Numerical simulation of temperature field during selective laser sintering

1 SLS molding principle and characteristics

SLS (Selective Laser Sintering) molding principle [1]: Using JY-ⅢA type continuous CO2 laser as the energy source, at the beginning of molding, the powder roller evenly spreads the powder on the processing platform. The laser beam scans at a certain speed and energy density under computer control. The powder is sintered into a solid layer of a certain thickness where the laser beam scans, and the places not scanned are still loose powder. After the first layer is made, the piston drops a distance equal to the thickness of the powder, and then the second layer of powder is spread. Repeat the process, and a three-dimensional solid can be manufactured. The schematic diagram of the SLS molding system is shown in Figure 1:

Fig.1 Schematic of selective laser sintering process

2 Mathematical model

The current reports on the numerical simulation of the rapid prototyping process are based on one-dimensional heat transfer using point scanning [2], which has a relatively large error. The author combined his own line scanning system and adopted a two-dimensional finite element model to make the calculation closer to reality. The

energy balance equation for two-dimensional unsteady heat conduction is [3,4]

(1)

The relationship between the thermophysical parameters used is shown in the following equations [2,4]

ρ _s =φ ₁ ρ ₁ +(1-φ ₁ ρ)(2)

ε=(ρ _s -ρ)/ρ(3)

c _p =w ₁ c _p1 +(1-w ₁ )c _p2 (4)

w ₁ =φ ₁ ρ ₁ /〔φ ₁ ρ ₁ +(1-φ ₁ )ρ ₂〕(5)

k=k _g (1-ε)/(k _g /k _s +Ψ)(6)

Ψ=0.193 ε ^1.854 (7)

(8)

(9)

d/D=1-(1-φ ₁ ) ^1/3 (10)

Where T is Celsius temperature; t is time; ρ is the average density of the powder bed; cp is the specific heat of the powder bed; k is the thermal conductivity of the powder bed; φ is the volume coefficient; x is the thickness direction of the powder layer; y is the laser scanning direction; ε is the porosity; w is the mass coefficient; d is the coating thickness; D is the particle diameter. Subscript 1 is resin; 2 is solid particles; s is solid; g is air. All are international units.

3 Boundary conditions

The selected molding machine can ensure that the energy density input of variable length lines can be achieved for products of any shape. When the first layer is scanned, the initial position is powder; when this position is scanned, it is a mixture of solid, liquid and powder. Since the liquid area and its physical properties have a certain randomness during the sintering process, the program divides each layer into two areas. The area scanned by the line is the solid area, and the area in contact with or to be contacted by the line is the powder area. Therefore, the division of the finite element mesh is controlled by the scanning line width and the powder thickness. The bottom of the first layer is the heat conduction between the powder and the working platform, the part where the scanning line contacts the powder is the steady heat flow input, and the rest of the parts are the convection heat exchange with the air (the heat transfer coefficient is the comprehensive coefficient including radiation). For the sintering process with more than two layers, the heat conduction between the layers is realized by defining the internal unit, as shown in Figure 2. In fact, the boundary conditions can be simplified into two categories: ① Steady heat flow is loaded on the surface of the powder layer with different positions; ② Convection heat exchange between the air and the boundary except the heat flow loading unit.

Fig.2
Boundary condition varying with sintering process[page]

4 Analysis of calculation results

The temperature value can be used to determine whether the powder is solidified. Assuming the melting point of the powder is Ts, when the temperature of the calculation point T>Ts, it indicates that the powder has melted; when T
Based on the established mathematical model, the author compiled a two-dimensional finite element program [5] and verified the program with an example.

The powder selected in this example is a mixed powder of polyethylene wax, aluminum oxide and zirconium oxide. The relative density of the powder is 58%, the scanning power is (15-25) W, the line width is 0.4 mm, the scanning speed is 4 mm/s, and Ts=80 °C. The author conducted a numerical simulation of the temperature field, and the finite element model and calculation results are shown in Figure 3.

Fig. 3 Isoline
of temperature during sintering progress

As shown in Figure 3, under the selected sintering parameters, the sintering width is (0.4-1.2) mm and the maximum sintering depth is 0.15 mm. This indicates that under the selected sintering parameters, the powder is sintered in a fully molten state, the overlap between the layers is good, and the sintering control parameters are optimal. The

temperature variation curve over time was measured using a WRe5-WRe25 thermocouple, and the calculated value was compared with the measured value. The results are shown in Figure 4. As can be seen from Figure 4, the calculated results are very close to the measured results (the first measuring point is located in the middle of the powder layer, and the second measuring point is located at the contact between the layers).

Fig.4
Comparison between tested value and calculated value

5 Conclusions

A mathematical model of the SLS sintering process was established, and its boundary conditions were reasonably processed. This model and method are also applicable to the solution of the temperature field of other powder materials in the variable length line scanning laser sintering process. The

temperature field of the mixed powder sintering process of polyethylene wax and alumina and zirconia was numerically simulated and compared with the measured values. The calculated values ​​are basically consistent with the measured values. The

calculation results can be used to determine the matching sintering process parameters, such as powder thickness, scanning speed, scanning power, etc. Du Jianhong (1969-), female,

lecturer
, master. Major: automotive engineering.
Du Jianhong (Department of Mechanical and Electronic Engineering, North China Institute of Technology, Taiyuan 030051, Shanxi)
Bai Peikang (Department of Materials Engineering, North China Institute of Technology, Taiyuan 030051, Shanxi)
Cheng Jun (Department of Materials Engineering, North China Institute of Technology, Taiyuan 030051, Shanxi)

References:
[1] Feng Tao, Sun Jianmin, Zong Guisheng, etc. Rapid precision casting by selective laser sintering
[2] Nelson JC, Vail NK, Barlow JW, et al. Select laser sintering of polymer-coated silicon carbide
[3] Kong Xiangqian. Application of finite element method in heat transfer
[4] Nelson JC, Xue S, Barlow JW, et al. Model of the selective laser sintering of bisphenol-a polycarbonate
[5] Cheng Jun. Application of computers in casting (end)