John Wiley and Sons, Inc. [2] Sandven, O., Laser Surface Transformation ... [4] Woolman, J., Mottram, R.A., The Mechanical and. Physical Properties of the British ...
Proceedings of the 23rd International Congress on Applications of Lasers and Electro-Optics 2004
MODELLING THE EFFECTS OF LASER BEAM GEOMETRY ON LASER SURFACE HEATING OF METALLIC MATERIALS Shakeel Safdar, Lin Li , M.A.Sheikh and M.J.Schmidt Laser Processing Research Centre, Department of Mechanical, Aerospace and Manufacturing Engineering, UMIST, Sackville Street, Manchester, M60 1QD.
Abstract Optimisation of different laser processes requires control over the fundamental parameters of laser processing i.e. heating / cooling rate and thermal gradient. Different processes have different requirement of heating/cooling rate and thermal gradient. If we can control these parameters we can optimise laser processing of materials. Knowing these parameters and relevant metallurgical information we can predict the microstructure and hence control the material properties. The effect of laser beam geometry on laser processing of materials has received very little attention. Laser material processing have been carried out in the past using circular or rectangular beams. This paper presents an investigation of the effects of different beam geometries including circular, rectangular and triangular shapes. Finite element modelling technique has been used to simulate the transient effects of a moving beam for laser surface heating of metals. The temperature distributions, cooling rates and thermal gradients have been calculated. Some of the results have been compared with experimental data. Introduction Laser material processing over the years has developed into a major industrial tool. Laser processing of materials is mainly a thermal process. The way the temperature is distributed inside the material is of prime importance in any thermal process. Based on the temperature distribution one can determine the heating/cooling rate and thermal gradients and subsequently predict the microstructure and material properties. At present the variation in temperature distribution during laser processing is either caused by the variation of laser power or scanning speed. Variations in these parameters are often limited by other processing conditions. Reducing the laser power might affect the heating depth and changing the scanning speed may affect the coverage rate. This fact identifies a limit to the control of temperature
distribution during laser processing. If one can identify any other parameter, such that variation of this parameter alone (.i.e. without changing the laser power or scanning speed) can alter the temperature distribution, it would provide us with added flexibility. A possible method of varying the temperature distribution hence the heating /cooling rate and thermal gradient (without changing input power or scanning speed) is by modifying the geometry of laser beams. The effect of the laser beam shape on temperature distribution has received very little attention. Majority of laser material processing is carried out either with circular or rectangular beam geometry. A variation in beam geometry may offer advantage by altering the temperature distribution and cooling rates across and along the beam. The beam geometry can be varied by the use of various optical systems and diffraction optics [2]. The effects of circular and square beam on laser surface transformation hardening of steels were investigated by Sandven [2]. He established a relationship between the lateral heat losses and beam spot. Kock [13] suggested that the shape of the hardened zone in heat-treating varies with the shape of the spot. A circular spot produces a hemispherical or meniscus-shaped hardened zone while a square spot produces a relatively flat based or even hardened zone. This is due to the energy absorbed per unit area across the surface perpendicular to the direction of travel of laser beam. Some theoretical work on beam geometries was carried out by Chen et al. [11]; it was found that a square shape led to lower cooling rates when compared to line and rectangular beam shapes. Modelling the effects of beam geometries in laser material processing is a demanding task, mainly due to the complex geometries, boundary conditions and material properties. The general expressions found in literature to determine the temperature distribution in the work piece usually consider semi-infinite body and a one-dimensional heat flow normal to the input heat
flux. However in reality heat diffuses in all directions into the work piece from the moving laser spot and not only normal to the surface. Therefore assumptions necessary for an analytical solution may be too compromising for realistic estimation of thermal results. The evolution of numerical techniques and their use in high-speed computers has enabled complicated calculations to be performed in relatively short periods of times with acceptable accuracy. Finite element analysis has been used in the past to model various laser processes [5 - 9,12]. This paper presents an investigation of the effects of various beam geometries on cooling rates and other useful parameters. A finite element model has been constructed to analyse the effect of various beam shapes on laser processing. A commercial finite element package, ANSYS, has been used to simulate the process for the different beam shapes. Some of the results have been compared with experimental