University of Manchester Institute of Science and Technology, Manchester, UK ... of M echanical, A erospace and M anufacturing Engineering, University of.
531
The development of temperature elds and powder ow during laser direct metal deposition wall growth A J Pinkerton* and L Li Laser Processing R esearch Centre, D epartment of M echanical, Aerospace and M anufacturing Engineering, U niversity of M anchester Institute of Science and Technology, M anchester, U K Abstract: The additive manufacturing technique of laser direct metal deposition (D M D ) has had an impact in rapid prototyping, tooling and small-volume manufacturing applications. Components are built from metallic materials that are deposited by the continuous injection of powder into a moving melt pool, created by a defocused laser beam. The size of the melt pool, the temperature distributions around it and the powder ux are critical in determining process characteristics such as deposition rate. In this paper, the effects that changes in the distance between the laser deposition head and the melt pool have on these factors as a part is built using a coaxial powder feeding system are considered via a two-part analytical model. A heat ow model considers three-dimensional temperature distributions due to a moving G aussian heat source in a nite volume and a simple mass- ow model considers changes in powder concentration with distance from the deposition head. The model demonstrates the effect of adjusting the melt pool standoff in different ways on melt pool and powder ow characteristics as a D M D structure is built, and hence allows the effect on build rate to be predicted. Its validity is veri ed by comparison with a series of 316L stainless steel walls, built using different standoff adjustment methods. The model is found to be able to explain the dimensional characteristics found. Keywords: rapid prototyping, laser, deposition, modelling, heat ow, powder ow
NOTATION
Q
V w x y z X Y Z
absorbed laser power per unit volume (W/m 3) laser spot radius in the x y plane (m) normalized laser spot radius r time (s) dimensionless time s temperature (8C) ambient temperature (8C) laser traverse velocity (m/s) normalized laser traverse velocity v wall width (m) linear dimension (m) linear dimension (m) linear dimension (m) normalized dimension x normalized dimension y normalized dimension z
T he M S was received on 28 October 2003 and was accepted after revision for publication on 6 February 2004. * Corresponding author: L aser Processing R esearch Centre, Department of M echanical, A erospace and M anufacturing Engineering, University of M anchester Institute of S cience and T echnology, PO Box 88, S ackville S treet, M anchester M 60 1QD, UK.
a b d l
absorptivity laser beam divergence half-angle (deg) powder stream divergence half-angle (deg) absorption depth (m)
C22003 # IM echE 2004
Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
C d d0 D D0 h…z† K m0 m 0tot n P
speci c heat capacity (J/kg K ) melt pool standoff (head to melt pool) (m) initial melt pool standoff (m) normalized d normalized d0 step function thermal conductivity (W/m K ) powder mass owra te per unit area (kg/m 2 s) total powder mass owrate (kg/s) summation integer laser power (W)
r R s S T Ta
v
532
A J PIN KERTON AN D L LI
thermal diffusity (m 2/s) density (kg/m)
A schematic diagram of a typical coaxial laser direct metal deposition system
protected from harmful oxidation via a further ‘shroud’ inert gas stream or by enclosing the process in a chamber lled with an inert gas. M azumder and K ar [1] studied thermal characteristics in laser cladding and Pustovalov and Bobuchenko [2] presented a model of a laser cladding process that included consideration of the moving powder particles and allowed temperature distributions near the melt pool to be derived. Both models were one-dimensional. H oadley and R appaz [3] produced a two-dimensional nite element model of the process using a deforming mesh technique. The model allows more realistic modelling of the D M D process, but, as the authors point out, it is not strictly valid for a circular beam and requires signi cant simpli cation of input parameters. It is clearly applicable only to very thin-walled structures. M ore recently, Vasinonta et al. [4–7] used numerical, analytical and experimental methods to produce process maps for the control of residual stresses in the LEN STM process (a patented laser D M D system). Clear results for melt pool size are obtained, but they are applicable only to thin-walled structures, and, as noted by the authors [7], the accuracy could be improved by considering a distributed rather than a point heat source. A nite element model for both laser remelting and laser cladding by Picasso and H oadley [8] allowed for a G aussian laser intensity distribution and considered heat transfer, uid motion and powder injection forces. H owever, it considers none of the important threedimensional aspects of the process. Both infrared [9] and visual range [10] image sensing techniques have been used to verify theoretical results, establish melt pool limits and provide feedback control. M odelling of a laser-induced melt pool has been undertaken numerically [11] and analytically [12, 13] in other elds, but these do not account for the material addition required for D LD and have not been veri ed against D LD systems. In this paper a more realistic three-dimensional model is presented. A moving surfa ce heat source with G aussian intensity distribution is used to predict heat ow in the upper part of a wall produced by D LD . F rom this, changes in the dimensions of the melt pool are predicted as the wall grows and the distance between the top of the wall and deposition head (the ‘melt pool standoff ’ ) varies. The melt pool length has been identi ed as the critical factor dictating cooling rates and general build conditions [14], so control of it is essential to maintain consistent material properties. This model is combined with another of coaxial powder ow to predict material assimilation rates. An experimental investigation of the effect of different melt pool standoff adjustment strategies during the building of a thinwalled structure by a coaxial laser D M D system is then undertaken and the equivalent process variables are used in the model. The theoretical results are able to explain the practical trends seen.
Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
C22003 # IMechE 2004
k r
1
INTRODUCTION
The use of rapid prototyping (R P) and rapid tooling (R T) techniques has steadily increased due to the economic advantages afforded by reducing the concept to market delay of a product. Improvements in laser ef ciency and reductions in the price of laser systems, automated positioning equipment and control apparatus means that some methods originally conceived for R P and R T are now nding wider application for part refurbishment and small volume manufacturing. D irect metal deposition (D M D ) by laser is one such method. Currently, the most widely adopted D M D equipment con guration is that of a CO 2 or N d:YAG (neodymiumdoped yttrium aluminium garnet) laser with a coaxial powder feed nozzle (the deposition head) positioned orthogonal to a laterally mobile deposition surface (the substrate), but interest is growing in the use of highpowered diode lasers (H PD Ls). A typical D M D system is shown schematically in F ig. 1. D uring the deposition process, a defocused laser beam creates a moving melt pool on the surface of the substrate and metal powder is simultaneously conveyed into it from the nozzle via an inert gas stream (usually argon). The additional material increases the size of the melt pool, with a resultant raised track when the power source moves and the pool solidi es. R epeating the process, following the same or offset paths, allows multiple tracks to be deposited and walls or bulky parts to be deposited. The process is
Fig. 1
THE D EVELOPMENT OF TEM PER ATUR E F IELD S AN D POWDER F LOW
2
MATHEMATICAL MODEL DEVELOPMENT
2.1 Assumptions The multiple transformation mechanisms involved in a moving heat source problem with material addition, as created by a laser D M D system, mean that some carefully de ned simpli cation is necessary for a practical, yet realistic, model to be created. H ere, the shape of the melt pool presented to the incoming powder stream is taken to be determined by the shape of the melt pool that would be induced on the wall without material addition. This is a technique that has been used successfully for models of single-layer cladding [15]. It is the central simpli cation that allows the problem to be divided into two stages: a heat ow model to establish melt pool boundaries and a powder ow model to establish the mass owrate into that bounded area. The other assumptions and simpli cations made, and their justi cations, are as follows.
A ssumption 1 The wall material is homogeneous, isotropic and initially isothermal. The added material is of the same type, with the same thermophysical properties and absorptivity to laser radiation. These are all reasonable assumptions. F irstly, functionally graded structures are possible [16], but currently account for only a small proportion of the D M D market. Secondly, thermal conductivity generally increases with temperature, so by adopting a constant value thermal gradients will be overestimated in high-temperature regions and underestimated in low-temperature regions. D ue to the rate of increase (e.g. 0.013 W/m K 2 for 316 stainless steel [17]), however, this will not signi cantly impair the model’s accuracy. F inally, the assumption of initially isothermal conditions assumes complete dispersion of the heat from previous depositions, which is a reasonable approximation given the high thermal diffusity of the metals commonly used and the size of most D M D parts.
533
A ssumption 3 Attenuation of the laser beam by the powder is offset by the energy imparted to the pool by the heated particles to an extent that the net power loss can be discounted. There is considerable evidence to suggest that the two counteract each other in this way [18, 19] and it is further justi ed by assuming that all particles incident on the melt pool are absorbed, while all others impart no energy and do not adhere to the surface. This has been the basis for work to estimate catchment ef ciency [20] and was shown to be a valid model assumption by the work of Picasso et al. [21]. The energy lost due to heated, but non-adherent, particles has been estimated at 0.8 per cent of the total laser power [15] and is discounted.
A ssumption 4 The laser power distribution is unchanged (G aussian) on reaching the melt pool, because of the generally low concentration of the powder particles and varying axial concentration patterns between the nozzle and melt pool [22–24]. Some distortion may occur, but due to the axisymmetric nature of the stream it is unlikely to be as signi cant as for a lateral powder ow system [25].
A ssumption 5 The wall has reached a suf cient height for the effect of the substrate as a thermal heat sink to have diminished suf ciently to be discounted. Work by Vasinonta et al. [4] and Beuth and K lingbeil [26] showed that the melt pool length is reduced for short walls, but that a transition to steady state conditions occurs, after which the wall can effectively be considered in nite in the ‡ z direction. Their process maps indicated this to be at a wall height of approximately 6K =…rC v† [6], where K is the thermal conductivity, r is the density, C is the thermal capacity and v is the laser traverse speed. The model presented here should therefore be used with caution below this wall height.
A ssumption 6
A ssumption 2 N o surface losses due to radiation, convection or element vaporization are accounted for. This is common in the analytical modelling of surface heat treatment and cladding (e.g. reference [3]); it has been shown not to reduce model validity and is justi ed in respect to this process by the empirical calculations of H ofmeister et al. [14]. C22003 # IM echE 2004
The system is in a quasi-stationary state (i.e. stationary in a reference frame attached to the laser beam). This is reasonable when the wall length is large compared to the extent of the heat source [27], which is likely to be the case due to the small laser spot diameter.
