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Zhang Jian, Li Deying, Zhao Longzhi
YßK 669.719:629.014+629.014
SIMULATION OF 3-D TRANSIENT TEMPERATURE FIELD IN SELECTIVE LASER SINTERING*
1 Introduction
Since the advent of aluminum industry in 1888, aluminum has been in close contact with the railway industry for its features of light weight, corrosion resistance and good overall durability. Aluminum is not only applied in goods vehicles, light rail trains and intercity transport trains, subways, fast trains, intercity passenger trains as a mature material, but also in today's high-speed trains, such as Ace-la^ TGV Transrapid, Japanese Shinkansen and Pendolinotype, and in future maglev trains [1]. Therefore, the prospect of aluminum applied in the railway industry is very broad.
* Sponsored by Foundation of ECJTU Science and Re-search(01308013)
Selective Laser Sintering (SLS) is a rapid prototyping technology, which sinters the metal powder with high-power laser layer by layer to form 3-D part according to the established paths. It has many advantages, such as short cycle to manufacture, insensitivity to the shape complexity and wide range of materials [2,3]. SLS technology is applied not only to produce accurate models and prototypes, but also of direct functional metal part with reliable structure. As aluminum has strong reflectance to the light and heat, and oxidizes easily in the air to produce Al2O3 with high MP, so it is difficult to control in the selective laser sintering process. Therefore, the studies of aluminum and aluminum matrix composites introduced to SLS have been rare reports.
In SLS, the distribution of temperature field has a direct impact on sintering mechanisms, and then
МЕХАНИКА. ТРАНСПОРТ. МАШИНОСТРОЕНИЕ. ТЕХНОЛОГИИ
affects the quality of sintered part. Because of high heating speed and drastic temperature changes in the laser thermal processing, to measure the temperature of sintered part is almost impossible, so numerical simulation applied to predict the distribution of temperature field in the SLS process is vitally important. At present, many scholars at home and abroad study the distribution of transient temperature field in the SLS process with numerical simulation, and have achieved certain results. A. Greco, et al [5] simulated the temperature field of polymer powder; Y. F. Shen, et al [6] simulated the 3-D transient temperature field of nickel matrix composites; W. X. Zhang, et al [7] simulated the temperature field in the SLS process, and the process parameters are optimized. But these studies focused on the powder of polymer matrix composites, nickel-based matrix composites, and iron matrix composites, etc, the study of aluminum has not yet been reported. In this paper, a finite element model is developed to simulate the 3-D temperature field in the SLS process of aluminum powder with ANSYS commercial package, to predict its distribution of temperature field. By analyzing the distribution of temperature field, it provides a basis for improving the process. It also has an important meaning for the selection of suitable parameters, the reduction of the temperature gradient and the analysis of stress field.
2 Establishment of mathematical model
To calculate the temperature field of laser sintering, the mathematical model of powder should be established first of all. The physical changes of laser processing are described by the mathematical method, so that the parameters of beam have contact with the property parameters of material [8]. In selective laser sintering, the molten pool has heat exchange with the surrounding air and powder bed, the thermal conduction can be described by equation (1) [7]:
д 2T ô 2T д 2T
Hrf +~ôyr+~ÔZ2
+qc+qg = pc
ÔT
~ôt
(1)
substrate and powder bed, which belongs to the third type boundary condition, the expression as follows:
, ôT I
- K &l
+ h(T - TE) + œ (T4 - T4) = q
(3)
Where: ks-effective thermal conductivity of metal powder;h-heat convection coefficient;T-temperature of metal powder at a certain moment; c-Stefan-Boltzmann constant; TE-initial temperature; s-heat radiation coefficient of actual objects.
3 Establishment of physical model 3.1. Establishment of Finite Element Model To simulate the temperature field by ANSYS, the finite element model should be first determined. The finite element model of sintering is shown in Figure 1. The established finite element model is divided into two part, namely, substrate and powder. The size of substrate is 4.8mm*2mm*0.5mm, and that of powder is 3.4mm*1.6mm*0.2mm. The finite element model is divided by Solid70 with hexahedral and eight-node. For the substrate has little effect on the temperature field of sintering area, the different sizes of mesh are made between the substrate and powder. In order to save time and ensure the accuracy of the calculation, the smaller grids are applied to sintered layer, namely, 0.1mm*0.1mm*0.1mm; while the larger grids are applied to substrate.
where: A,s-effective thermal conductivity of powder; p-compaction of powder density; C—heat capacity of material; qg-laser power density. And A,s, p, C varies with temperature.
