Determination of Geometric and Kinematic Characteristics of FDM 3D Print Process

The process of applying a polymer thermoplastic material in the 3D printing process using the FDM technology (Fused Deposition Modeling) was investigated. The object of study was the discrete layer of the prototype. To determine the geometric parameters, samples were made with a thickness of one nozzle diameter (0.5 mm) of the print head of a 3D printer. The obtained samples were cut into sections of the same width (10 mm), in each section a separate layer of the deposited material was cut off. This made it possible to determine the change in thickness from the initial to the final point of the layer. It turned out that the layer thickness is less than the diameter of the nozzle at the beginning of the movement of the print head, gradually grows and at a certain stage begins to exceed the diameter of the nozzle. The obtained values were from 0.4 to 0.6 mm for a nozzle with a diameter of 0.5 mm. The reason is that at the beginning of the supply of the consumable material there is a highly elastic delay in the reaction of the polymeric material to the pressure in the print head and for a certain period of time this part of the material is not applied to the sample, and then the polymer melt swells. Moreover, with an increase in the nozzle diameter, the effect of these phenomena also increases. Also, the printing process was recorded on a wide-format camera in HD-quality with a frequency of 50 frames/s, which allowed to study the dynamics of the application of consumable polymer thermoplastic material. The results showed a difference in speeds from those specified in the executive code. Moreover, for different designs of kinematic schemes for moving the print head, the deviations of the parameters were different – real values were more than theoretical (set) by 20–50 %, depending on the type of FDM 3D printer. This is due to the difference in the inertial characteristics of the various structures of the kinematic patterns of movement of the print head. The results are the basis for further more detailed study of the influence of the configuration of the forming organs and the design of FDM 3D printers on the spatial printing process.


Introduction
The technology of additive production in recent years has become widespread in almost all spheres of human life and industries. Every second manufacturer in the world is increasing investments in additive manufacturing. Already more than 80 % of prototypes and 60 % of functional units are manufactured using 3D printing [1]. Analysts around the world see explosive growth in additive manufacturing technology. Equipment manufacturers usually invest the main resources in the development of new models and types of equipment. However, the process of product formation itself remains poorly understood. The instability of the 3D printing process is often observed, it is difficult to foresee at the stage of product modeling. The operators of this equipment often deal with various defects resulting from 3D printing. The causes and nature, and most importantly, the prediction of the appearance of such defects are unknown.
The basic principle of additive manufacturing is the layering of structural material according to the digital model of the product. The most common additive technology is FDM (Fused Deposition Modeling) [2]. The devices of this technology use a polymer consumable in the form of a rod of a stable diameter -filament. When forming the product, the molten material is applied to an already frozen layer. It is known that polymeric materials have characteristics that are interchangeable with temperature and strain rate. It is this feature that creates problems when printing with one or another consumable polymeric material. The main place for the appearance of defects is the line between the cold and hot layer. Therefore, it is of interest to study the properties between the layers of the material. To study this issue, tests of printed samples for strength were carried out. Similar studies were conducted by scientists from the University of Florida and the College of Engineering at the University of California at Berkeley [3]. The researchers tested a number of samples for tensile and shear forces made of ABS and PC. One of the main conclusions is the anisotropy of the mechanical properties between stretching along and across the layers of the material (about 30 %). However, research does not allow to establish the strength of interlayer adhesion and geometric characteristics in the contact zone of the layers.
Similar studies were also carried out [4][5][6], in which various materials were tested with different printing parameters. The main disadvantages are that in all studies, ISSN 2664-9969 the conditions for the manufacture of samples were very variable. Comparing the results for the same materials, a difference in values should be noted. This can be explained by the anisotropy of properties and the heterogeneity of the structure of printed samples.
Of particular interest is the study [7]. This study shows a macro photo of the cross section of the structure of samples printed by nozzles of various diameters and with different layer thicknesses. They show that the internal volume includes a large number of cavities, and their shape and size are unstable.
The structure of printed products is generally poorly defined, so the physical characteristics of the samples are also ambiguous. Therefore, it is necessary to study the process of applying the material along the layer, to determine the geometric parameters of a single layer.
So, the object of research is the geometric parameters of the discrete layer of the prototype. The aim of research is to establish patterns of influence such as kinematics and operating modes of 3D printers on the uniformity and speed of spatial printing.