results. Experiments were conducted with a fiber optic coupled high power diode laser. Finite Element Model A total of five different beam geometries were simulated each with the same effective area (i.e. 10 mm2). The basic shapes were circular, rectangular and triangular. However both rectangular and triangular beam were simulated for forward and reverse directions respectively. Table.1 shows the beam geometries analysed. The power distribution of fiber optic coupled high power diode laser is uniform therefore a uniform power distribution was used in the model. The scanning speed of laser was set at 10 mm/sec. The power density was kept constant to allow comparison between different beam shapes at similar scanning speeds. The power density was set at 2.5 kW/cm2 to avoid melting of material. The processing of a single surface track length of 20 mm was modelled. Table1: Beam Geometries (dimensions in mm) Circle
Traingle (i) & (ii)
Rectangle (i) & (ii)
The material used was mild steel EN-43A. The size of the work piece was 50×50×10 (mm). Temperature dependent material properties were used for the model [4]. The material was assumed to be homogenous and isotropic. The ambient temperature was set at 20°C. The temperature field caused by a moving laser beam is transient in nature. To simulate the process accurately a three-dimensional transient heat transfer model was formulated. Laser beam was input as a surface heat flux. Heat losses due to convection and radiation are very small [10] therefore they were not considered as they make the calculations highly nonlinear thus causing convergence problems and increasing the computational time by a great amount. The transient thermal analysis in FEM is governed by the following equation, which is written in the matrix form as follows. [C]{Ť} + [K]{T}={Q (t)} Where [C] {Ť} [K] {T} {Q (t)}
(1)
Specific Heat Matrix Time derivative of Temp Thermal Conductivity Matrix Temperature Load (Heat) Matrix
The laser beam was modelled as a moving heat flux which traverses step wise in scanning direction, changing its spatial position in small time steps. Each area sector of the surface was subjected to a heat load for a time period equal to the interaction time dictated by the processing speed. Figure 1 shows schematically the simulation of the motion of the circular beam. At one time step a group of areas representing the shape of the modelled beam were subjected to heat load. After one time step a certain group of areas, depending on the position and motion direction were free of heat load where as the group of areas on the opposite side of beam shape in the direction of motion, which were free of heat load in previous time step, were subjected to heat load. This method was followed for all the time steps simulating the beam motion in one direction for the entire analysis time period.
b D
d d
h b
U D=3.56
U b=5 ; d=2
c U(i) U(ii) c=4.8 ; h=4.16
sector deleted sectors added Heat Flux at time t
Heat Flux at time t+ t′
Figure 1: Simulation of moving laser beam
Experimental Set up The laser source used was a fiber coupled, 1.5kW high power diode laser (LDL 160-1500) with a uniform power distribution. Due to the fiber coupling the efficiency of the laser was reduced to 72 %. The spot of the fiber coupled diode laser was circular in shape. The diode laser operates in the range of 800 - 980 nm. Reflectivity of investigated material (EN 43A) was calculated experimentally at the above said wavelengths, it was found to be between 41-43 % for different work pieces. Aluminium masks were used to shape the beam to the required geometry. The beam shapes were cut on the mask using Nd-Yag laser. As the original beam was circular in shape so the circular beam was scanned without any mask. As shown in table 1 a total of five beam shapes were used during the experiments. All the beams had the same effective area of 10 mm2. The masks were placed at a predetermined height between the laser and the material surface such that the beam shape was inscribed in the circular spot. A circular spot of 5.5 mm (diameter) fully inscribed both the triangular and the rectangular beams. The material surface was placed close to the mask to avoid any diffraction effects. A CNC table was used to move the material under the beam. The table velocity was set at 10 mm/sec. The input power was adjusted before each experiment (depending on the material absorptivity) such that the power density was maintained at 2.5 kW/cm2. A 20mm track was scanned on the material surface for each beam shape. An Impac Pyrometer was used for temperature measurement. The pyrometer had an upper limit of 2000°C (2273°K) and lower limit of 250°C (523°K). The temperature sensitivity at the lower limits was poor. The emmissivity of the investigated material was measured experimentally and was found out to be 0.35. The pyrometer was fixed to the CNC table so that it always looked at a one particular spot (.i.e. middle of the 20mm track) on the material surface. Due to the experimental arrangement the pyrometer could not be placed directly above the measured point but was fixed at an angle. This arrangement made the pyrometer spot a little elliptical. For accurate maximum temperature measurement the spot size of the pyrometer should be smaller or at least equal to the laser beam spot size [3]. The pyrometer was always focused such that the pyrometer spot was always less than the laser beam spot. Figure 2 below shows the schematic arrangement of experimental set up.
