Design and analysis of equipment intended for the production of prototypes

The article deals with the design of a device working on the principle of Fused Deposition Modeling - FDM and its peripherals. Among the most important performing activities of the designer is the analysis of the proposed model with regard to the strength and the resulting accuracy of the created three-dimensional object. The input requirements that the proposed device should meet were defined. Based on these criteria, a numerical and strength analysis was developed using the FEM finite element method. The simulation was carried out on the basis of the hypothesis of shear stress transformation work, which is among the most accurate for the tough materials used. The analysis monitored and evaluated the deformations in the extreme positions where the largest deformations were expected to occur.


Introduction
In mechanical engineering, one of the essential components of every manufactured part is their structural design, the production of prototypes and, of course, the testing of durability, bearing capacity and load.One of the effective and affordable technologies that could be used to eliminate this deficiency is the additive manufacturing technology, which enables the creation of three-dimensional objects using various additive methods.This technology becomes a very powerful tool for the modern approach to the development of prototype products in all branches of industry, allowing a significant reduction in development and implementation time.The basic prerequisite for the success of a new product is that it achieves the highest possible quality, both in terms of utility for the consumer and in terms of technology in relation to the production process.
Initial attempts at 3D printing were made by Dr. Kodama in 1981 and made progress in the rapid development of proto-compositions.He demonstrated the layer-by-layer assembly process to create a photosensitive rubber that was polymerized by UV light [1].In the article, we will focus on the construction of a printer that creates three-dimensional objects by successively applying thin layers of heated thermoplastic material unrolling from a coil.For this reason, there was pressure to develop a new progressive technology that would be able to meet these demanding market requirements.This progressive technology is Rapid Prototyping, which could be loosely translated as rapid prototyping and serves to produce a model, sample and initial prototypes based on 3D models created in CAD systems [2][3][4].In contrast to conventional technologies, where during the production of the part, the chips are gradually removed the so-called chip machining, the Rapid Prototyping technologies create the geometry of the model by gradually applying material layer by layer.With this technology, it is possible to produce any shaped part, whether solid or hollow, horizontal or bent, or containing a rib construction, where conventional machining methods would not be able to produce such geometrically complex shapes in a short time and acceptable tool costs.With the technology of rapid prototyping, it is possible to produce up to 90% of components in the automotive industry and save 30% to 70% of the time required for the design and production of the prototype.Based on this characteristic, it is obvious that rapid prototyping technology will be increasingly used industrially in the future [3].A wide range of materials can be used in prototyping, such as low-temperature metal alloys and composites, but the main materials in this process are thermoplastics and polymer-based composites [5].Achieving a satisfactory product with good mechanical properties is related to the assembly orientation, infill pattern, by filling density, nozzle temperature, nozzle diameter, printing speed and layer thickness [6].Suboptimal conditions and low temperature lead to problems in printing processes such as deformation and shrinkage [7].The prototyping process itself consists of several phases, after which a real three-dimensional object is achieved.The initial stages include product design, where the innovative idea is transformed into an innovative opportunity.In this phase, the object model is distorted using a CAD program.The digital model created in this way does not only represent its 3D image, but also carries information about the mechanical and physical properties of the proposed object.In the next phase, the created data in the form of a CAD model, in order to simplify further mathematical processing, will be bounded using triangular surfaces, the so-called triangulation and are mostly converted into the STL output format, which represents the standard output format for all devices working with RP technology, Figure 1.The output data in STL format are processed in the next phase in the so-called software "slicer", which enables slicing of 3D geometry in the horizontal direction into a larger number of layers of a defined thickness.The software can recognize the risk of deformation of a part of the object with a larger projection or an overhanging structure and will supplement it with a supporting structure.In the last phase, the software generates a G-code (machinereadable file) digital file with a code that is understandable by the printing device, which will control the actions of the printing device itself [2], [8].In some methods of RP technology, after creating a three-dimensional object, it is necessary to perform finishing operations such as cleaning, grinding, removal of supporting structures, etc.

Idea designs for the construction of a 3D printer
Before the construction design, it is necessary to define the input parameters, based on which the construction solutions of the 3D printer will be gradually developed.These input parameters reflect the functional characteristics of the printer, such as printing speed, printing accuracy and overall quality of printed three-dimensional objects, size of prints, use of support structure.1. input parameter: The printer will be designed taking into account the use of two basic thermoplastic materials, namely ABS and PLA.

input parameter:
The maximum size of the three-dimensional object in axes X, Y, Z; X = 180 mm, Y = 180 mm, Z = 180 mm.

input parameter:
The diameter of the so-called input material filament will be 1.75 mm. 4. input parameter: Using a single nozzle print head.

input parameter:
The achieved accuracies of printed three-dimensional objects are written in Table 1.±0.8 Design proposal 1 is based on a combination of two linear movements and rotary one.The displacement occurs in the "X" and "Z" axes and the rotational movement of the printing plate in the "R" axis, Figure 2.

