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Modelling of energy attenuation due to powder flow-laser beam interaction during laser cladding process
Journal of Materials Processing Technology 212 (2012) 516–522
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Modelling of energy attenuation due to powder flow-laser beam interaction during laser cladding process I. Tabernero ∗ , A. Lamikiz, S. Martínez, E. Ukar, L.N. López de Lacalle Department of Mechanical Engineering, University of the Basque Country, ETSII, c/Alameda de Urquijo s/n, 48013 Bilbao, Spain
a r t i c l e
i n f o
Article history: Received 5 May 2011 Received in revised form 20 October 2011 Accepted 22 October 2011 Available online 25 October 2011 Keywords: Laser cladding Energy attenuation Modelling
a b s t r a c t Laser cladding is becoming an emergent process with high interest for industries dedicated to high added value parts production. Laser cladding introduces new manufacturing concepts such as direct manufacturing of parts, avoiding in this way the excessive waste of material in the form of chips, inherent to traditional machining processes. This process is based on the use of a source of high energy density, such as laser beams, to generate a melt pool on a substrate where a filler material is injected. Thus, when studying the process it is necessary to know the effective energy that reaches the base material. This energy does not correspond to the one provided by the laser beam, considering that the laser beam has to go through a cloud of injected powder before it reaches the substrate. In this region there is an interaction between the laser beam and the filler material in which a significant amount of energy is absorbed by the powder. As a result, attenuation values can reach up to high percentages of the initial energy value. This paper presents a model based on the shadow created by powder particles on the substrate, with capabilities of estimating the attenuation suffered by the beam and characterizing the density of energy that reaches the surface of the substrate. The model starts from the initial energy density of the laser and the powder concentrations obtained from a CFD model, which has been experimentally validated. In addition, three different approaches have been introduced for the model solution. Initially a constant powder particle size and a perfectly cylindrical laser beam are considered. Subsequently, an experimentally measured particle size distribution and the divergence of the beam are introduced in order to accurately adjust the model and the real process. The attenuation model has been experimentally adjusted and validated. The error average is below 10% of measured values. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The laser cladding is generating a great interest at both industrial and research levels due to the great advantages it introduces. Firstly, the possibility of accomplishing high quality clads with a minimal heat affected zone and minimum thermal distortions of treated zones makes it an alternative to traditional reparation processes such as TIG welding (Sexton et al., 2002), which is generally manually applied and requires a more complex finish machining to achieve the required accuracy. Therefore, when using the laser technology as an energy source, it is possible to generate a highly localized melt pool on a substrate where external filler material is injected, practically without damaging the surrounding areas of the material. In this way, clads with high metallurgical quality and high strength bonding with the substrate are obtained. If the clads are overlapped, a homogeneous layer is achieved. The overlapping layers allow manufacturing geometries layer-by-layer
∗ Corresponding author. Tel.: +34 946017347; fax: +34 946014215. E-mail address: [email protected] (I. Tabernero). 0924-0136/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2011.10.019
directly from a CAD file. Therefore, this technique can be used for direct manufacturing operations or repairing zones of high added value parts. Regarding the filler material, this can be injected into the melt pool in the form of powder or wire (Toyserkani et al., 2005). In general, additive processes using material in the wire form have higher addition rates but only allow the generation of tracks in the direction of the wire feeding, which greatly reduces the versatility of the process. In addition, it is difficult to adjust the exact position of the wire and the quality of the clads are usually lower than the ones obtained by filler material in powder form. Current efforts are focused on the application of laser cladding using powder as it achieves high quality material addition and it is much more versatile than wire. Thus, the most common configuration for carrying out laser cladding operations is the powder injection using coaxial nozzles. Coaxial nozzles inject powder material from all directions surrounding the melt-pool, so regardless of the direction, optimum injection of material is achieved. Industrial applications of the laser cladding process cover different fields: surfaces coating with a material of different nature of the substrate (Navas et al., 2005), of high added value parts reparation