Diode Laser
Thermal camera
Laser Pyrometer Spot Pyrometer
Mask Material EN43A
CNC Table Figure 2. Schematic representation of the experimental set-up As highlighted earlier that the spot of the fiber coupled diode laser was circular, therefore no mask was required for scanning circular beam on the material surface. To further verify modeling, a thermal camera was used to take the thermal image of the scan for the circular beam. The temperature limits of the camera were 250°C to 1500°C. For other beam shapes the use of thermal camera was not possible as the camera could only get valid results at angles above 45 degrees and at higher angles the mask obstructed the line of sight of thermal camera. Results and Discussion As discussed earlier a 20 mm track was simulated for different beam shapes. The temperature was measured in the middle of the track during experiments while in modelling the global coordinate system was placed such that the laser scanning started at origin. i.e. (0, 0, 0) and traversed along the x-axis and finished at (20, 0, 0). The beam geometry was equally weighted across the x-axis. To analyze the effect of various beam shapes on temperature distribution, a point in the middle of the track x=10, y=0, z=0 (i.e. 10,0,0) was selected. All the graphs and plots shown below are for the selected point. Figure 3 below shows the comparison of the modelling and experimental results for the circular beam at the selected point.
Model Vs Experiments Circular Beam 1200
Model
1000
Pyro Thermcam
800
Temp (K)
Figure 5 shows the Isotherms on the surface of the solid for the three beam shapes. Isotherms in front of the beam leading edge reflect the beam shape, whereas isotherms behind the trailing edge of the beam are almost similar in shape.
600
Circle
Rectangle
Rectangle Long
Triangle
400
200
0
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Time (sec)
Figure 3. Temp Vs Time (Model and Experiments) As can be seen the modeling results agree well with the experimental results, particularly for the thermal camera. The maximum temperature captured by the pyrometer and thermal camera is quite accurate. i.e. within 4% of the model. However the time vs. temperature profile of pyrometer differs from that of the model. This is because the time vs. temperature profile of the model has been calculated at a point in the middle of the track whereas the time-temperature profile of pyrometer is the average of a region or spot area of the pyrometer. Figure 4 below shows the comparison of temperature distribution across the laser beam spot for the model and thermal camera. The temperature profiles have been plotted by drawing a horizontal line across the laser beam spot beam passing through the maximum temperature point. The modeling results agree well with the experimental results. M od el V s E xp erim ents T em p d istrib ution across L aser b eam S p ot
Triangle Reverse Figure 5. Isotherms on the top surface Figure 6 and 7 similarly shows isotherms in the y-z plane and x-z plane respectively. Isotherms in the y-z plane (depth) are significantly different for the three beam shapes. The isotherms in the y-z plane for the circular and rectangular beam agree well with Kock’s [13] work in which he highlighted that a circular spot produces a hemispherical or meniscus-shaped hardened zone while a square spot produces a relatively flat based or even hardened zone
Circle
Rectangle
Rectangle Long
Triangle
1200 C ircle(M odel)
1000
Thermcam
Temp (K)
800 600 400 200 0 -10
-5
0 D istance (mm)
5
10
Figure 4. Temp Vs Distance (Model and Experiment)
Triangle Reverse Figure 6. Isotherms in y-z plane
z y
Tem pVsTim e(Exp) 1200
Circle
Circle
1100
Rectangle
RecLong Rec
Temp(K)
1000
Rectangle Long
Triangle
TriF
TriR
900
800
700
Triangle Reverse
600
z
Figure 7. Isotherms in x-z plane
0
0.25
0.5
0.75
1 1.25 Time(sec)
1.75
Figure 10 shows the heating/cooling rate for the different beams. Triangular reverse beam has the maximum heating rate (4355.69 K/sec). It is significant to note that though rectangular short beam had the least maximum temperature but has the second maximum heating rate (4325.57 K/sec) followed by the circular beam (4095.83 K/sec). The circular beam has the maximum cooling rate (-4235.84 K/sec) followed by the rectangular long beam (6069.87 K/sec). From this graph it can be seen that the beam with shortest dimension in the scanning direction tends to have a high heating rate but has the lowest cooling rate. This is because of the fact that the leading edge of the beam is closer to the trailing edge thus the rise in temperature from leading edge of the beam to the trailing edge of the beam is very rapid however the same fact inhibits a higher cooling rate. DT/dt 5000 Circle
4000
Trif
T em p V sT im e 3000
Trirev
1200
Recshort
T R IR E V T ri F C ircle
800
R ecL ong R ecS hort
600
dT/dt (K/sec)
2000 1000
Reclong
1000 0 -1000 -2000 -3000
400
-4000 200
-5000 0.00
0 0 .0 0
0 .2 5
0 .5 0
0 .7 5
1 .0 0 1 .2 5 T im e (sec)
1 .5 0
2
Figure 9. Temp Vs Time (Exp)
x
Figure 8 and 9 shows the time-temperature history for different beam shapes for the model and experiments. The experimental results have the similar trend as the model. The maximum temperature attained is for circular beam (1103.3K(mod) : 1130.04K (exp)) followed by triangular reverse beam (1101.7K(mod) :1087.3K (exp)). The rectangular short beam has the least temperature (1027.3K(m) :1011.3K (exp)). It is seen from both the modelling and experimental results that the beams having longer dimension in the scanning direction with respect to its lateral dimension, attains higher temperature for the same power density. However the triangular beam had a longer dimension in the scanning direction as compared to the circular beam, but the temperature attained is more for circular beam. This is due to the fact that the ratio of difference in dimensions in the scanning direction (4.16/3.56) is lesser than the ratio in difference in then lateral direction (4.8/3.56).
