS-A and QFS-B), and the pulling force f A (internal bonding force of the material inside the print head). QFS-B segment is under the action of the gravity G B , the supporting force F B , and the pulling forces f AB and f B (internal bonding force). These forces are dynamically balanced during printing. The forces f AB , f A , and f B are strongly correlated with the material heat, which comes from the print head, the worktable, and the print workspace with heating function. The temperature field of the whole printing process is complex. In order to simplify the analysis, this paper only focuses on the temperature change at QFS-A.
Under the same printing conditions, the four forces of QFS-A are regarded as unchanged. Thus, the geometric shapes of QFS-A and QFS-B are in a relatively stable state. When the temperature or support area of QFS-A changes, this dynamic balance will be broken, and the geometric shapes of QFS-A and QFS-B should be changed. This includes the following possibilities: 1) When the temperature conditions change, the internal bonding force should be changed, f AB or f A changes 2) When the supporting area changes and F A disappears, the dynamic force balance of QFS-A will be seriously broken, its geometry shape will change, then resulting in print quality problems. 3) When the temperature conditions and the supporting area are both changed at the same time, the dynamic force balance of QFS-A will be lost immediately.

Experimental model design
In order to analyze and verify the possibility of printing with support-free, a cylindrical model with a part cut obliquely shown in \* MERGEFORMAT Fig. 5 is designed. D is diameter. H and h are, respectively, the highest and lowest heights of the cylinder. After slicing, a variety of unsupported monofilaments with different bridge spans can be generated, and the span also can be adjusted by changing the diameter D. The deformation of monofilaments with different spans can be compared intuitively.

Printing experiment
The PAM equipment used in this paper was developed by the author's team, whose printing size is 800 × 600 × 500 (mm). It was totally enclosed for heat preservation and equipped with a simple quick air cooling auxiliary component on the print head (see \* MERGEFORMAT Fig. 6). The diameters of the printing nozzle include 1 mm, 2.5 mm, and 3.5 mm, and 2.5 mm was adopted in this paper. The printing material used in this paper was acrylonitrile butadiene styrene (ABS) pellet. The screw print head was heated in two stages, and the upper part was heated at 175 °C and the lower part was heated at 200 °C. The printing ambient temperature was 40 °C. The printing process parameters were set as follows: the layer thickness was 1.5 mm, the layer width was 4 mm, and the printing speed was 70 mm/s. The theoretical diameter of extruded monofilament was calculated as 2.76 mm. The parameters of the experimental model were D = 200 mm, H = 100 mm, h = 73 mm. The sag of unsupported suspended monofilament increased regularly   Fig. 7). The smallest end diameter of the suspended monofilament was 1.51 mm, which was only 54% of the theoretical diameter.

Mechanical state of ABS material
The ABS material used in this experiment is POLYLAC PA-757, which is an amorphous polymer. It is divided into three mechanical states according to the temperature region-glassy state, elastomeric state, and viscous flow state (see Fig. 8). The glass transition temperature T g = 88 ℃, flow temperature T f = 190 ℃, the deformation of the material increases with the increase of temperature.
In the glassy state, due to the low temperature and low molecular motion energy, it is not enough to overcome the potential barrier of rotation in the main chain, and the chain segment is frozen. When the external force is exerted, only the bond length and bond angle of the main chain can be slightly changed. Therefore, from a macro perspective, the deformation of polymer under external force is very small, and it is directly proportional to the force. When the external force is removed, the deformation energy recovers immediately. At this time, ABS is in a state of general elasticity, and the degree of deformation is 0.01-0.1%.
In the elastomeric state, the energy of molecular thermal motion is enough to overcome the potential barrier of internal rotation. The molecule continuously changes the conformation through the internal rotation of the single bond in the main chain. At this time, the chain segment motion is excited, when an external force is exerted, the molecular chain can change the conformation through the internal rotation of the single bond and the chain segment to adapt it. For example, the molecular chain can change from the curled state to the extended state when a tensile force is exerted, so great deformation can occur macroscopically. Once the external force is removed, the molecular chain will return to the original curled state, which is shown as elastic retraction. This deformation is a process of internal rotation of the polymer main chain caused by the external force. Therefore, a small external force can produce large deformation, and the high elastic deformation is about 100-1000%.
In the viscous flow state, the whole molecular chain segment motion relaxation times are shortened, and they slide to each other. This state is similar to the flow of low molecular liquid. It is irreversible deformation. After the external force is removed, the deformation cannot be recovered.