To solve the heat balance equation, the initial conditions and boundary conditions should be first determined. Before sintering, assume that powder bed has a uniform distribution of initial temperature T0, then the initial conditions as follows:
T(x, y, z, t )| t=0 = T0
Assume that there is no heat loss on the bottom of substrate, but there are heat dissipation by convection and radiation cooling on the upper and the side of
Fig.1 Finite element model
3.2. Load of Gauss Heat Source
In the process of sintering, laser energy moving at a certain rate comes into the powder in the form of heat flux, which obeys the Gaussian distribution [9]:
jrn
2 AP r2
q( x y) =-T exp( ~2—)
(4)
a
Where: —laser power density; p —laser
power; A —absorption rate of powder bed to laser;
r = (x -xo) + (У -Уо)2
—distance between any
point on the powder bed and laser spot center; a — radius of laser spot.
The laser beam moves back and forth on the upper surface of powder, the method of scanning is like grating. The load of moving heat resource is carried out by the technique of "element birth/death" of
ИРКУТСКИМ государственный университет путей сообщения
APDL, and the distribution of temperature field could be eventually obtained in the forming process of SLS.
As the structure of aluminum without isomer is face-centered cubic, so there is no phase change in the heating and cooling process. Therefore, it is no need to consider the effect of latent heat of phase change in the SLS process.
3.3. Thermal Physical Properties of Material The thermal physical properties of material include density, heat capacity, thermal conductivity, melting point, etc. The substrate material is 45 # steel, the parameters of which are shown[10]. The powder is
aluminum, the related parameters are listed in Table 1
[11]
Table 1 Thermal physical properties of Al
Temperature T/°C 20 100 300 400 500 600
Heat capacity 876.8 939.82 1035.72 1057.64 1098.74 1139.84
Ck/J (kg-k)
Thermal conduc- 177 176 198 214 230 241
tivity X /W(m-k)"1
Density ^ /kg m-3 2696 2690 2650 2620 2580 2550
4 Simulation results and discussion
The process parameters used to simulate are shown in Table 2. Figure 2 shows the temperature distribution at different moments. As seen from figure 2, the temperature field distribution is elliptical with the movement forward of laser beam, and the highest temperature area is always close to the sintered frontend. The reason is that the thermal conductivity of powder bed is much smaller than that of metal in the process of high-temperature sintering; and the thermal conductivity of sintered part after densification increased. Therefore, the temperature of spot center is easier to sintered part. As the part without sintering play a role of forced cooling in sintered or sintering part, there is great temperature gradient in the sintered front-end.
Table 2 process parameter to ^ simulate
Physical quantity and units Value
Laser power P/W 420
Spot diameter <t /mm 0.4
Scanning spacing h/mm 0.3
Scanning rate v/(m- s-1) 0.08
Powder thickness d/mm 0.1
Heat absorption rate r0 10%
Initial temperature T0 20
With the increase of scanning time, the temperatures of substrate and powder are gradually increased. Minimum temperature of substrate is 457K and maximum temperature of spot center is 945K at 0.13875s; while minimum is 615K, maximum is
1033K at 0.2525s. These are caused by effects of heat accumulation and heat conduction in the process of sintering. After the sintering of the first layer having finished, it plays a role of preheating in second layer, so the temperature of the second layer is higher than that of the first layer. At the same time, heat spread around the powder particles and substrate by thermal conduction, so that the temperature of heat-affected parts and substrate is gradually increased.
(b) t=0.2525s
Fig. 2. Temperature distribution at different moment
Assume that point 1 is the mid-point of the fourth sintering path of the first layer, and point 2 is the mid-point of the fifth sintering path of the second layer. Figure 2 shows the temperature of point 1 and point 2 various with time. The temperatures of Point 1 and point 2 show upward trends, and the laws of increase are identical, that is, temperature of every point presents fluctuations with the increase of scan-line.
Before point 1 being sintered, its temperature will also increase for the influence of preheating from sintered parts. The spot makes a close to point 1, the temperature is increased with a greater magnitude. Only when it comes to point 1, the peak temperature (950K) exceeds the melting point of aluminum (660°C/930K), and the molten pool is formed. After the spot is far away from point 1, its temperature will also gradually reduce, but the overall average temperature is still increased, without exceeding the melting point of aluminum. These are in line with the mechanism of SLS forming process.