Temp (K)
1.5
1 .7 5
Figure 8. Temperature vs. time (Model)
2 .0 0
0.25
0.50
0.75
1.00
1.25
1.50
Time (sec)
Figure 10. dT/dt vs. time
1.75
2.00
Temp Dist across T.E 1200 Circle
Trif
1000
Trirev Recshort
800
Reclong
Temp (K)
This fact is further illustrated in figure 11. It shows the temperature distribution within the beam. i.e. from leading edge of the beam to the trailing edge. All the beams trailing edges are at the same point (i.e. at (10,0,0)) from the start to allow a reasonable comparison. The absorption starts at leading edge of the beam and the maximum temperature is attained just before the trailing edge of the beam. This temperature remains almost steady till the trailing edge with the exception of triangular reverse beam. This is because the beam geometry is tapering down vary rapidly towards the trailing edge thus the area of heat flux is now lesser to sustain the temperature in the bulk material.
600 400 200
Temp Distribution from L.E to T.E
0
1200
-10 -8 circle
1000
-6
Trirev
Temp (K)
6
8
10
Temp Distribution in Depth
Recshort Reclong
-2 0 2 4 Distance (mm)
Figure 12. Temp dist across the beam
Trif
800
-4
1200
circle TriF
600
1000
Trirev Recshort
400
Reclong
Temp (K)
800
200
600
400
0 0
1
2 3 Distance (mm)
4
5
Figure 11. Temp distribution from L.E to T.E
Figure 12 shows the temperature distribution across the trailing edge of the beam. The distance is 10 units to the left and right from the middle of trailing edge (. i.e. at point (10, 0, 0)). The temperature distribution across the trailing edge is reflective of the beams spread at trailing edge. Rectangular beam has the maximum spread therefore it has almost a top hat temperature distribution whereas the circular beam with a point at trailing edge has a Gaussian temperature distribution. The temperature distribution in depth is shown in figure 13 (at the selected point).
200
0 0
2
4
6 Depth (mm)
8
10
Figure 13. Temp distribution in Depth The temperature distribution on the surface and in the depth affects the temperature gradient in different directions. figure 14,15,16 and 17 shows the variation of temperature gradient at the considered point with respect to time in the x, y and z direction. The thermal gradient can be validated by analytical equations. The heating/cooling rate is related to the thermal gradient in the direction of motion by (∂ T /∂ t) = - V. (∂ T /∂ x) Therefore (∂ T /∂ x) = - (1/V). (∂ T /∂ t)
(2)
Heating/cooling rate vs. time has already been plotted in Figure 10. Figure 14 shows the thermal gradient in x or scanning direction. The plot in figure 14 is the inverse of heating/cooling rate with a reduced magnitude. This result agrees to what is represented by equation 2.
