Numerical simulation of temperature field during selective laser sintering of polymer-coated molybdenum powder

BAI Pei-kang(白培康), CHENG Jun(程  军), LIU Bin(刘  斌), WANG Wen-feng(王文峰)

School of Materials Science and Engineering, North University of China, Taiyuan 030051, China

Received 10 April 2006; accepted 25 April 2006

Abstract: The technology of length-alterable line-scanning laser sintering was introduced. Based on the research of laser heating property, powder thermal physics parameters and laser sintering process, a numerical model of the temperature field during length-alterable line-scanning and laser sintering of polymer-coated molybdenum powder was presented. Finite element method (FEM) was used to simulate the temperature field during laser sintering process. In order to verify the simulated results, a measuring system was developed to study the laser sintering temperature field. Infrared meter was introduced to measure the surface temperature of sintering powder; the temperature of its inside part was measured by thermocouple. The measured results were compared with the numerical simulation results; the conformity between them is good and the relative error is less than 5%.

Key words: polymer-coated molybdenum powder; selective laser sintering; temperature field; numerical simulation

1 Introduction

The technology of length-alterable line-scanning laser sintering is a novel method for rapidly producing parts and other freeform solid articles in a layer-by-layer fashion. Its process is schematically shown in Fig.1.

Fig.1 Schematic of length-alterable line-scanning process

First, a computer solid model of the part is created and sliced to provide data layer by layer to the laser and optical system. When the forming process begins, a thin layer of heat-fusible powder is deposited on the top surface of a container by powder leveling drum. The optical system can transform laser beam with circular shape into a long and thin beam, which is 0.3 mm wide. The laser coupled to the computer-control optical system is then scanned selectively over the power surface. Where the part cross section in the data base is solid, the laser is on and the powder under the beam is sintered to itself and to the previously sintered layer. Where the part cross section is nonexistent, the laser is off, the powder is not fused and remains loose to be removed and recycled, once the part is completely formed. The length of laser beam is altered according to the geometry of the portions to be produced under the control of computer. On accomplishing the first layer, the base is lowered and a second layer of loose powder is spread over the previous layer. The process repeats by altering the shape of each scanning layer. A complete three-dimensional object is created, which can be easily removed from the loose, unsintered powder surrounding the object.

The process can be used to produce metal components or moulds with complicated contour, the process includes: fabricating the polymer-coated metal powder→laser sintering→post treatment. Compared with the traditional process of powder metallurgy and mechanical manufacturing, it has the advantages of short producing cycle, low cost and working flexibility[1, 2].

NELSON and VAIL (University of Texas, US) have presented studies on the temperature field during Selective Laser Sintering(SLS) of polymer-coated silicon carbide materials, a one-dimensional numerical model has been set up, the conformity between calculated results and experimental results is good. There is still no report on the numerical simulation of temperature field during laser sintering of length-alterable line-scanning at present, both in China and abroad [3, 4].

Based on the study of laser heating property, power thermal physics parameters and laser sintering process, a numerical model of the temperature field during length- alterable line- scanning laser sintering of polymer-coated molybdenum was presented in this study. Finite element method (FEM) was used to simulate the temperature field during laser sintering process. In order to verify the simulated results, a measuring system was developed to study the laser sintering temperature field.

2 Parameters in process of length- alterable line-scanning laser sintering

The fabricating process of polymer-coated metal powder includes:

1) The molybdenum powder (maximum particle size of 45 μm) was used, 3% liquid polymer was added, and the mixer was mixed in the high-speed mixing machine. The material is of block shape after the mixed material was crashed out.

2) Then, the blocks were dried and broken to little pieces in crucial point machine, the polymer-coated metal powder was produced. The particle size is 200 mesh, with the maximum particle diameter of 71 μm.

The sintering experiments of polymer-coated molybdenum powder were conducted on the prototyping machine, shown in Fig.1. The sintering power is 100 W Synrad CO₂ laser，with the laser beam width of 0.25 mm , laser beam length of 0.25-50 mm. The depth of powder layer is 0.2 mm [5].

When the laser beam scans the powder layer, the powder is sintered with the temperature increasing. The sintered layer exchanges heat with the unsintered layer and surrounding atmosphere by the way of conduction and radiation. The temperatures of various points in sintered powder change with time.