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(Gao et al., 2008), or even in direct manufacturing of complex parts (Jeng and Lin, 2001). In any case, the industrial introduction of this process is relatively slow because it requires a previous parameter fitting which in general means long and costly experimental work (Chryssolouris et al., 2002; Zhang et al., 2007). Although design of experiments techniques (DoE) minimize this work, the effort required to adjust the parameters of this process in the industry is still important. Thus, the development of models that simulate the laser cladding process are becoming a tool of great interest for significantly maximizing the reduction in number of previous tests and also reducing the necessary adjustments prior to applying the process to the real part. The main problem with this solution is the great complexity of the phenomena that occur during the laser cladding process, so the laser cladding modelling is often dealt studying the different phases separately, i.e., powder flow from the nozzle (Wen et al., 2009), interaction with the laser beam (Liu and Lin, 2003), generation of the melt pool (Pinkerton and Li, 2004) and the generation of the clad (Liu, 2007) are studied separately. Regarding the interaction between beam and particle flow, this is of great importance to the process because at this stage there is a substantial reduction of beam energy, reaching values of 35% of beam power for lateral laser cladding (Partes et al., 2005). This absorbed energy cannot be considered as a loss because it is used for the subsequent fusion of the particles, but its study is necessary to know what is the real power that reaches the surface, and therefore, the energy that generates the molten pool on the base material. The phenomenon of energy attenuation during the laser cladding process was first studied by Vetter et al. (1993), who developed an experimental setup for attenuation measuring, and the principal causes of attenuation were stated: beam scattering and energy absorption by the particles. In addition, it was detected that the attenuation suffered by the beam increases below the consolidation plane, which is the plane where the powder flow starts to be concentrated resulting in a Gaussian mass distribution. This plane has also been detected in previous works focused on the particle flow in coaxial nozzles (Tabernero et al., 2010). Thus, the first models of attenuation developed were based on the shadow generated by the powder particles on the laser beam (Picasso and Rappaz, 1994), these models proposed that the beam attenuation was proportional to the area occupied by the powder particles in each plane. Consequently, the typical simplifications of attenuation models based on shadows began to be considered, such as ignore the effect of beam divergence or consider constant particle size (Fu et al., 2002). Moreover, other models are based on the phenomenon of light scattering, in which the attenuation was calculated using the Mie theory (Huang et al., 2005). In general, these models are much more specific and are only valid for a narrow range of particle size-laser wavelength ratios. Thus, the most common attenuation models are based on shadow effect in which the area occupied by the particles is estimated using the powder concentration, either analytically (Liu et al., 2005) or adjusted by optical methods (Pinkerton, 2007). In this paper a model based on shadows is developed from a classical approach that considers an average of constant particle size and a cylindrical beam that does not diverge. The model has been adapted incorporating other aspects to be considered such as variable particle size (following the measured particle size distribution) or beam divergence. As these effects are incorporated, its influence on the results of the attenuation model can be observed and furthermore its increase in the approximation degree between model and experimental values. The model has been experimentally validated using two different materials: a thermal resistant nickel based alloy Inconel© 718 and AISI D2 tool steel. Three ranges of particle size have been also tested, satisfactorily adjusting the estimated results with those experimentally measured in the different cases.