TGZ 800 700 600
TGX Circle 600
Trif Trirev
400
TGZ (K/mm)
500
800
Recshort
Trirev Recshort
400
Reclong
300 200
Reclong
TGX (K/mm)
Circle Trif
200
100
0
0
-200
-100 0.00
0.25
0.50
0.75
-400
1.50
1.75
2.00
Figure 16. Thermal Gradient in z-direction Vs Time
-600 -800 0.00
1.00 1.25 Time (sec)
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
TG Sum
Time (sec)
800
Figure 14. Thermal Gradient in x-direction Vs Time
700 Circle
TGY
0
-50 dT/dt (K/mm)
Trif TriRev
500
TG (K/mm)
50
600
Recshort Reclong
400 300 200 100
-100 Circle
trif
-150
Trirev Recshort Reclong
-200
0 -100 0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Time (sec)
Figure 17. Overall Thermal Gradient Vs Time -250 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Time (sec)
Figure 15. Thermal Gradient in y-direction Vs Time
Conclusions Based on the results mentioned above it is evident that the beam geometry provides a useful tool to manipulate temperature distribution in order to optimise the process during laser material processing. The applications of laser beam geometry are unlimited. Different beam geometries have different features, depending upon the process requirement we can select the most suited beam geometry giving us better results
as compared to conventional beam geometries. In the current investigation a total of five beam geometries were considered. The effects of laser beam geometry on temperature distribution (within and across beam geometry), heating/cooling rate and thermal gradients has been presented. The results have been calculated using Finite Element Analysis. Circular beam had the maximum attainable temperature followed by the triangular reverse beam. Triangular reverse beam had the maximum heating rate whereas circular beam had the maximum cooling rate. Thermal gradients were also calculated with respect to each axis. Resultant or an overall thermal gradient was also calculated. Rectangular Long beam had the maximum resultant thermal gradient followed by triangular reverse and circular beam. Thermal gradient in the scanning direction for the different beam shapes had similar plots but had different timings and magnitude. From this study it will not be wrong to say that variation of beam geometry as a process controlling parameter in the quest to process optimisation has huge potential .
Book [1] Incropera, Dewit, Fundamentals of Heat Transfer, 4th Ed., Pub. John Wiley and Sons, Inc [2] Sandven, O., Laser Surface Transformation Hardening. Metals Handbook, 9th Ed., Vol. 4: Surface Engineering, Pub. ASM, pp 507-517. Pyrometer
[9] Matsumoto, M., Shiomi, M., Osakada, K., Abe, F., Finite Element Analysis of Single Layer Forming on Metallic Powder Bed in Rapid Prototyping by Selective Laser Processing. Int. J. Mach. Tools Manuf. Vol. 452: 2002, pp. 61-67 [10] Yeung, K.S., Thornton, P.H., Transient Thermal Analysis of Spot Welding Electrodes. Supplement to the Welding Journal: January, 1999, pp. 1s-6s Conference paper [11] Chen, Y.X., He, Y.Y., Jun, P.S., Nian, S.J., The Role of Beam shape in Convection and Heat Transfer in Laser Melted Pool. Proceedings of ICALEO ’90, Nov. 1990, Boston, USA, Vol. 82: pp. 480-491. [12] Shankar, V., Gnanamuthu, D., Computational Simulation of Heat Transfer in Laser Melted Material Flow. AIAA 24th Int. Aerospace Sci. Meeting, Reno, Nevada: 1986, pp. 1-10
References
[3] Autorenkollektiv, The IMPAC Electronic GmbH.
[8] Dai, K., Shaw, L., Thermal and Stress Modelling of Multi-Material Laser Processing. Acta Mater, Vol. 49: 2001, pp. 4171-4181
URL [13] De Kock., J., Lasers Offer Unique Heat Treating Capabilities. Industrial Heating: 2001 via URL www.industrialheating.com.
Handbook,
[4] Woolman, J., Mottram, R.A., The Mechanical and Physical Properties of the British Standard EN Steels, Vol. 3, First Ed., 1968, Pergamon Press Ltd. Journal paper
Author Autobiography
[5] Wei, P.S., Ho, C.Y., Shian, M.D., Hu, C.L., Three-Dimensional Analytical Temperature Field and its Application to Solidification Characteristics in High- and Low-Power-Density-Beam Welding. Int. J. Heat and Mass Transfer. Vol. 40: 1997, pp. 2283-2292
Mr. Shakeel Safdar is currently studying for a PhD degree in Modeling the Effects of Laser Beam Geometry on Laser Surface Processes in the University of Manchester Institute of Science and Technology (UMIST). He did his two semesters of M.Sc. form NUST Pakistan with a GPA of 4.0 before being selected for Govt of Pakistan scholarship for PhD.
[6] Shuja, S.Z., Yilbas, B.S., 3-Dimensional Conjugate Laser Heating of a Moving Slab. App. Sur. Sci. Vol. 167: 2000, pp. 134-148
His PhD is being supervised by Professor L.Li and Dr. M.A.Sheikh in the Department of Mechanical, Aerospace and Manufacturing Engineering.
[7] Kar, A., Scott, J.E., Latham, W.P., Effects of Mode Structure on Three Dimensional Laser Heating Due to Single or Multiple Rectangular laser beams. J. Appl. Phys. Vol. 80: July, 1996, pp. 667-674