A ssumption 7 Circulation in the melt pool due to the M arangoni effect, thermal buoyancy or convection is not considered. Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
534
A J PIN KERTON AN D L LI
N umerical simulations have shown that the rst of these is dominant and can cause melt pool shape changes when welding or cladding on a plane surface [28, 29]. The most signi cant is, however, pool widening, which is partly limited by the wall once established. Possible changes to melt pool geometry due to element vaporization are also discounted, based on the ndings of Lei et al. [29], whose numerical heat modelling showed that it is insigni cant for surface tension–temperature coef cients greater than 3 6 104 N /m K .
A ssumption 8 The melt pool is beyond the focal distance of the objective lens, so the focal point remains in a constant position, which is above the deposition point on the wall at all stages. The melt pool is also beyond the point of maximum concentration of the powder stream. This point normally occurs within 10 mm of a typical deposition head [24], which is too near for deposition to occur safely due to overheating caused by re ected radiation and potential damage due to ricocheting particles, so this is reasonable.
2.2 Heat ow and temperature Seminal work by Jaeger [30] and Carslaw and Jaeger [31] provided much of the foundation for heat conduction theory. H owever, a large amount of their work addresses steady state or stationary source problems and, for mathematical simplicity, moving heat source solutions were simpli ed to a uniformly distributed moving band or rectangle [30]. Later work by Tian and K ennedy [32] allows the temperature eld due to moving circular or elliptical sources to be calculated, but their solutions are valid only for a semi-in nite substrate.
Fig. 2
Consider the initial situation of a high-powered laser beam of total power, P, and G aussian pro le, normal to a plane, semi-in nite substrate and with a traverse velocity, v. N ormalized over a spot of radius r, the absorbed power per unit volume, Q, is given by [30] Q ˆ aP
¡ expf¡ ‰…x ¡ vs†2 ‡ y 2 Š…2r2 † 1 g h…z† 2 l 2pr
…1†
where a is the absorptivity of the wall material, s is time, l is the absorption depth and the step function h…z† ˆ 1 for 0 < z 4 l and 0 for z > l. Application of G reen’s function allows the temperature, T , within the substrate due to this to be written as [33] T …x , y, z†
( "
…x ‡ vs†2 ‡ y 2 z2 ‡ … ? exp ¡ 2r2 ‡ 4ks 4ks aP ˆ Ta ‡ rC 0 …p3 ks†1=2 …2r2 ‡ 4ks†
#)
ds …2†
where T a is the ambient temperature, C is the thermal capacity, k is the thermal diffusity and r is the density of the substrate material. This solution has been widely used in studies of laser surface treatment, but is suitable only for a semi-in nite plane surface. By applying the method of images [31] to it, it is possible to consider three-dimensional heat ow due to a moving heat source on the surface of a structure, such as a wall, without needing to reduce the problem to two dimensions [34]. Consider the situation as illustrated in F ig. 2, with the substrate bounded by x z planes positioned at y ˆ +w/2 and the laser beam moving along the x axis …y ˆ 0, z ˆ 0†. This de nes a wall of width w with a heat source moving along its centre-line. By positioning virtual heat sources at the positions of images of the source in mirrors located at the boundary
A schematic diagram of the heat ow model formulation
Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
C22003 # IMechE 2004
THE D EVELOPMENT OF TEM PER ATUR E F IELD S AN D POWDER F LOW
planes, equation (2) becomes aP rC nX ˆ? … ? exp‰¡ f …x , y, z, v, s, w, r, k, n†Š
equation (4) gives the result
T …x, y, z† ˆ T a ‡ 6
…p3 ks†1=2 …2r2 ‡ 4ks†
nˆ¡ ? 0
ds …3†
aP T ˆ T a ‡ p 2p3 Kw nX ˆ? … ? exp ‰¡ f …X , Y , Z , D, D 0 , V , S , b†Š 6 dS £1 ¤2 ‡ …D ¡ D 0 † tan b ‡S 2 nˆ¡ ? 0 2
…6†
where
where "
…x ‡ vs†2 ‡ …y ‡ nw†2 z2 f …x , y, z, v, s, w, r, k, n† ˆ ‡ 2 2r ‡ 4ks 4ks
#
for ¡ w/2 4 y 4 w/2, r 4 w/2 and z 5 0. This is made dimensionless, using the wall width w, as the characteristic linear dimension instead of the more commonly chosen beam radius. M aking the substitutions X ˆ x =w,p Y ˆ y=w, Z ˆ z=w, R ˆ r=w, V ˆ wv=k and S ˆ 2ks=w and simplifying the result, equation (3) becomes aP T ˆ T a ‡ p 2p3 Kw … nˆ? X ? exp‰¡ f …V , R , X , Y , Z , S †Š 6 dS R2 ‡ S2 nˆ¡ ? 0
…4†
f …X , Y , Z , V , S , R , n†
¡ ¢2 2 Z 2 …Y ‡ n† ‡ 12V S 2 ‡ X ˆ 2‡ 2S 2…R 2 ‡ S 2 †
and K is the thermal conductivity. This solution is valid for R 4 12, ¡ 12 4 Y 4 12 and Z 5 0. N oting that material addition is not considered at this stage, the position of the melt pool boundaries on the upper surface of the wall can be obtained from equation (4) by setting Z ˆ 0 and T equal to the melting point of the build material. In order to relate the above calculations to the melt pool standoff, the laser spot size must be expressed in terms of it. Assume that the laser is diverging at a halfangle b, the original melt pool standoff is d0 and the spot diameter was initially equal to the wall width (so R ˆ 12). Then (noting Assumption 8, that the melt pool is beyond the focal point), when the melt pool standoff is d, the spot radius r is given by w ‡ …d ¡ d0 † tan b 2
…5†
Converting to dimensionless values and substituting in C22003 # IM echE 2004
f …X , Y , Z , D, D 0 , V , S , b† ˆ
Z2 4…Y ‡ n†2 ‡…V S 2 ‡ 2X †2 ‡ 2S 2 2‰1 ‡ 2…D ¡ D 0 † tan bŠ2 ‡8S 2
and D ˆ d/w, D 0 ˆ d0/w. This is true for ¡ 12 4 Y 4 12, Z 50 and D 4 D 0 . Equation (6) contains no singularities and can be solved numerically. F or practical applications, in nite summation and integration limits are not necessary.