Temperature field of suspended monofilament printing
The temperature distribution in the suspended monofilament with the largest span is shown in Fig. 9. The temperature in QFS-A at the right end of the suspended monofilament was 211.3 ℃, in QFS-B was 207.3 ℃, in the center of the Relation curve between temperature and deformation of amorphous polymer [34] monofilament was 184.5 ℃, at the left end of the monofilament was 147.3 ℃. The farther away from the print head, the lower the temperature in the monofilament. But the temperature of the cylindrical part connected with monofilament was 189.2 ℃. This showed that the left half of the monofilament cooled faster, and the temperature of the former layer had a great influence on this layer.

Deformation analysis of suspended monofilament
Thermal deformation analysis of monofilament The suspended printed monofilament was taken out separately for analysis (see Fig. 10). The temperature in the L circle was close to T f of ABS, and the temperature in the R circle was above its T f . For the suspended monofilament, the deformations at these two positions were the most serious. The temperature in other places of the monofilament was between T g and T f . Therefore, under the force of gravity G′, the whole ABS material deformed large, and the material easily flowed at both ends. Before the temperature dropped to T g , this deformation would last for a long time because gravity would not disappear, and it was irreversible. With the increase of bridge span, the weight of monofilament would also increase and the deformation would be more serious. Moreover, since there was no additional material to supplement, the junction between the left end and the cylindrical part would become a fracture risk. Fig. 5 could print bridge structures with free support. When the moving direction of the print head changed from circle to line, it could be inferred from Fig. 4 that the speed v changed, the support force F A disappeared, then the geometric stability of QFS-A would be broken at once.

Analysis of QFS The model shown in
The force state of QFS-A was analyzed qualitatively (see Fig. 11). It could be seen from Fig. 9 that the temperature at f A was higher than that at f AB , so it was inferred that f A < f AB according to the material characteristics. The resultant force F 1 in y direction and the total resultant force P A were shown in formulas (1) and (2). When F A was canceled, F 1 became larger, P A increased, and its direction would tend to the gravity direction. In this experiment, the temperature in QFS-A was above T f , P A was easy to make the material flow along its direction, and produce large deformation (see Fig. 7). If the materials were not supplemented in time, the cross-sectional area would be reduced and the fracture risk was increased.
The force state of QFS-B was relatively simple. If the temperature dropped slowly, f B could be considered to be the same as f AB . When F B disappeared, the resultant P B shown in formula (3) changed and the material would drop down. According to Fig. 10, in area L, the force f B was less than f AB and the resultant force would incline to the right of L and It can be seen from the above analysis that in order to realize support-free printing, the deformation of monofilament can be reduced by increasing f B , f AB , or reducing G A or G'. Lowering the temperature is an effective way to improve f B and f AB .

Air cooling
In this paper, the extrusion nozzle was not replaced, so the G A of QFS-A remained unchanged. In order to increase f AB , rapid cooling of QFS-A polymer material was a convenient method.
The air cooling auxiliary structure had two 7 mm diameter air nozzles to input high-pressure air. The pressure of the air compressor was 7 kPa and the flux was 45 L/min. The air volume was adjusted to not affect the geometric shape of QFS-A. Other conditions and parameters remained unchanged. The final printing results are shown in Fig. 12. The sagging of the same position changed from 80 to 38 mm, which was reduced to 47.5% compared with no air cooling. And the diameter of the thinnest suspended monofilament became 2 mm, reaching 72.5% of the theoretical diameter.