517
2. Attenuation model development This section describes the bases of the proposed laser attenuation model. This model is based on a typical shadow model, which incorporates some general aspects allowing its use in industrial laser cladding operations. It is therefore a semi-empirical model that requires a previous characterization of the interaction between the laser and the material, for subsequently being generalized to a range of parameter combination of the process. The proposed model is based on the following assumptions: 1. The attenuation is proportional to the shadow generated by the particles of powder, i.e., its projected area at the plane of study. The shadow between particles is also neglected since it can be considered that the powder concentration is much lower than the gas volume. 2. Attenuation does not depend on the laser power. This assumption is only valid for low powers because if the power increases, particles could be partially evaporated varying their diameter. 3. Particles are considered spherical and their projection on the plane is approximated to a circle. The powder material used in laser cladding operations is obtained by gas atomization. Observing these particles under a microscope shows a quasi-spherical shape, so the error introduced by this assumption is minimal. 4. Previously developed and validated CFD model provides powder concentration in the different planes. Full description of this model can be found in Tabernero et al. (2010). 5. Material properties are considered to be independent of temperature maintaining constant density and particle size. 6. The attenuation generated by plasma formation or the scattering phenomenon is considered by introducing an experimental ˛ factor that depends on the material. 7. It is considered that the attenuation is produced after a plane in which the distribution profile of concentration is consolidated and takes a Gaussian form. This hypothesis has been previously validated by other works that have studied the phenomenon of attenuation suffered by the beam due to its interaction with the powder flow (Vetter et al., 1993). Taking into account these assumptions, it is proposed that the attenuation is proportional to the ratio between the projected area of the particles and the interaction area. In addition, the attenuation is also proportional to the interaction time between the particles and the laser beam (Eq. (1)):
Patt = Katt · Pi ,
where Katt = f
˛,
Sparticles Stotal
, tint
(1)
where Katt is the attenuation factor, dimensionless with values between 0 and 1, Sparticles is the area occupied by the particles per time unit [m2 /s], Stotal is the total area occupied by the laser beam [m2 ] and tint is the interaction time between beam and particle flow [s]. The material attenuation factor ˛ is dimensionless and it is obtained experimentally. This factor includes most of the physical phenomena that have been neglected in the model such as the scattering effect or the generation of plasma. The area occupied by the particles can be considered equal to the number of particles multiplied by its area (Eq. (2)): Sparticles = Nparticles · Aparticle
(2)
where Aparticles is the projection of a particle in the plane [m2 ] and Nparticles is the number of particles per unit time [s−1 ]. The number of particles is calculated as the concentration of particles multiplied by the area occupied and divided by the mass
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Fig. 1. Discretization of the material flow for a powder mass flow of 6.2 g/min.
of one particle. The mass of a particle can be estimated by its volume multiplied by density (Eq. (3)): [C] · Stotal [C] · Stotal = mparticle Vparticle ·
Nparticles =
(3) 3. Model resolution
where [C] is the mass flow of powder particles [kg/(m2 s)], mparticle is the mass of a particle [kg], Vparticle is the volume of a particle [m3 ] and is the density of the material used [kg/m3 ]. The interaction time between the beam and the particles can be considered as the thickness of the plane divided by the speed of the particles along the axis of the nozzle (Eq. (4)): tint =
z
vz
(4)
particles
where z is the layer thickness [m] and vz particles is the speed component in the nozzle axis [m/s]. Developing the attenuation factor expression leads to an expression similar to that obtained by Pinkerton (2007). Katt = ˛ ·
[C] · Aparticle Vparticle ·
·
z
vz
particle
=˛·
z 3 · [C] · (5) 4 · Rparticle · vz particle
Finally, since the flux model can provide both the concentration and speed of the particles they are all grouped in the term [C]F , directly obtained from the CFD model. Thus, the expression of attenuation factor to be used in the model (Eq. (6)): Katt = ˛ ·
3 · [C]F · z 4 · Rparticle ·
(6)
Therefore, the equation to be solved by the model is obtained from Eqs. (1) and (6):
I(x, y, z + z) = I(x, y, z) ·
3 · ˛(material) · CF (x, y, z) 1− · z 4 · Rp ·
(7) where I(x,y,z) is the power density [W/m2 ] in z plane and I(x,y,z + z) the intensity in the plane at z + z. Finally, this work has been carried out using a high power laser diode, which has a top-hat power distribution, defined by the following analytical expression (Eq. (8)): I(x, y, z) =
P 4lx · ly
×
erf
erf
l − 2x x √ 2 2a
ly − 2y √ 2 2a
+ erf
+ erf
Obviously, other types of laser can be modelled introducing different energy densities shapes, such as Gaussian or multimode energy densities.