Methods of research
Based on the previous studies performed by the authors, uneven results were revealed for each type of sample. In addition, in each group of strength tests there were a certain number of experiments that fall out of the general picture. Therefore, it is necessary to study in detail the geometric parameters and dynamics of the process of applying the material within a single layer.
The t d = determination of the geometric parameters of an individual layer was carried out according to the following procedure: 1. 10 rectangular samples are produced (Fig. 1) with a length of 100 mm, a height of 20 mm and a thickness equal to the diameter of the nozzle 0.5 mm.
2. The print parameters are as follows: printing speed V p = 30 mm/s; printing temperature V p = 220 °С; layer thickness h l = 0.2 mm. The resulting samples were cut every 10 mm. For the obtained segments, the thickness and mass were measured.
As a recyclable material, polylactide (PLA) was used. The determination of the dynamics of the layer was carried out according to the following method: 1. The samples were modeled 100 mm long and 20 mm high with a scale in the form of walls every 10 mm (Fig. 2). The thickness of the samples is equal to the diameter of the nozzle.
2. Printing parameters met the most optimal conditions in accordance with previous studies: t p = 220 °C; V p = 30 mm/s. The transition to the next layer occurred at one point, so the material is applied when moving the extruder from left to right, in the opposite direction, the idle stroke. 3. The sample was placed along the X axis of the 3D printer. On the contrary, a video camera is installed at the level of the working platform, focuses on the sample. 4. After completion of the scale, the camera turns on and the process of printing several layers is removed. For one sample, the survey is repeated 2-3 times.
5. These operations must be done for printers with mechanics such as Prusa i3 and H-Bot. 6. For the captured videos, frames are selected that correspond to the process of building one layer from the beginning of the application of the material to the return of the extruder to the zero position by reverse idle.
7. Each passage is reviewed frame by frame and the number of frames for each section is considered to be 10 mm. The number of frames per stop at the zero point of the layer is considered.

Research results and discussion
The results of measurements of the geometric parameters of the layer are as follows (Fig. 3, 4).
Based on the results, it is found that the thickness of the layer is uneven. At the beginning of the layer, the thickness is less than the diameter of the nozzle, gradually increasing and toward the end of the layer becomes larger than the diameter of the nozzle. Also, in the interval from the beginning of the layer to the middle, delamination Is present. That is, at the beginning of the movement there is an underextrusion, and at the end a «swelling» of the layer (Fig. 4, 5).
The distribution of the print head movement speeds within the framework of the formation of one layer for two types of 3D printers: Prusa i3 [8] and H-Bot [9] is established. The results are shown in Fig. 5, 6.  The obtained results show the dynamics of the extruder along the layer. Data from the speeds shows a difference from the settings in Cura Slicers [10]. For both types of mechanics, it turned out that the actual average speed is less than the specified one. Moreover, for each type of mechanics this difference is different.
To determine the difference, let's determine the difference in the printing time of the samples from theoretical at different printing speeds for various designs of 3D printers (Fig. 7). As can be seen from Fig. 7, with increasing printing speed, the difference from the theoretical printing time from the actual one gradually decreases. Moreover, prints for H-Bot mechanics are always more than printing on Prusa i3.

Conclusions
The results of experimental studies of 3D printing show that each polymer layer is applied unevenly, increasing in length. Actual printing is always more theoretical, the time difference gradually increases with decreasing printing speed. Printers with H-Bot kinematics show a greater deviation from the theoretical printing speed than printers with Prusa kinematics. The results are the basis for further more detailed study of the influence of the configuration of the forming organs and the design of FDM 3D printers on the spatial printing process.