Deceleration + air cooling
According to the optimization results in Fig. 12, further improvement scheme was proposed: the moving speed of the print head was reduced to 20 mm/s on the basis of air cooling.
The experimental results showed that the deformation of the same position became 1 2 mm, which was reduced to 15% compared with no air cooling. The diameter of the thinnest suspended monofilament became 2.48 mm, reaching 90% of the theoretical diameter (see Fig. 13). Obviously, improving f AB was an effective and feasible method to reduce the deformation of suspended printing.

Deceleration + air cooling + span reduction
If G' was reduced by shortening the bridge span while increasing f AB , the deformation of monofilament would be reduced more. On the basis of air cooling and printing speed of 20 mm/s, the cylinder diameter was adjusted to 150 mm. The maximum sagging of the suspended monofilament became 5 mm. The minimum diameter of one end of the monofilament was 2.52 mm, while the other end was 2.79 mm, reaching 91% and 101% of the theoretical diameter, and the diameter of the middle position was 2.76 mm, which was the same as the theoretical diameter (see Fig. 14). This meant that the overall diameter error of the suspended monofilament was within 8.7%, indicating that the migration caused by the chain reaction of the material was greatly reduced.
Theoretically, if at the point of maximum deformation, the next layer surface can still contact the previous layer  surface, the subsequent layer will be in a supportive state. That is, when the sag of a suspended monofilament was no bigger than its theoretical radius, its next layer could contact it and realize continuous printing. The deformations at different spans are shown in Fig. 15. The maximum deformation of the monofilament under the 71-mm span was only 3 mm, which was close to the theoretical diameter of the monofilament. Its upper and lower contact conditions were analyzed through actual drawing (see Fig. 16); there were many contact surfaces, this would greatly reduce the the suspended span on the next layer and make support-free printing possible.

Thermal deformation analysis
Comparing the thermal fields of the three deformation reduction schemes, when the printing speed dropped from 70 to 20 mm/s under air cooling conditions, the time required for printing the same length increased, then there was more time for the material to dissipate heat. It could be seen that the overall temperature on the suspended monofilament decreased significantly (see Fig. 17a and b). When the model diameter changed from 200 to 150 mm (see Fig. 17c), although the monofilament

Deformation analysis
The deformations at the same position of the 200 mm diameter model in three states are shown in Fig. 18. The deformations under different spans were in the form of parabola. The larger the temperature drop, the smaller the deformation; and the larger the span, the greater the deformation. The parabolic model could be derived easily by fitting the sample data, which could provide some reference for the deformation analysis of bridge structure.

Conclusions and future work
In this paper, the principle of large flow printing was analyzed, the QFS was defined, and its dynamic balance was analyzed. A possible solution for support-free printing of large flow printing was proposed and verified by experiments. The qualitative results show that the scheme of rapid cooling of QFS is conducive to improve f AB and decrease the deformation of suspended monofilament. The span should be within a reasonable range, so that f AB , GA, and G′ can achieve appropriate dynamic balance. This will help to make the sag deformation within an allowable range. If necessary, this layer will also become the support of the next layer.
In order to further explore and improve the theoretical analysis of support-free printing, the following work needs to be carried out: 1) The quick cooling structure needs to be further improved to avoid the influence of blowing QFS-A during cooling and realize more accurate cooling control to quantify the entire analysis.
2) The thermal deformation model of monofilament needs to be further quantitatively studied, and the corresponding stress-heat relationship model of QFS at A and B positions should be built to give a reasonable cooling rate.
3) The deformation that not affecting the next layer printing should be quantified, so as to get the critical span value with different diameters for support-free printing.
Author contribution Huaying Wu contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Xiao Wang and Yuqiang Li. The first draft of the manuscript was written by Huaying Wu and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding This work was supported by National Natural Science Foundation of China (grant numbers: 51805417).

Competing interests
The authors declare no competing interests.