Once the expression of the attenuation model is obtained it is solved by using an algorithm implemented in Matlab© 6.8. In order to do this, the powder flow is analyzed in different planes perpendicular to the nozzle axis. Laser cladding process results are optimum if the laser beam is focused onto the substrate; therefore, the discretization of the powder flow should be performed from the substrate surface up to the consolidation plane of powder flow. Thus, for a conventional coaxial nozzle like the one used in this work, the discretization should be performed from the substrate up to about 5 mm in height. Each of these planes is discretized with a mesh of 0.1 mm × 0.1 mm, in order to obtain the necessary resolution (Fig. 1). The model resolution algorithm is shown in Fig. 2, where it can be seen that the energy of each point is calculated by multiplying the energy that reaches each plane by the attenuation factor calculated with the process parameters and the information coming from the concentration model. Thus, the algorithm allows to estimate the energy radiated to the focal plane and Eq. (9) calculates the attenuation of the laser beam due to the interaction with the flow of powder: Att =
P − P att 0 P0
Once the model and the resolution algorithm are raised, three alternatives have been developed taking into account different aspects of the process: 1. Model 1 (M1 ): Particle size is considered constant using an average diameter, moreover, the beam divergence has been neglected, i.e., a cylindrical beam is considered.
l + 2x x √ 2 2a
ly + 2y √ 2 2a
(9)
(8) Fig. 2. Resolution algorithm for the attenuation model.
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519
Fig. 3. Sketch of the experimental setup.
2. Model 2 (M2 ): Variable particle size is introduced using an experimentally adjusted Rosin–Rammler distribution (Tabernero et al., 2010). In this case the attenuation factor is considered as a summatory of attenuation factors. These are obtained by Eq. (6) for each diameter and multiplied by the corresponding weight within the range of particle size (Eq. (10)):
Katt = ˛ ·
n
w i
i=0
100
·
3 · [C]F · z 4 · Rparticlei ·
4. Experimental setup The attenuation measurement is carried out using a similar setup to that presented by Picasso and Rappaz (1994). Additionally, an aluminum protective plate has been added. This plate determines accurately the plane where the attenuation measuring is being carried out (Fig. 3). The experimental setup consists of the following elements (Fig. 4):
(10)
3. Model 3 (M3 ): Besides the variable particle size, the beam divergence is introduced by its analytic expression. So, attenuated power is calculated for each plane and distributed on the next one by Eq. (8), in order to obtain these values, lx and ly are reduced depending on the angle of beam divergence. The beam divergence value is usually provided by the manufacturer or it is possible to be obtained experimentally by laser calibration.
1. Protection plate: It is an aluminum disk located just above the power meter and allows to set the measuring plane. The protection plate has a central hole through which the powder flow crosses. It is a 10 mm diameter hole, allowing a minimum loss of powder. 2. Main cross-jet: This element deflects the powder flow in order to stop the interaction with the beam. So, it is possible to measure the energy attenuation on the measuring plane, fixed by the protection plate. The cross-jet injects compressed air at 6 bar.
Fig. 4. Experimental setup for the attenuation measuring.
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the real value of the attenuation suffered by the beam for each mass flow using Eq. (9).
5. Results
Fig. 5. Graph of power evolution in an attenuation measurement.