2.3 Mass ow
where
rˆ
535
Powder ow from an annular nozzle has been modelled by Lin [22] and Pinkerton and Li [23, 24] and visualization of the stream has been conducted by these authors. F indings indicate that there is a convergence of powder steams to a point of maximum concentration (the ‘merge point’ [14]), followed by a single expanding stream with a G aussian powder concentration pro le. F or a correctly aligned deposition head, this is coaxial with the laser beam. As stated in Assumption 8, the melt pool is taken as occurring after the merge point. Therefore, if the distance between the head and melt pool is d and the stream is diverging at a half-angle d, extrapolation back to the plane of the head [23, 24] gives the diameter of the stream in the x y plane as 2d tan d. Consider now the gas stream and powder as coupled and owing at a single speed. If the total powder mass owrate from the nozzle 0 is m tot , then a normalized G aussian distribution, with width equal to that of the powder stream, can be taken such that the powder concentration is e¡2 of its peak value at the stream limits. The powder mass owrate m 0 at any point in an x y plane positioned at a distance d below the head is then given by µ ¶ 2m 0tot 2…x 2 ‡ y 2 † m 0 …x , y, d, d† ˆ p exp ¡ 2 d tan 2 d 2pd tan d
…7†
This is normalized as before, using the wall width w as the characteristic linear dimension and the substitutions X ˆ x =w, Y ˆ y=w and D ˆ d=w. This leads to the Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
536
A J PIN KERTON AN D L LI
Table 1
result m 0 …X , Y , D, d†
µ ¶ 2m 0tot 2…X 2 ‡ Y 2 † ˆ p exp ¡ D 2 tan 2 d 2pD tan d
…8†
The rate at which powder is owing into an arbitrary region within the x y plane can be obtained by a double integral with respect to X and Y , or, if the region is symmetrical about the central axis, can be simpli ed by converting to radial coordinates to give a single integral. This will never be completely true with a moving heat source, but it may provide an acceptably accurate solution under some conditions.
Operating parameters for the experimental investigation
Sample set
Power (kW)
Powder ow (g/s)
Traverse speed (mm/s)
A B
1 1.1
0.271 0.136
8 8
A common problem facing industrial users of D M D equipment is the amount of adjustment to make to the distance between the deposition head and the original substrate (the ‘substrate standoff ’) between deposition tracks, or how sophisticated a system to purchase in order to do this automatically. Together with the part height, the substrate standoff clearly determines the melt pool standoff. Three-axis D M D systems, with automatic control systems to maintain a constant melt pool standoff, have grown in use, but add to equipment capital costs and can slow the production process. The effect of using different strategies for adjustment of the substrate standoff has not been investigated in detail. The model was applied to this problem and the two limiting control strategies assessed. The rst is perfect adjustment, where the position of the substrate is moved by a variable amount, so the melt pool standoff remains constant. In this case, the laser spot size relative to the wall width and powder concentration pro le will remain constant. H ence, to model the process, the variables in equations (6) and (8) will remain constant. The second strategy is zero adjustment, where the substrate is not moved, so the melt pool standoff decreases as the wall grows. In this case, the diameter of the laser beam and
the powder stream reduce according to their respective angles of divergence. The perfect adjustment and zero adjustment strategies were rst investigated experimentally. Straight, vertical walls consisting of 20 deposition tracks were built using a typical coaxial laser D M D system, similar to that illustrated in F ig. 1, and two sets of operating parameters. These are summarized in Table 1. The walls were consolidated from 316L stainless steel (16.0–18.0% Cr, 10.0–14.0% N i, 2.0–3.3% M o, 2.0% M n, 1.0% Si, 0.03% C [17]) gas-atomized powder of 53–150 mm particle size onto EN 43A (AISI 1050) mild steel blocks that had been milled at, grit-blasted to approximately 5 mm R a (ISO) surface roughness and degreased. The blocks were of nominal size 50 mm 6 50 mm 6 5 mm and the walls were straight, vertical and approximately 40 mm long. The deposition head was supplied by a SIM ATIC OP3 disc powder feeder and a R OF IN -SIN AR 1.2 kW CO 2 laser, with a pre-calibrated digital power display and coaxial nozzle. Argon was used both as a conveyance gas (5 l/min ow) and as a shroud gas (40 l/min ow). D uring the consolidation of a wall, the substrate block was clamped to a water-cooling system to maintain it at approximately room temperature, and this was then mounted on a vertical positioning stage, allowing manual adjustment to an accuracy of 0.01 mm. M otion of this assembly in the horizontal …x y† plane was via a U nimatic two-axis motorized table with an AM C controller. Each sample produced was cold-mounted in epoxy resin, sectioned in transverse planes and then ground and polished to a surface nish of 6 mm. G eneral layer boundaries were revealed by electrolytically etching at 6 V and a current density of approximately 2.5 mA/mm 2 in a 10 per cent solution of oxalic (ethanedioic) acid. Layer dimensions were measured in three evenly spaced transverse planes using optical microscopy. In each plane, the layer depth was measured along the centreline of the wall and the width was taken as the maximum value at any horizontal position within a layer. The nal value taken for each layer was the mean of the three measurements. U nder both sets of tested conditions, the highest wall was produced when the melt pool standoff was allowed to decrease as the wall grew (F ig. 3). The increases in height appear approximately linear with both adjustment methods and under both sets of operating conditions. As expected, the wall height was increased
Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