Figure 2. Design 1 of 3D printer
The structural node of the "Z" axis of the proposed 3D printer is the part of the printer that has the task of applying the molten thermoplastic material layer by layer, the so-called magnifier of the object in the "ZY" plane.Movement in this plane is derived from a stepper motor with a torque of 0.5 Nm and a basic step angle of 1.8°, which ensures the transmission of torque to a trapezoidal screw with a diameter of 10 mm and a trapezoidal nut, which are connected together by a flexible coupling.Guide rods with a diameter of 10 mm together form the supporting part of the "X" axis.They are stored in linear carriages that represent the linear guidance of the "Z" axis.These guide rods are anchored to the frame of the proposed 3D printer by means of the guide rod holder SHF 10, through which they ensure the parallelism of the "Z" axis.
Extruder that ensures drifting of the print headis formed by a guide rod, a trapezoidal screw with a diameter of 10 mm and a trapezoidal nut, the length of which represents the maximum limit of the possible size of the created three-dimensional object in the "X" axis.The trapezoidal nut is stored in a sleeve that performs the function of the supporting part of the print head.As in the previous design unit, the transmission of the torque is provided by a stepper motor with a torque of 0.5 Nm and a basic step angle of 1.8°.The reduction between the motor and the trapezoidal screw is provided by a flexible coupling.The trapezoidal screw is stored in bearings of an axial-radial nature due to shock absorption during start-up and braking.
In the design of the 3D printer, the printing space is represented by the rotation axis "R".A stepper motor (Figure 3.b) with a torque of 0.5 Nm and a basic step angle of 1.8° was chosen as the drive.The printing pad holder (Figure 3.c) is pushed onto this drive, which is fixed by an adjusting screw with a groove (Figure 3.a) with a diameter of 4 mm.The complete design of the 3D printer was designed in Autodesk Inventor and Siemens NX CAD.Construction of the 3D printer, design no. 2 (Figure 4.) represents the portal composition.This construction solution is characterized by the fact that all "X", "Y" and "Z" axes perform linear movement.

Figure 4. Design 2 of 3D printer
The construction node of the 3D printer -the "X" axis is driven by a stepper motor, which is placed in the direction perpendicular to the "X" axis.The transmission of torque to linear movement is ensured by means of a belt transmission.When the shaft of the stepper motor is turned, this movement is transmitted via a flexible coupling and a shaft with a diameter of 8 mm to a toothed pulley.The toothed pulleys together with the belt subsequently change the rotational movement from the stepper motor to rectilinear when it is turned, and thus movement in the "X" axis occurs.The shaft is stored in the bearing housing.The "X" axis is guided on two guide rods, on which the linear carriages are wrapped.These carriages have the task of carrying both the "X" axis and the "Y" axis.The entire structure designed in this way is firmly connected to the frame of the 3D printer using the SHF 10 guide rod holders.The "Y" axis is used to apply the heated building material in a horizontal, linear direction.The axis is driven by a system of pulleys, a belt gear and an open toothed belt.
The construction node -axis Z (Figure 5.) carries the printing plate with the heating pad in the vertical direction and thus ensures the growth of the printed three-dimensional object layer by layer.The movement of this axis is indicated by an electric stepper motor (Figure 5.j) with a torque of 0.5 Nm and a basic step angle of 1.8°.The motor is stored in the stepper motor holder (Figure 5.i), with which it is then firmly connected to the frame of the 3D printer.The printing (Figure 5.d) and heating (Figure 5.e) plates move vertically using a trapezoidal screw (Figure 5.f) with a diameter of 10 mm, to which the torque of the stepper motor is transmitted through a flexible coupling.The screw is firmly connected to the printing plate by means of a trapezoidal nut, Figure 5 detail "X".In order to ensure the torsional stiffness and stability of this structural node, two guide rods with a diameter of 8 mm are incorporated in the design (Figure 5. c, g), which are firmly connected with the frame of the 3D printer through the SHF 08 guide rod holder, (Figure 5. a, b, k, l).As in the previous design, it is necessary to ensure the required parallelism between the print headextruder and the heating plate.For reasons of simplicity and affordability, the same levelling system is used using the screw, nut and spring system as shown in Figure 5. "Y" detail.

Static strength analysis of structural designs
The accuracy of the printed object is significantly influenced by the deformation of the individual arms and the resulting rigidity of the proposed device structure.By calculating the deformation, we reach the size of the deflection.We can also talk about the resulting inaccuracy in the axis, which is affected by an external load.With the help of numerical simulations, we can describe the behavior of the structure in the place of the smallest and largest deformation, either in the process of printing or at rest.The most widely used method for solving such, but also various other tasks, is the finite element method, known by the abbreviation FEM.The principle of the variation numerical method of FEM consists in dividing the investigated object into a smaller number of finite elements, the so-called meshing of the investigated object, with the help of which the investigated area is approximated [9].