3. Secondary cross-jet: The air flow generated by this cross-jet avoids that surrounding powder will be deposited on the power meter. 4. Power meter Coherent PM3K-100: It is a thermopile type sensor that measures instantaneous power radiated by the laser with a measuring uncertainty of ±5% (±1% according to the calibration certificate). 5. Coax-8 coaxial nozzle developed by Alotec and IWS Fraunhoffer center. It is an industrial coaxial nozzle responsible of creating the powder flow. 6. Protective window: It is an optically neutral glass that is transparent to the wavelength of the laser. Protective windows practically do not absorb energy from the laser beam, but protects the power meter from powder projections. Therefore, this setup allows energy attenuation measurements due to the interaction between the beam and the injected powder, without considering other factors. Fig. 5 shows the evolution of the laser power. First, the power is stabilized at the nominal power (Pi ), then the powder material is injected and the measured power drops until posterior stabilization. In this way, it is possible to calculate
The adjustment and model validation tests have been performed on two different materials: a tool steel usually used for die and moulds (AISI D2), and a nickel-based superalloy mainly used in the aeronautical sector (Inconel© 718). For the aeronautical material, two particle diameter distributions have been included in order to verify the validity of the model for different particle sizes (Table 1). Before adjusting and validating the model, some tests have been carried out using different values of the laser power in order to verify the assumption No.2. It can be observed in Table 2 that the measured attenuation for the studied powers possesses a low standard deviation in most cases. Thus, initially a series of tests have been carried out in order to characterize the ˛ parameter for each material and for each version of the model (Table 3). All tests were carried out at constant power (1000 W) and repeated three times in order to avoid measurement errors. In all cases the variation between measurements was less than 1%. It can be observed from the results how the material attenuation factor (˛) is dependent, as expected, on the type of material and on its range of particle size. In addition, these results allow the study of the relevance of the different improvements added to the model. It can be observed how for the AISI D2, introducing a variable particle size significantly changes the value of material attenuation factor, whereas for the Inconel© 718 this value is practically constant. Therefore, it can be concluded that adjustment parameter for Inconel© 718 depends more on the nature of the material than the size of particle or the beams divergence. Once the model has been adjusted for the studied materials, validation tests have been carried out for different mass flow rates in order to compare the attenuation estimated by the model with the experimentally measured values (Table 4). It can be observed that the average error does not exceed 10% of the measured values and the maximum error reaches a 17% value. Therefore, it can be concluded that the presented model allows an estimation of the