C22003 # IMechE 2004
2.4 Resultant layer depth Based on Assumption 3, the rate of assimilation of powder can now be estimated from the mass of powder impacting within the boundary of the calculated melt pool. Any quantitative calculation at this stage could be simpli ed by considering the melt pool as an ellipse, de ned by its maximum length and width in the manner of previous models for plane surfaces [15]. D ifferent situations are possible, depending on the wall width and the limits of the melt pool and the powder stream on reaching the upper surface of the wall (x y plane, z ˆ 0).
3
APPLICATION AND VERIFICATION
THE D EVELOPMENT OF TEM PER ATUR E F IELD S AN D POWDER F LOW
Fig. 3
Accumulated wall heights of walls produced using alternative methods to adjust the melt pool position
signi cantly by the higher powder ow of conditions B [35], indicating that laser power was not the limiting factor for this combination of parameters. It was not possible to determine any clear trends from the measurements of the layer widths of the walls, either with respect to operating conditions or the adjustment method used. In all cases, they are between 0.95 and 1.3 mm and exhibited non-uniform variations from one point to the next. The mean value of each of the four sets of results was 1.2 mm (+ 5 per cent), so this value was taken for the theoretical calculations. Based on the material used, the experimental parameters chosen and measurements during the practical work, it was possible to set, or approximate, values in the heat and mass ow models. These values are summarized in Table 2. Based on them, equation (4) was solved numerically using the adaptive G auss– K ronrod integration method for a laser power of 1 kW and dimensionless traverse speed, V , of 1.79, corresponding to conditions A. Solutions for three different laser spot diameters, corresponding to the full width of
Table 2
537
the wall, half of the wall width and a quarter of the wall width, were derived. This progression models the laser heat ux differences due to reduction of the melt pool standoff that would be caused by the growth of a wall with no adjustment to the substrate position away from the deposition head (the zero adjustment stra tegy). Because the spot diameter was initially equal to the wall width (and noting Assumption 8), in this case these correspond to the deposition point being positioned 19, 15 and 13 mm respectively from the deposition head. R esults, in the form of isotherms (temperature contour plots) on the top surfa ce of the wall (x y plane, z ˆ 0), are shown in F ig. 4 and, in terms of isotherms in the x z plane …y ˆ 0†, in F ig. 5. H igher peak wall temperatures are predicted to occur using the zero adjustment strategy because it leads to smaller laser spot sizes. The maximum modelled temperatures for the full wall width, half wall width and quarter wall width spot diameters were 2440, 3710 and 7000 8C respectively. F igure 6 shows simulations for the same spot sizes and illustrates how the temperature along the centre-line of the top of the wall (x y plane, y ˆ 0, z ˆ 0) changes. The length and width of the melt pool can be determined from the range of x and y values over which the temperature exceeds the
R eference and experimentally obtained parameter values for application of the theoretical model
Parameter
Value [17, 36]
Absorptivity Thermal diffusity (m 2/s) Thermal conductivity (W/m K)* Speci c heat capacity (J/kg K) Ambient temperature (8C) Laser traverse velocity (mm/s) M ean wall width (mm) Initial distance between the head and melt pool (mm) Powder stream divergence half-angle (deg) Initial powder stream diameter (mm) Laser beam divergence half-angle (deg)
0.11 5.375 6 10¡ 6 21.5 500 19 8 1.2 19 5.3 3 3.6
* The reference thermal conductivity at 500 8C is taken [17]. C22003 # IM echE 2004
Fig. 4
M odelled temperature contours on the top of a wall (xy plane, z ˆ 0) due to a moving G aussian heat source of diameter (a) full wall width, (b) half wall width, (c) quarter wall width
Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
538
Fig. 5
A J PIN KERTON AN D L LI
Fig. 6
M odelled temperature on the top of a wall due to a moving Gaussian heat source (a) parallel to motion (x axis, y ˆ 0, z ˆ 0) and (b) perpendicular to motion (y axis, x ˆ 0, z ˆ 0)
Fig. 7
M odelled changes in a powder stream concentration pro le with decreasing melt pool standoff
M odelled temperature contours in the central plane of a wall (x z plane, y ˆ 0) due to a moving G aussian heat source of diameter (a) full wall width, (b) half wall width, (c) quarter wall width
material solidus temperature. It is clear that the melt pool size is modelled to increase as the spot size decreases when using the zero adjustment strategy. N o change would occur when using the perfect adjustment strategy. F or both adjustment strategies, the powder stream diameter always remains greater than both the melt pool length and width. The modelled changes in the powder stream concentration pro le in three x y planes are shown in F ig. 7. The mass ow becomes more concentrated close to the axis of the stream as the melt pool standoff decreases when using the zero adjustment strategy. The model has predicted a hotter, larger melt pool and a greater powder concentration owing into the region of the pool when using the perfect adjustment strategy. This will intuitively lead to an increased deposition rate. Additionally, the positive links between the powder owrate and track height [37] and between higher laser power (and therefore a larger, hotter melt pool) and an increased deposition rate [3, 35] are well established. The predictions of the model are therefore in agreement with the experimental results recorded Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
under both experimental conditions. F urther quanti cation of the modelled results is not possible at this stage, due to the inherent simpli cations in the model and the non-linear powder stream concentration distribution.
