Determination of fan height based on FDM nozzle temperature field analysis—an example of babbitt alloys

In this paper, the phenomenon of nozzle clogging or drooling droplets in the process of FDM metal 3D printing of tin-based Babbitt alloys was evaluated by simulation to assess the effects of different heights of cooling fans on the printer’s nozzle cooling module, and the optimal height of the fans was determined. Based on the thermal analysis results, a thermodynamic coupling analysis was carried out to analyze the thermodynamic changes of the nozzle at a given temperature. Finally, the printing trials of tin-based Babbitt alloy were carried out using self-developed forming equipment to verify the accuracy of the theory. The results show that the print quality can be effectively improved by controlling the heat dissipation module of the printer nozzle. The printed material exhibited a uniform and fine microstructure in the 3D printing trials of tin-based Babbitt alloy.


Introduction
FDM (Fused Deposition Modeling) metal 3D printing technology is an additive manufacturing technology based on the discrete stacking principle, where the digital model of the object is used to build a three-dimensional entity by stacking material layer by layer.This technology is efficient, accurate, and capable of creating complex objects, making it a valuable tool in modern manufacturing.It can use molten materials for continuous superposition and stacking to rapidly manufacture complex shapes with great design freedom and realize structural shapes that are difficult to complete by traditional processes.Its substantial performance has been recognized in various fields, including mechanical manufacturing, medical, aerospace, military, and automotive industries [1] [2].3D printing technology is conducive to promoting industrial production to produce digital, networked, intelligent direction, transforming and upgrading the traditional manufacturing industry, and has huge development prospects [3] [4].
Babbitt alloy holds a significant position in the material of axle shaft tiles, with a wide range of applications in large-scale industrial machinery.Due to the rapid iteration of the current industrial machinery and equipment, the existing bearing performance has been unable to meet the ever-increasing performance requirements.Therefore, exploring new Babbitt alloy preparation technology has become an urgent problem to solve.Tin-based Babbitt alloys are commonly prepared by centrifugal casting, which can cause defects such as tissue segregation and coarse organization due to the influence of centrifugal force and non-equilibrium crystallization [5][6][7] [8].They are prone to fatigue damage, abrasion, pitting, and other failures during the operation of bearings.
In this paper, tin-based Babbitt alloy (SnSb11Cu6) is prepared by FDM technology, and firstly, the finite element simulation method is used to analyze the heat dissipation module of the FDM printhead using Fluent in ANSYS workbench.The simulation of the temperature field with the addition of fans of varying heights was performed to ascertain the optimal location for installing the heat dissipation fan [9].Based on this, a thermal coupling analysis of the nozzle device was also carried out.Finally, selfdeveloped forming equipment was used to test the printing of tin-based Babbitt alloys.

Mathematical model of nozzle temperature distribution
The 3D printing process is primarily characterized by heat conduction and convection.The heating rod is chiefly responsible for generating heat transfer as the heat source.Convective heat transfer is further classified into forced convection heat transfer and natural convection heat transfer.In this paper, the wind pressure is selected as the design standard.The temperature of the heat sink is affected by the wind pressure and the position of the fan.Under the premise of ensuring the installation distance and the installation size, selecting the fan with the largest airflow can accelerate the airflow and reduce the temperature of the heat sink.The area not affected by the fan is subject to the natural convection of the air to dissipate heat.The following is a mathematical description of the design's temperature field changes during printing.
(1) Mathematical description of thermal conductivity processes The general form of the three-dimensional unsteady thermal conductivity differential equation in the right-angle coordinate system is: Where ρ, C p , λ, S, and t denote the density, specific heat capacity, thermal conductivity, and heat generated by the endothermic source per unit volume per unit time and time of the object [10].
In the process of 3D printing, the printer starts to print when the temperature of the nozzle reaches the set value, and the heating process of the heating rod is not studied, so the temperature field calculated in this paper is the steady state temperature field when the nozzle temperature reaches the extrusion temperature.There is only a heating rod as an energy source in the system and no internal heat source.In the calculation, the physical properties of the object are assumed to be constant physical properties.The differential equation for the thermal conductivity of the 3D printing process with constant physical properties, steady state, and no internal heat source is given by: (2) Mathematical description of the convective heat transfer problem Assuming that air is an incompressible fluid, the differential equation for the incompressible, no internal heat source, steady state, and constant physical properties three-dimensional convection heat transfer problem is given by: Mass conservation equation: Conservation of momentum equation: Energy conservation equation: Where u, v, and w denote the components of velocity in the x, y, and z directions, respectively.F x , F y , and F z, denote the components of volumetric force in the x, y, and z directions, respectively.ρ denotes the density of the air, C p denotes the specific heat capacity, λ indicates the thermal conductivity, μ denotes the kinetic viscosity, and p denotes the pressure.