Table 1 Composition and particle size of the used materials.
AISI D2 Inconel© 718
Al
C
Cr
Fe
Mn
Mo
Ni
Nb
Si
Ti
V
Particle size
– 0.2–0.8
1.55 0.08
11.8 17–21
Bal. 17
0.4 0.35
0.8 2.8–3.3
– 50–55
– 4.75–5.5
0.3 0.35
– 0.65–1.15
0.8 –
−150 + 45 m −110 + 40 m −160 + 80 m
Table 2 Values of measuring deviation for different powers. P (W)
Att (%)
Att (%)
150.2 300.0 460.2 615.0
36.5 75.0 115.7 155.8
19.6 20.0 20.1 20.2
20.0
0.29
188.9 390.0 590.9 778.5
145.4 300.0 457.0 599.9
43.5 90.0 133.9 178.6
23.0 23.1 22.7 22.9
22.9
0.19
189.8 383.0 583.0 783.0
156.6 316.0 480.0 639.0
33.2 67.0 103.0 144.0
17.5 17.5 17.7 18.4
17.8
0.43
Power (W) Theoretical
Initial
Attenuated
AISI D2 (−150 + 45 m)
200 400 600 800
186.7 375.0 575.9 770.8
Inco 718 (−110 + 40 m)
200 400 600 800
Inco 718 (−160 + 80 m)
200 400 600 800
I. Tabernero et al. / Journal of Materials Processing Technology 212 (2012) 516–522
521
Table 3 Characterization tests of ˛ parameter. AISI D2 (−150 + 45 m)
Flow (g/min)
Attenuation (%)
Inco 718 (−110 + 40 m) ˛
Model
Real
M1 : Constant powder size
3.5 4.5 5.5 6.5 7.5
0.96 1.50 1.72 2.13 2.09
6.09 8.13 10.26 11.65 13.56
6.3 5.4 5.9 5.5 6.5
M2 : Variable powder size
3.5 4.5 5.5 6.5 7.5
0.79 1.23 1.41 1.75 1.72
6.09 8.13 10.26 11.65 13.56
7.7 6.6 7.3 6.7 7.9
M3 : Variable size and beam divergence
3.5 4.5 5.5 6.5 7.5
0.77 1.20 1.38 1.70 1.67
6.09 8.13 10.26 11.65 13.56
7.9 6.8 7.4 6.9 8.1
˛ ¯
Inco 718 (−160 + 80 m) ˛
Attenuation (%) Model
Real
5.9
1.54 1.77 2.35 2.67 3.02
6.15 7.61 9.38 10.55 11.64
4.0 4.3 4.0 4.0 3.9
7.2
1.50 1.73 2.29 2.61 2.95
6.15 7.61 9.38 10.55 11.64
4.1 4.4 4.1 4.0 4.0
7.4
1.44 1.68 2.21 2.52 2.84
6.15 7.61 9.38 10.55 11.64
4.3 4.5 4.3 4.2 4.1
˛ ¯
Attenuation (%)
˛
˛ ¯
Model
Real
4.0
0.43 0.57 0.70 0.94 0.94
4.4 6.32 7.07 7.81 9.33
10.2 11.1 10.1 8.3 9.9
9.9
4.1
0.43 0.58 0.70 0.95 0.95
4.4 6.32 7.07 7.81 9.33
10.2 10.9 10.1 8.2 9.8
9.9
4.3
0.42 0.56 0.68 0.92 0.96
4.4 6.32 7.07 7.81 9.33
10.5 11.3 10.4 8.5 9.7
10.1
Table 4 Validation tests of the model. Flow (g/min)
AISI D2 (−150 + 45 m) Attenuation (%)
|err| (%)
Model
Real
M1
4 5 6 7 8
6.72 8.21 8.74 10.83 11.82
6.79 8.71 10.2 12.56 13.39
1.0 5.7 14.3 13.8 11.7
M2
4 5 6 7 8
6.71 8.22 8.75 10.82 12.83
6.79 8.71 10.2 12.56 13.39
1.2 5.6 14.2 13.9 4.2
M3
4 5 6 7 8
6.74 8.09 8.68 11.02 12.58
6.79 8.71 10.2 12.56 13.39
0.7 7.1 14.9 12.3 6.0
Inco 718 (−110 + 40 m) |err| (%)
Attenuation (%)
|err| (%)
Model
Real
9.30
6.96 11.18 9.36 12.71 13.58
6.5 9.67 11.24 12.22 13.74
7.1 15.6 16.7 4.0 1.2
8.81
6.96 8.17 9.37 12.73 13.60
6.5 9.67 11.24 12.22 13.74
7.1 15.5 16.6 4.2 1.0
8.21
6.71 8.50 12.75 13.21 13.40
6.5 9.67 11.24 12.22 13.74
3.2 12.1 13.4 8.1 2.5
Inco 718 (−160 + 80 m) |err| (%)
Attenuation (%)
|err| (%)
|err| (%)
Model
Real
8.92
4.70 6.54 6.60 8.73 11.47
4.92 6.22 7.19 9.84 10.3
4.5 5.1 8.2 11.3 11.4
8.05
8.88
4.69 5.88 6.58 8.71 11.45
4.92 6.22 7.19 9.04 10.3
4.7 5.5 8.5 3.7 11.2
6.69
7.87
4.64 5.83 6.52 9.43 11.37
4.92 6.22 7.19 9.04 10.3
5.7 6.3 9.3 4.3 10.4
7.20
Fig. 6. Images of the interaction zone obtained with a thermographic camera for a 6.3 g/min mass flow: (a) 200 W and (b) 400 W.