4
DISCUS SION
F or a laser spot size equal to that of the wall, F ig. 4 shows that the heat ow is almost completely twodimensional, but for decreasing spot diameters the heat ow tends further to that seen with a plane surface, with C22003 # IMechE 2004
THE D EVELOPMENT OF TEM PER ATUR E F IELD S AN D POWDER F LOW
539
temperature gradients in the y direction. F or the smaller spot sizes, the temperature isotherms have a generally elliptical shape that is more elongated in the ¡ x direction, behind the pool. This is in agreement with three-dimensional models of heat ow on a semi-in nite, smooth substrate [33, 38] and thermal images of this process [39, 40]. Isotherms in the x z plane (F ig. 5) followed the same general pattern seen with twodimensional moving heat-source models [34]; the maximum temperature decreased and shifted further behind the source of heat as the distance below the top of the wall increased. It is clear from F igs 4 and 5 that the large differences in temperature distribution caused by the changes in laser spot diameter are a local effect. Because the same amount of energy is imparted to the substrate, the temperature differences beyond approximately twice the wall width from the source in this case are negligible. This distance is naturally dependent upon the material and process parameters. The peak wall temperatures modelled are slightly higher than have been previously measured in D LD systems of this type [14, 39], which is consistent with the foundations of the model. F irstly, the additional power required to heat and melt incoming powder is not accounted for in the power ow model. Secondly, circulation of molten material would in practice lead to a more uniform temperature distribution on the melt pool surface and therefore reduce the peak temperatures [11]. Thirdly, it can also be attributed to a slight overestimation of power reaching the melt pool. Assumption 3 is a reasonable approximation, but may underestimate the amount of power re ected from the powder, especially when using a CO 2 laser with consequential high surface re ectivity. F inally, absorptivity is taken as constant, but work by Bamberger and G eler [41] indicates that the coupling ef ciency of CO 2 radiation and a stainless steel surface decreases with temperature. This would act to reduce energy absorption by the melt pool and substrate in high-temperature regions. G iven these factors, a slight overestimation of the heating of the substrate is not unexpected. M odelling these effects analytically would complicate the model and is outside the scope of this paper, but after accounting for them the modelled results shown in section 3 are realistic. As evaluation of the shape of the melt pool has been recognized by previous researchers as a major source of error in analytical models of this process [15], the similarity with thermal images indicates that the model provides an accurate portrayal of the thermal process. F or both adjustment strategies, the powder stream diameter always remains greater than both the melt pool length and width. The low powder catchment ef ciencies that are often achieved in laser D M D indicate that this is commonly the case. The differences in powder ow seen at the melt pool when using the zero adjustment strategy were due to changes in the powder stream
concentration pro le (F ig. 7). This indicates that the logic of the melt pool being ‘either-in-or-out’ of the powder stream, as used for previous theoretical models of cladding with lateral-feed nozzles [3, 21], may need re nement to allow the powder ow concentration pro le to be accounted for when applied to coaxial cladding. It should be noted that the melt pool and powder stream are not coaxial, especially at higher traverse speeds. Compilation of the temperature distribution and powder ow results makes it possible to build an overall picture of a D LD system as the position of the deposition point changes. As the wall height increases using a zero adjustment strategy, three basic effects occur: the powder stream becomes more concentrated near the central axis, the upper surface of the melt pool becomes longer (x axis) and, after a critical height is reached, the pool width decreases (y axis). Together this allows a greater proportion of powder to impact the melt pool, a greater rate of new material assimilation and consequently a greater track height. When a perfect adjustment strategy is adopted these effects do not occur. This explains the greater wall heights found when using a zero adjustment strategy (F ig. 3). The change in process characteristics that are directly related to a melt pool standoff are shown in F ig. 8; adopting a zero adjustment strategy results in movement along the horizontal axis during the process. Any effect of pool lengthening due to an overall increase in the temperature of the substrate as the process continues is equal for both strategies. It should be noted that these effects apply only within a certain ‘operating range’. If the deposition point is too far from the laser head then the laser intensity may be insuf cient to melt the substrate surface or sustain a steady track. If it is too close, then excessive melting of the substrate or plasma effects may occur near the laser focal point, or the point of maximum powder concentration [22–24] may be passed, invalidating the mass ow model used.