3 Analysis of laser sintering course

The influence of laser on powder material includes two stages:

1) Powder surface reflection and absorption to laser;

2) Heat conduction in the powder material.

The powder under the laser absorbs the energy where the temperature rises. It conducts heat exchange with surrounding sintered powder as well as loose powder according to the thermo-mechanical law, which consists of conduction, radiation and convection, as shown in Fig.2.

Fig.2 Scheme of laser heating course: Q₁－absorbed energy of powder; Q₂－conducted energy to surrounding area; Q₃－heat to atmosphere through convection and radiation

The laser beam is a moving heating source，whose reaction time with the powder is less than 1 ms. During the heating process, the powder’s thermal physics parameters, such as specific heat, thermal conductivity are changing with the temperature, which is changing with time. The laser sintering course of polymer-coated metal powder is dynamic and unsteady.

4 Numerical model

4.1 Basic Equation

Because the length of laser beam is longer than its width and powder layer depth, so it can be considered a line heat source, whose temperature field is two- dimensional. Fig.3 shows the schematic diagram of temperature field during laser sintering.

Fig.3 Scheme of two-dimensional temperature field coordinate

The two-dimensional unsteady state equation is

                         (1)

where λ, ρ ,c are the thermal conductivity, density, and the specific heat of the material; T is the temperature of boundary unit.

The thermo-physical properties of polymer-coated metal powder are

                          (2)

                         (3)

where  w₁, Ф₁, ρ₁, c₁ are the mass fraction, the volume fraction, the density, and the specific heat of the polymer; w₂,, c₂ are the mass fraction and the specific heat of the molybdenum [6, 7].

4.2 Boundary Condition

 The heat exchanging boundary is given as follows:

                             (4)

                                 (5)

where  e is the void fraction, ρ_s is the density of the solid; K_g, K_s are the convection heat transfers of gas and solid; K₁,K₂ are the convection heat transfers of polymer and molybdenum; H is the synthetic radiation-heat exchange coefficient[8].

1) Second boundary condition

The heat flow on the boundary is described as

                              (7)

                          (8)

where  p is a unsteady point on the boundary, n is the outer normal on the boundary; d, D are the coating film thickness and particle diameter of polymer-coated ceramic powder.

In calculations, the FEM units are in the area of x×y=10 mm×0.2 mm, the units in divided face are absolute units, q=0. The units accept laser radiation:

2) Third boundary condition

Free heat exchange is conducting on boundary:

                           (9)

where  T is the temperature of boundary unit, and  is the surrounding temperature.

During the laser sintering course，the upper surface(discounting the laser irradiating units),  as well as left side units of sintered powder are the third boundary condition[9, 10]. And the heat exchange can be calculated by radiant heat quantity:

                        (10)

                      (11)

where  ε is radiation coefficient.

5  Calculating method

Finite element method (FEM) was used to calculate the numerical model. A unit plotting method of alterable grids has been adopted, the grids near the laser power are smaller, the grids far from the laser power are bigger. The calculating precision are guaranteed, and the calculation working had been diminished by the using of this method. The program was edited by FORTRAN，with the advanced program planning method, viz simplifying the master program module, introducing a quantity of subroutines in subprograms. Fig.4 shows the computation flow chart. The program can be modified easily, with the advantage of good understanding and less mistakes [11, 12].

Fig.4 Computation flow chart of temperature field

6 Experiment verification of calculated results

Because the laser sintering course of polymer- coated metal powder is dynamic, the spreading powder layer is thin, as well as the restriction of responding speed of testing meter and disturbance by reflected laser, the temperature field during laser sintering is difficult to test. In this paper, a temperature testing system was developed. Infrared meter was introduced to measure the surface temperature of sintering powder; the temperature of its inside part was measured by the using of thermo-couple method. The temperature testing system is shown in Fig.5.

The Infrared thermometer is used to measure the powder surface temperature, the thermocouple is used to test the interior temperature of powder [5].

Fig.5 Scheme of temperature testing system

The temperatures of numerical simulation and measurement are shown in Fig.6. The conformity between the experimental results and numerical simulation ones is good, with a relative error less than 5%.

Fig.6 Temperatures of numerical simulation and measurement

Fig.7 shows the scheme of simulated temperature field during selective laser sintering process, with the laser power of 20 W, scanning velocity of 4 mm/s，and preheating temperature of 30 ℃. In the polymer - coated molybdenum powder system, the polymer is polythene wax, with a melting point of 80 ℃.