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attenuation suffered by the beam due to its interaction with the particle flow. Finally, it can be observed both in the adjustment and validation tests how a smaller particle size produces higher attenuation. This fact has been predicted by the model (Eq. (6)), and it can be verified by the images provided by a IR camera. Fig. 6 shows how, for a fixed mass flow, if a smaller average particle size is used, the radiated energy by the heated powder flow is higher, i.e., the powder flow absorbs more energy from the laser beam and the attenuation generated is higher. 6. Conclusions This paper presents a model that estimates the attenuation suffered by the laser beam due to the interaction with the powder flow during the laser cladding process. The model is based on the shadow generated by the powder particles on the beam and uses the concentration obtained by a CFD model. Three versions of the model have been developed: the first one uses a constant particle size and the beam divergence is neglected. In the second version a variable particle size is introduced using an experimentally measured Rosin–Rammler distribution. Finally, the beam divergence has been introduced in order to obtain a more realistic model. The model has been adjusted and validated for two different materials and two ranges of particle size. The estimate average error in respect to the measured attenuation does not exceed 10%. The model also estimates a higher value of attenuation for a smaller particle size, a fact that has been shown both experimentally and by using images provided by an IR camera. Therefore, it can be concluded that the model presented could be considered a useful tool for estimating the attenuation suffered by the beam due to the interaction with the flow of powder material, i.e., for estimating the real energy that radiates the substrate surface and generates the melt pool. Acknowledgement The authors wish to thank the Spanish Ministry of Science and Innovation for financial support provided through the SURFACER project (Ref: DPI2010-20317-C02-01).
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Contents lists available at SciVerse ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Modelling of energy attenuation due to powder flow-laser beam interaction during laser cladding process I. Tabernero ∗ , A. Lamikiz, S. Martínez, E. Ukar, L.N. López de Lacalle Department of Mechanical Engineering, University of the Basque Country, ETSII, c/Alameda de Urquijo s/n, 48013 Bilbao, Spain
a r t i c l e
i n f o
Article history: Received 5 May 2011 Received in revised form 20 October 2011 Accepted 22 October 2011 Available online 25 October 2011 Keywords: Laser cladding Energy attenuation Modelling
a b s t r a c t Laser cladding is becoming an emergent process with high interest for industries dedicated to high added value parts production. Laser cladding introduces new manufacturing concepts such as direct manufacturing of parts, avoiding in this way the excessive waste of material in the form of chips, inherent to traditional machining processes. This process is based on the use of a source of high energy density, such as laser beams, to generate a melt pool on a substrate where a filler material is injected. Thus, when studying the process it is necessary to know the effective energy that reaches the base material. This energy does not correspond to the one provided by the laser beam, considering that the laser beam has to go through a cloud of injected powder before it reaches the substrate. In this region there is an interaction between the laser beam and the filler material in which a significant amount of energy is absorbed by the powder. As a result, attenuation values can reach up to high percentages of the initial energy value. This paper presents a model based on the shadow created by powder particles on the substrate, with capabilities of estimating the attenuation suffered by the beam and characterizing the density of energy that reaches the surface of the substrate. The model starts from the initial energy density of the laser and the powder concentrations obtained from a CFD model, which has been experimentally validated. In addition, three different approaches have been introduced for the model solution. Initially a constant powder particle size and a perfectly cylindrical laser beam are considered. Subsequently, an experimentally measured particle size distribution and the divergence of the beam are introduced in order to accurately adjust the model and the real process. The attenuation model has been experimentally adjusted and validated. The error average is below 10% of measured values. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The laser cladding is generating a great interest at both industrial and research levels due to the great advantages it introduces. Firstly, the possibility of accomplishing high quality clads with a minimal heat affected zone and minimum thermal distortions of treated zones makes it an alternative to traditional reparation processes such as TIG welding (Sexton et al., 2002), which is generally manually applied and requires a more complex finish machining to achieve the required accuracy. Therefore, when using the laser technology as an energy source, it is possible to generate a highly localized melt pool on a substrate where external filler material is injected, practically without damaging the surrounding areas of the material. In this way, clads with high metallurgical quality and high strength bonding with the substrate are obtained. If the clads are overlapped, a homogeneous layer is achieved. The overlapping layers allow manufacturing geometries layer-by-layer