C22003 # IM echE 2004
Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
5
CONCLUSIONS
A three-dimensional approach has been used to formulate a thermodynamic model for the temperature pro le in a thin-wall structure produced by laser direct metal deposition. It has been shown appropriate to approach the problem in this way, due to the threerather than two-dimensional ow of heat seen if the laser spot size is noticeably less than the wall width, as can occur in practice. The quasi-stationary temperature pro le, and therefore the melt pool shape, has been shown to evolve as the distance between the laser head and melt pool changes and therefore, given a suf ciently divergent laser beam, the laser spot diameter changes. Application of this model is not limited to laser direct metal deposition.
540
A J PIN KERTON AN D L LI
Fig. 8
Changes in process variables at the top of a laser D M D wall for different deposition head to melt pool standoffs
Coupling the thermodynamic model with one of mass ow has allowed the model explaining and predicting changes in the rate of deposition of metal as a wall grows to be formulated. Experimental results show that, with tested con guration and conditions, higher walls were produced when the distance between the melt pool and deposition head decreased than when it was kept at a constant value by adjustment of the substrate position. This can be attributed to a smaller laser spot size and increased powder ux on the melt pool. Layer height consistency was comparable, but no clear trends in layer width could be determined. It can be concluded that substrate repositioning between layers is not always necessary, provided the deposition point remains within a de ned operating range.
ACKNOWLED GEMENT The authors gratefully acknowledge the nancial assistance of the U K Engineering and Physical Sciences R esearch Council (EPSR C).
REFERENCES 1 Mazumder, J. and Kar, A. N onequilibrium processing with lasers. W orld L aser A lmanac, 1988, 1, 17–24. 2 Pustovalov, V. K. and Bobuchenko, D. S. Thermal processes in gas-powder laser cladding of metal materials. Int. J. H eat and M ass T ransfer, 1993, 36(9), 2449–2456. Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
3 Hoadley, A. F. A. and Rappaz, M. A thermal model of laser cladding by powder injection. M etall. T rans. B ( Process M etallurgy) , 1992, 23B, 631–642. 4 Vasinonta, A., Beuth, J. and Grif th, M. Process maps for laser deposition of thin-walled structures. In Proceedings of the 10th Solid F reeform Fabrication Symposium, Austin, Texas, 1999, pp. 383–391. 5 Vasinonta, A., Beuth, J. and Grif th, M. Process maps for controlling residual stress and melt pool size in laser-based SF F processes. In Proceedings of the 11th Solid F reeform F abrication Symposium, Austin, Texas, 2000, pp. 200–208. 6 Vasinonta, A., Beuth, J. L. and Ong, R. M elt pool size control in thin-walled and bulky parts via process maps. In Proceedings of the 12th Solid F reeform F abrication Symposium, Austin, Texas, 2001, pp. 432–440. 7 Vasinonta, A., Beuth, J. L. and Grif th, M. L. A process map for consistent build conditions in solid freeform fabrication of thin-walled structures. T rans. A SM E, J. M fg S ci. Engng, 2001, 123, 615–622. 8 Picasso, M. and Hoadley, A. F. A. F inite element simulation of laser surface treatments including convection in the melt pool. Int. J. N um. M eth. Heat and Fluid Flow, 1994, 4(1), 61–83. 9 Hu, D., Mei, H. and Kovacevic, R. Improving solid freeform fabrication by laser-based additive manufacturing. Proc. Instn M ech. Engrs, Part B: J. Engineering M anufacture, 2002, 216(B9), 1253–1264. 10 Meriaudeau, F. and Truchetet, F. B. Image processing applied to the laser cladding process. Proc. S oc. Photo-opt. Instrum. Engrs ( SPIE) , 1996, 2789, 93–103. 11 Yang, L. X., Peng, X. F. and Wang, B. X. N umerical modeling and experimental investigation on the characteristics of molten pool during laser processing. Int. J. H eat and M ass T ransfer, 2001, 44(23), 4465–4473. 12 Chan, C. L., Mazumder, J. and Chen, M. M. Threedimensional model for convection in laser weld pool. In C22003 # IMechE 2004
THE D EVELOPMENT OF TEM PER ATUR E F IELD S AN D POWDER F LOW
13
14
15
16
17
18
19
20
21
22
23
24
25