Numerical simulation of nozzle temperature distribution
The calculations ignore small structures such as threads and small holes to save computational resources.At the same time, air domains and fan inlets are created to represent the areas of airflow and cooling fans.The calculation model for simulating the heat sink block's temperature field is depicted in Figure 1, with Air Domain 1 indicating the airflow area and Air Domain 2 as the schematic range of the cooling fan's action area, which will be different in actual calculations due to the influence of gravity, object obstruction, airflow, and other factors.The selected fan is DC12V (radius is 20 mm, air pressure is 25.9 Pa), and the air domain calculated size is 80 mm × 60 mm × 90 mm.On the other hand, this paper selects the printing silk material for SnSb11Cu6, the printing nozzle material using aluminum alloy, steel, and its related material parameters, which are shown in Table 1.The meshing tool Meshing in Fluent performs different meshing thicknesses for the computational model.In the division process of the fluid-solid coupling model, the solid domain selects a finer mesh to better calculate the temperature transfer in the nozzle, the first layer of the wall mesh is only conductive heat transfer in the normal direction during the flow process, and a laminar transition mesh region is set up in the air-fluid domain and the solid domain of the nozzle, as shown in Figure 2. The relevant boundary conditions are set as shown in Table 2.  Heating rod area 360℃ In addition, 100 temperature observation points were set equidistant from the silk as the central axis in the simulation model to obtain the temperature values of the inside of the silk and the air near the nozzle.The main body of the nozzle is divided into five parts, as shown in Figure 3. L 1 (0~30 mm) is the region where the silks inside the heat sink are not in contact with the throat.L 2 (30~50 mm) is the region where the silks inside the heat sink are in connection with the heat sink in the throat.L 3 (50~60 mm) is the region where the exposed throat and the heating compartment are connected to the heat sink in the throat.L 4 (60~70 mm) is the region where the exposed nozzle and the heating compartment are connected to the nozzle region.L 5 (70~72 mm) is for the extrusion nozzle outside the silk, and outside the nozzle is the air region.

Analysis of calculation results
The velocity cloud of the heat sink module is shown in Figure 4. Based on the cloud diagrams (a) and (c), we need to analyze how the installation position of the cooling fan affects the printer printhead temperature.To do this, we will use CFD-Post to obtain the heat flow and surface area of the model heating compartment and heat sink.We will then use the empirical formula to calculate the convective heat transfer coefficients hs and hb for the heating compartment and heat sink respectively.By quantitatively analyzing these coefficients, we can better understand how the installation position of the cooling fan affects the temperature of the printer printhead.L is the distance from the center of the cooling fan to the top of the heat sink.When L = 35 mm, hs = 38.165(W/m 2 ꞏ℃), and hb = 205.61(W/m 2 ꞏ℃).When L = 45 mm, hs = 18.362 (W/m 2 ꞏ℃) and hb = 212 (W/m 2 ꞏ℃).According to the calculation results, when the installation height is 35 mm, the temperature loss of the heating compartment is less, which is conducive to the temperature aggregation of the heating compartment.The temperature loss of the heatsink area is faster than that of silk feeding, at which time the cooling fan is utilized with the best effect.In the printing process, the silk emerges in three stages.At room temperature, the state is solid.When the temperature rises to 161℃, the silk appears embrittlement.Premature material embrittlement caused by the increase in silk feeding resistance is not conducive to extrusion.When the temperature rises to 355°C, the material changes to a molten viscous flow state.When studying the heating and heat dissipation process, it is crucial to focus on the temperature of the silk at the nozzle and the temperature of the silk in the heat dissipation block.The primary goal is to ensure that the temperature at the nozzle remains constant to enable the material at the nozzle to become a printable molten state.This helps avoid clogging of the nozzle due to low temperature or droplets due to high temperature.Secondly, the critical point of silk softening should be lowered so that the silk softens as late as possible to ensure that the silk can be extruded smoothly.Figure 5 shows the temperature cloud of the nozzle structure when the fan mounting position is 35 mm, and the constant temperature of the heating rod is 360°C.As can be seen in Figures 5 and 6, the temperature of L 2 decreases due to the heat dissipation effect of the heat sink.The temperature of L 3 increases rapidly due to the insufficient heat dissipation capability of the heat sink.The temperature of L 4 increases due to the heating of the specified temperature of the heating compartment wire heating to a molten state.The temperature of L 5 decreases due to the extrusion of the wire out of the nozzle, which results in a decrease in the temperature of the wire in the air, and the temperature of L 5 decreases sharply after the temperature gradually tends to room temperature.The temperature of the silk at the nozzle is measured at a steady state when the temperature of the heat source is different.Among them, it can be seen from Figure 6 that the temperature of the silk at the nozzle is 356.95°C when the temperature of the heat source is 360°C, and the silk is in a molten state and can be cooled to a solid state quickly after printing and extruding.And see in figure 7.After the thermal analysis, the steady state temperature data model of the nozzle unit at L=35 mm obtained in Figure 5 was transferred to Workbench for thermal coupling analysis.As depicted in Figure 8, the region where the heat sink ring is fixed at the upper end and where the heating rod is installed requires attention.Stress-strain is most apparent.The maximum equivalent force is 227.58MPa, and the maximum equivalent strain is 0.002663 mm/mm.The upper end of the heat sink block is fixed on the support frame through the ring and bolt.The inner side of the heat sink in contact with the ring is subjected to the greatest stress strain, followed by a particular stress-strain on the contact surface of the parts of the heating rod and the heating compartment.Still, the overall structure of the stress-strain is small, far below the yield limit of the material, in line with the requirements of the design of the material.Figure 8(c) shows that the heating block area is subject to the most serious thermal deformation.The maximum thermal strain is 0.00525 mm/mm, and the deformation amount meets the design requirements.Figure 9 shows the maximum thermal deformation at the nozzle is 0.0018 mm, the deformation is minimal, and the impact on the silk extrusion printing is almost negligible to meet the actual requirements.