МЕХАНИКА. ТРАНСПОРТ. МАШИНОСТРОЕНИЕ. ТЕХНОЛОГИИ
Point 3 also follows above law. When point 2 is being sintered, maximum temperature is 1042K, the peak temperature of point 2 is higher than that of point 1. The reason is the sintered part plays a role of preheating fully on point 2, which is easy to concentrate heat.
0 15 0.20 0.25 Time Is
Fig. 3. Temperatures of point 1 and point 2 vary with time
1020-, ■4
4
4
4
N
N
V
1000980360 940
920-
900
0.00000
0.00005
0.00010 Z-direction /m
0.00015
0.00020
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 X -direction /m
(b) Temperature distribution of X-direction Fig. 4. Temperature distribution of molten pool at 0.23s.
Figure 4 is the temperature distribution of molten pool at 0.23s. The temperature of spot center is 1016K, exceeding the melting point of aluminum, and the molten pool is formed. Figure 4(a) is the tempera-
ture distribution of Z-direction, to determine the sintering depth. Figure 3(b) is the temperature distribution of X-direction, to determine the sintering width. Figure 3(a) shows that the peak width is about 0.14mm at the temperature of 930K in Z- direction, namely, the sintering depth is 0.14mm. Figure 4(b) shows the peak width is about 0.42mm at the temperature of 930K in X-direction, namely, the sintering width is 0.42mm. For the scanning spacing of simulation is 0.3 mm, it is larger than sintering width and there's a difference of 0.12mm. It ensures the metallurgical bonding between scan lines, so as to ensure the surface finish of sintered parts. For the powder thickness of simulation is 0.1 mm, it is less than sintering depth and there's a difference of 0.04mm. It ensures the metallurgical bonding between layers, so as to ensure the bonding strength between layers of sintered parts.
5 Conclusions
The temperature field in the selective laser sintering was simulated, and factor such as thermal conduction, heat radiation, heat convection and changeable thermal physical properties were taken into account comprehensively. Conclusions are shown as follows.
1) The temperature field distribution is elliptical with the movement forward of laser beam, and the highest temperature area is always close to the sintered front-end. With the increase of scanning time, the temperature of molten pool is gradually increased. These are caused by effects of heat accumulation and heat conduction in the process of sintering.
2) The mid-points of the fourth sintering path of the first layer and the fifth sintering path of the second layer have the same law of temperature variation. The temperature of every point presents fluctuations with the increase of scan-line. When spot comes to the point, the peak temperature exceeds the melting point of aluminum, and the molten pool is formed.
3) By analyzing the temperature distribution of molten pool, the sintering depth and width are determined. The powder thickness is less than sintering depth and scanning spacing is less than sintering width, which make the partial remelt between scan lines and between layers. It ensures that the surface finish of sintered parts, as well as, the bonding strength between layers of sintered parts.
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ИРКУТСКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ ПУТЕЙ СООБЩЕНИЯ
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Anakhin V. D., Anakhin T. V.
Y^K 534
CHALLENGE EQUATIONS FOR THE DYNAMIC VIBRATORY PROCESSING SYSTEM
Advanced vibratory processing system involves completely new method of application of vibration technology for efficient transport-related separation of chemicals, minerals, pharmaceuticals, foods, metallic powders (lead, copper, zinc, steel) and all types of powder products common in many industries: abrasive, powder metallurgy, paint and varnish, diamond, construction, mining and chemical [1]. These new screen-less methods can be effectively used in the abrasive industry to produce materials in which more than 90% of the grains are isometric. Grinding wheels made from such grains are twice as effective as those made from regular grains which are unclassified by shape. Powder products generally are separated by particle size or shape without forming dust. In the diamond tool industry the vibrating equipment is used for selecting isometric, plane and needle-shaped diamond grains. In
the agriculture and food Industry this advanced machinery can utilized for removing harmful inclusions in grains. In the mining and chemical industries high efficiency processing machinery with accurate separations in sizes from 15 mm down to 20 microns can be used for selection many types of the ore. The proliferation of the mechanical design of powder processing machinery for special applications and the incentive to design and operate vibrating equipment have led to an expansion of the role that process control and monitoring the condition of machinery play in the industries. As a result, the focus has expanded from the tuning and performance of vibrating equipment for individual unit operations to the context of controlling and coordinating the broadest range of the appropriate vibration and other parameters. The advantage is that it makes effective use of current technology and provides a