Proceedings of International Congress on A pplications of L asers and Electro-optics (ICA L EO’84), Boston, M assachusetts, 1984, Vols 43–48, pp. 17–27. Hoadley, A. F. A., Rappaz, M. and Zimmermann, M. Heat ow simulation of laser remelting with experimental validation. M etall. T rans. B: Process M etallurgy, 1991, 22(1), 101–109. Hofmeister, W., Grif th, M., Ensz, M. and Smugeresky, J. Solidi cation in direct metal deposition by LEN S processing. J. M etals (JOM ), 2001, 53(9), 30–34. Gedda, H., Powell, J., Wahlstrom, G., Li, W.-B., Engstrom, H. and Magnusson, C. Energy redistribution during CO 2 laser cladding. J. L aser A pplic., 2002, 14(2), 78–82. Noecker II, F. F. and DuPont, J. N. F unctionally graded copper–steel using LEN STM process. In Proceedings of the M inerals, M etals and M aterials Society (TM S) F all M eeting, 2002, pp. 139–147. American Society of M echanical Engineers (ASM E) A SM S peciality H andbook— Stainless S teels, 1994, p. 10 (ASM International, M etals Park, Ohio). Diniz Neto, O. O. and Vilar, R. Physical–computational model to describe the interaction between a laser beam and a powder jet in laser surface processing. J. L aser A pplic., 2002, 14(1), 46–51. Pinkerton, A. J. and Li, L. R apid prototyping using direct laser deposition—the effect of powder atomization type and owrate. Proc. Instn M ech. Engrs, Part B: J. Engineering M anufacture, 2003, 217(B6), 741–752. Lin, J. and Steen, W. M. Powder ow and catchment during coaxial laser cladding. Proc. S oc. Photo-opt. Instrum. Engrs ( SPIE) , 1997, 3097, 517–528. Picasso, M., Marsden, C. F., Wagniere, J.-D., Frenk, A. and Rappaz, M. Simple but realistic model for laser cladding. M etallurgical Trans. B ( Process M etallurgy), 1994, 25(2), 281–291. Lin, J. Numerical simulation of the focused powder streams in coaxial laser cladding. J. M ater. Processing T echnol., 2000, 105(1), 17–23. Pinkerton, A. J. and Li, L. A veri ed model of the axial powder stream concentration from a coaxial laser cladding nozzle. In Proceedings of International Congress on A pplications of L asers and Electro-optics (ICA L EO’02), Scottsdale, Arizona, 2002, U19SA CD . Pinkerton, A. J. and Li, L. M odelling powder concentration distribution from a coaxial deposition nozzle for laserbased rapid tooling. T rans. AS M E, J. M fg S ci. Engng, 2004, 126(1), 34–42. Li, W.-B., Engstrom, H., Powell, J., Tan, Z. and Magnusson, C. Redistribution of the beam power in laser cladding by powder injection. L asers in Engng, 1996, 5(3), 175–183.
C22003 # IM echE 2004
541
26 Beuth, J. and Klingbeil, N. The role of process variables in laser-based direct metal solid freeform fabrication. J. M etals (JOM ), 2001, 53(9), 36–39. 27 Bornefeld, H. Temperature measurement in fusion welding (in G erman). T echnische Z entralblatt fur Praktische M etallberbeitung, 1933, 43, 14–18. 28 Thompson, M. E. and Szekely, J. Transient behavior of weldpools with a deformed free surface. Int. J. Heat and M ass T ransfer, 1989, 32(6), 1007–1019. 29 Lei, Y. P., Murakawa, H., Shi, Y. W. and Li, X. Y. N umerical analysis of the competitive in uence of M arangoni ow and evaporation on heat surface temperature and molten pool shape in laser surface remelting. Comput. M ater. S ci., 2001, 21(3), 276–290. 30 Jaeger, J. C. M oving sources of heat and the temperature at sliding contacts. Proc. R . S oc. N SW , 1942, 76, 203– 224. 31 Carslow, H. S. and Jaeger, J. C. Conduction of H eat in Solids, 2nd edition, 1959 (Oxford U niversity Press, Oxford). 32 Tian, T. and Kennedy Jr, F. E. M aximum and average ash temperatures in sliding contacts. T rans. AS M E, J. T ribology, 1994, 116(1), 167–174. 33 Cline, H. E. and Anthony, T. R. H eat treating and melting material with a scanning laser or electron beam. J. A ppl. Physics, 1977, 48(9), 3895–3900. 34 Rosenthal, D. The theory of moving sources of heat and its application to metal treatments. T rans. A S M E, 1946, 68(11), 849–866. 35 McLean, M. A., Shannon, G. J. and Steen, W. M. M ouldless casting by laser. Proc. Soc. Photo-opt. Instrum. Engrs ( S PIE) , 1997, 3102, 131–141. 36 Dausinger, F. and Shen, J. Energy coupling ef ciency in laser surface treatment. Iron and S teel Inst. Japan (IS IJ) Int., 1993, 33(9), 925–933. 37 Steen, W. M., Weerasinghe, V. M. and Monson, P. Some aspects of the formation of laser clad tracks. Proc. S PIE, 1986, 650, 226–234. 38 Eager, T. W. and Tsai, N. S. Temperature elds produced by travelling distributed heat sources. W eld. J., 1983, 62(12), 346s–355s. 39 Doumanidis, C. and Kwak, Y.-M. Geometry modeling and control by infrared and laser sensing in thermal manufacturing with material deposition. T rans. A S M E, J. M fg S ci. Engng, 2001, 123, 45–52. 40 Meriaudeau, F., Truchetet, F., Grevey, D. and Vannes, A. B. Laser cladding process and image processing. L asers in Engng, 1997, 6, 161–187. 41 Bamberger, M. and Geler, M. Energy coupling between CO 2-laser irradiation and metallic substrates. L asers in Engng, 1997, 6(3), 213–234.
Proc. Instn M ech. Engrs Vol. 218 Part C: J. M echanical Engineering Science