FDM metal 3D printing forming test
In this paper, based on the above simulation results of the temperature field of the molten metal 3D direct writing process, the 3D printing forming test of tin-based Babbitt alloy (SnSb11Cu6) was carried out by using self-developed forming equipment.of 0.2 m, silk feeding speed of 9 mm/s, scanning speed of 9 mm/s, molten metal temperature of 360°C, and substrate temperature of 60°C.From Figure 10, it can be seen that the length × width × height of the molded parts and thin-walled parts are 10.0 mm×10.0mm×10 mm, with a total of 45 layers.
The microstructure of the 3D printed, prepared tin-based Babbitt alloy was observed using a Phenom XL SEM scanning electron microscope.It is evident from Figure 11 that the 3D-printed prepared Babbitt alloy has a fine and uniform microstructure.

Conclusion
In this paper, the temperature field simulation of the heat dissipation module of the printhead is first verified to analyze the effect of different fan positions and the thermodynamics of the printhead.Then, the FDM printer printhead structure is optimized.In addition, based on the nozzle temperature field simulation results, 3D printing experiments of tin-based Babbitt alloys were carried out using selfdeveloped forming equipment.The corresponding conclusions are as follows: (1) After optimization of the printer printhead structure, when the fan height is 35 mm, there is less temperature loss in the heating compartment, which is conducive to temperature aggregation in the heating compartment.The temperature loss in the heatsink area is faster, thus improving the silk-guiding performance of the silk-feeding system.
(2) At a heat source temperature of 360°C, the silk is molten and cools quickly to a solid state after printing and extruding, greatly improving nozzle clogging and premature softening.
This paper provides a theoretical and practical basis for further improving the printing accuracy of 3D printers and a reference for the optimized design of printhead structures.

Figure 4 .
Figure 4. Fan airflow diagrams for different mounting positions.(a) X-axis view at L=35 mm; (b) Zaxis view at L=35 mm; (c) X-axis view at L=45 mm; (d) Z-axis view at L=45 mm.In the printing process, the silk emerges in three stages.At room temperature, the state is solid.When the temperature rises to 161℃, the silk appears embrittlement.Premature material embrittlement caused by the increase in silk feeding resistance is not conducive to extrusion.When the temperature rises to 355°C, the material changes to a molten viscous flow state.When studying the heating and heat

Figure 5 .
Figure 5. Temperature cloud diagram.(a) Temperature cloud in the Z-axis direction for L=35 mm; (b)Temperature cloud in the X-axis direction for L=35 mm.

Figure 6 .
Figure 6.The temperature at each point is in axial direction of the silk.

Figure 7 .
Figure 7. Effect of heat source temperature on nozzle temperature.

Figure 8 .
Figure 8. Stress-strain cloud of nozzle structure.(a) equivalent force map of nozzle structure; (b) equivalent strain map of nozzle structure; (c) thermal strain cloud of the nozzle structure.