Fig.7 shows that the area where temperature above 80 ℃ is melting zone, and the normal depth of the sintering process is 0.15 mm. The distribution of temperature equivalent line forecasts the sintering depth to optimize the laser sintering process parameters.

Fig.7 Distribution of laser sintering temperature

7 Conclusions

1) A numerical model of the temperature field during length-alterable line-scanning laser sintering of polymer-coated molybdenum powder was built. This model can also be used to calculate the temperature field during length-alterable line-scanning laser sintering of other kinds of powders, such as polymer-coated ceramic and polymer-coated sand.

2) A measuring system was developed to verify the simulated results. Infrared meter was introduced to measure the surface temperature of sintering powder; the temperature of its inside part was measured by thermocouple. The measured results were compared with the numerical simulation results. The conformity between them is good, with a relative error less than 5%.

3) The distribution diagram of temperature equivalent line obtained from the calculated results can forecast the laser sintering depth, and it can be used to optimize the laser sintering process parameters.

[1] BAI Pei-kang, CHENG Jun, ZHU Lin-quan. The rapid prototyping technology of length-alterable line- scanning[A]. Proceedings of the First International Conference on Rapid Prototyping Manufacturing[C]. Beijing, 1998. 121-125.

[2] ZHANG Ren-ji, SUI Guang-hua, GUANG Liang. Selective laser sintering and its materials[A]. Proceedings of the First International Conference on Rapid Prototyping Manufacturing’98[C]. Beijing, 1998. 506-514.

[3] GRIFFIN C. Rapid prototyping of structural ceramic components using selective laser sintering[J]. J of Material Technology, 1996(11): 48-49.

[4] BOURELL D L, MARCUS H L, BARLOW J W, et al. Selective laser sintering of metals and ceramics[J]. Journal of Powder Metallurgy, 1992(4): 369-381.

[5] BAI Pei-kang, CHENG Jun. Study on selective laser sintering of polymer-coated metal powder[A]. Proceedings of The Second International Conference on Rapid Prototyping & Manufacturing[C]. Beijing, 2002. 449-453.

[6] AGARWALA M, BOURELL D L, BEMAN J. Direct selective laser sintering of metals[J]. J of Rapid Prototyping, 1995(1): 26-31.

[7] GUSAROV A V, LAOUI T, FROYEN L, et al. Contact thermal conductivity of a powder bed in selective laser sintering[J]. International Journal of Heat and Mass Transfer, 2003, 46(6): 1103-1109.

[8] SYVENKYY Y, KOTLYARCHUK, B, ZAGINEY A, SAHRAOUI B. Laser- induced properties modification of CdTe:Cl and (Cd, Hg)Te: Computer simulation and experimental investigation[J]. Optics Communications, 2005(256):342-346.

[9] ZHANG Xiao-ming, LI Chang-sheng, DI Hong-shuang, et al. Simulation of the temperature field of the continuous casting slab during the transporting to the direct rolling[J]. Dongbei Daxue Xuebao, 2001, 22: 99-101. (in Chinese)

[10] CHEN Tie-bing, ZHANG Yu-wen. Numerical simulation of two- dimensional melting and resolidification of a two-component metal powder layer in selective laser sintering process[J]. Numerical Heat Transfer, 2004, 46(7): 633-649.

[11] FANG Jian-cheng, ZHANG Hai-ou, WU Gui-lan, et al. Study on temperature field measurement of plasma stream during rapid sprayed tooling[A]. Proceedings of SPIE-The International Society for Optical Engineering[C]. 2000. 310-314.

[12] CHENG Jun. Applications of Computer in the Casting[M]. Beijing: Mechanical Industry Press, 1993.

[13] BAI Pei-kang, CHENG Jun, LIU Bin. Measurement of temperature field during laser sintering of polymer-coated metal powder[A]. ISTM/2003, Hunan, China, 2003. 3427-3430.

(Edited by PENG Chao-qun)

Foundation item: Project(03022) supported by the Key Science Research Program of Education Ministry of China; Project(200410250) supported by Shanxi Youth Science Foundation

Corresponding author: BAI Pei-kang; Tel: +86-351-3557443; E-mail: baipeikang@sohu.com