Static strength analysis design no. 1
To perform the calculations and simulation, it was necessary to enter the boundary conditions on the basis of which the simulation calculation will take place.The first condition is the determination of the part of the structure that will be fixed, the so-called woven in, it won't move.In the case of design proposal no. 1 this condition is represented by two guide rods of the "Z" axis (Figure 6.).The second condition represents the determination of the forces acting on the model.In both proposals, it is necessary to consider the effect of gravitational force and the force created by the weight of the proposed extruder.The weight of the extruder is approximately 1.5 kg.The last condition is the definition of the material properties of the model, the so-called defining the materials for the individual proposed components of the "Z" axis of the 3D printer.The material of the guide rods is defined as steel CF 53 (12051) (E = 1.9.105MPa).
The numerical simulation takes place in two steps, in an unloaded state, the so-called in the position of the "Z" axis with the least expected occurrence of deformation and in the loaded state, where the external load affects the proposed structure by the occurrence of deformations.Before starting the simulation, itself, in the last step, it is necessary to divide the geometric model of the "Z" axis into a finite number of elements (Figure 7.).Each step was simulated in the three axes "X", "Y" and "Z" and then plotted in a graphic display.From the simulation in individual axes and after subtracting the maximum displacements, it was found that the proposed structure deforms in space in all three axes due to the external load.This deformation takes on a maximum value in the unloaded state of Δly  0.07 mm, which is satisfactory from the point of view of the accuracy requirements.In the loaded state, the maximum value of this deformation is Δly  0.31 mm.In Figure 8. and Figure 9. is a graphic representation with the maximum displacement in the unloaded and loaded state.

Static strength analysis design no. 2
As in the previous simulation, in this proposal it was necessary to enter the boundary conditions, namely the definition of the structure that will be woven, the determination of the forces acting on the geometric model, the definition of the material of the individual components of the geometric model.Unlike the previous design, this one is characterized by the fact that the extruder only moves linearly in the "XZ" plane.This movement is realized by the printing plate, which means that the loading force in the unloaded state is given only by the weight of the printing plate itself m=0.37kg.In the loaded state, we must add the weight of the printed object.This weight represents approximately 3.21 kg, which represents a printed cube of the maximum printed dimensions.The weaving conditions are represented by two guide rods defined as steel CF 53 (12051) (E = 1.9.105MPa), (Figure 10.).).The simulation took place in two steps, in the unloaded state and in the loaded state, while it was followed in three axes "X", "Y", "Z".On the basis that the largest deformations in the unloaded state take place in the "Z" axis in the Y direction and reach values of Δly  0.098 mm.The simulation shows that the proposed structure is deformed in space in all three axes due to the external load.In the loaded state, the value of this deformation is the largest in the "Z" axis in the Y direction Δly  0.17 mm (Figure 12., Figure 13.).  1 and Table 2 The first part contains the achieved values from the strength analysis in the unloaded state, and the second part represents the results in the loaded state.In each structural design, the "Z" axis and its displacement in the coordinate system in the monitored directions where the displacement was interpolated was monitored by simulation.It was assumed that the greatest deformations due to external loads will occur in these directions.

Conclusion
The activity of the designer includes the analysis of the proposed model with regard to the strength and resulting accuracy of the created three-dimensional object.For this reason, numerical and strength analysis was performed in the work using the FEM finite element method.The simulation was performed on the basis of the work hypothesis of shear stress transformation, which is among the most accurate for the tough materials used.Through the analysis, deformations in extreme positions, where the greatest deformations were expected, were detected and evaluated.The results show that structural design 2 achieves a smaller degree of deformation with respect to the external load.However, the largest simulated deformation in structural design 1 represents a value of 0.31 mm, which can be considered satisfactory in terms of the accuracy of the printed three-dimensional object in view of the defined dimensional accuracy of the prints, which was set among the required criteria.
From the point of view of future research, the author's collective plans to focus on the debugging of undesirable influences during the 3D printing process and the elimination of unfavorable influences such as insufficient stiffness, unwanted deformations in the end positions depending on the specific arrangement of the individual axes of the proposed 3D printer.

Figure 1 .
Figure 1.Bounded object using triangular surface

Figure 3 .
Figure 3. Design node of the R-axis 3D printer a -slotted set screw; b -stepper motor; c -printing pad holder

Figure 5 .
Figure 5. Design node of the 3D printer axis "Z" a, b, k, l -guide rod holder SHF 08; c, g -guide rods with a diameter of 8 mm; dprinting plate; e -heating plate; f -trapezoidal screw; h -flexible coupling; istepper motor holder; j -stepper motor

Figure 6 .Figure 7 .
Figure 6.Applying conditions to a geometric model Figure 7.A geometric model divided into a finite number of elements From the simulation in individual axes and after subtracting the maximum displacements, it was found that the proposed structure deforms in space in all three axes due to the external load.This

Figure 8 .Figure 9 .
Figure 8. Simulation max.displacements in the unloaded state of the "Z" axis -displacement in the direction of the "Y" axis

Figure 10 .
Figure 10.Applying conditions to a geometric model

Figure 12 .Figure 13 .
Figure 12.Simulation max.displacements in the unloaded state of the "Z" axis -displacement in the direction of the "Y" axis

Table 1 .
Tolerances for length dimensions

Table 2 .
Results of strength analysis-structural Design 1

Table 3 .
Results of strength analysis-structural Design 2