∗ Corresponding author. Tel.: +34 946017347; fax: +34 946014215. E-mail address: [email protected] (I. Tabernero). 0924-0136/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2011.10.019
directly from a CAD file. Therefore, this technique can be used for direct manufacturing operations or repairing zones of high added value parts. Regarding the filler material, this can be injected into the melt pool in the form of powder or wire (Toyserkani et al., 2005). In general, additive processes using material in the wire form have higher addition rates but only allow the generation of tracks in the direction of the wire feeding, which greatly reduces the versatility of the process. In addition, it is difficult to adjust the exact position of the wire and the quality of the clads are usually lower than the ones obtained by filler material in powder form. Current efforts are focused on the application of laser cladding using powder as it achieves high quality material addition and it is much more versatile than wire. Thus, the most common configuration for carrying out laser cladding operations is the powder injection using coaxial nozzles. Coaxial nozzles inject powder material from all directions surrounding the melt-pool, so regardless of the direction, optimum injection of material is achieved. Industrial applications of the laser cladding process cover different fields: surfaces coating with a material of different nature of the substrate (Navas et al., 2005), of high added value parts reparation
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(Gao et al., 2008), or even in direct manufacturing of complex parts (Jeng and Lin, 2001). In any case, the industrial introduction of this process is relatively slow because it requires a previous parameter fitting which in general means long and costly experimental work (Chryssolouris et al., 2002; Zhang et al., 2007). Although design of experiments techniques (DoE) minimize this work, the effort required to adjust the parameters of this process in the industry is still important. Thus, the development of models that simulate the laser cladding process are becoming a tool of great interest for significantly maximizing the reduction in number of previous tests and also reducing the necessary adjustments prior to applying the process to the real part. The main problem with this solution is the great complexity of the phenomena that occur during the laser cladding process, so the laser cladding modelling is often dealt studying the different phases separately, i.e., powder flow from the nozzle (Wen et al., 2009), interaction with the laser beam (Liu and Lin, 2003), generation of the melt pool (Pinkerton and Li, 2004) and the generation of the clad (Liu, 2007) are studied separately. Regarding the interaction between beam and particle flow, this is of great importance to the process because at this stage there is a substantial reduction of beam energy, reaching values of 35% of beam power for lateral laser cladding (Partes et al., 2005). This absorbed energy cannot be considered as a loss because it is used for the subsequent fusion of the particles, but its study is necessary to know what is the real power that reaches the surface, and therefore, the energy that generates the molten pool on the base material. The phenomenon of energy attenuation during the laser cladding process was first studied by Vetter et al. (1993), who developed an experimental setup for attenuation measuring, and the principal causes of attenuation were stated: beam scattering and energy absorption by the particles. In addition, it was detected that the attenuation suffered by the beam increases below the consolidation plane, which is the plane where the powder flow starts to be concentrated resulting in a Gaussian mass distribution. This plane has also been detected in previous works focused on the particle flow in coaxial nozzles (Tabernero et al., 2010). Thus, the first models of attenuation developed were based on the shadow generated by the powder particles on the laser beam (Picasso and Rappaz, 1994), these models proposed that the beam attenuation was proportional to the area occupied by the powder particles in each plane. Consequently, the typical simplifications of attenuation models based on shadows began to be considered, such as ignore the effect of beam divergence or consider constant particle size (Fu et al., 2002). Moreover, other models are based on the phenomenon of light scattering, in which the attenuation was calculated using the Mie theory (Huang et al., 2005). In general, these models are much more specific and are only valid for a narrow range of particle size-laser wavelength ratios. Thus, the most common attenuation models are based on shadow effect in which the area occupied by the particles is estimated using the powder concentration, either analytically (Liu et al., 2005) or adjusted by optical methods (Pinkerton, 2007). In this paper a model based on shadows is developed from a classical approach that considers an average of constant particle size and a cylindrical beam that does not diverge. The model has been adapted incorporating other aspects to be considered such as variable particle size (following the measured particle size distribution) or beam divergence. As these effects are incorporated, its influence on the results of the attenuation model can be observed and furthermore its increase in the approximation degree between model and experimental values. The model has been experimentally validated using two different materials: a thermal resistant nickel based alloy Inconel© 718 and AISI D2 tool steel. Three ranges of particle size have been also tested, satisfactorily adjusting the estimated results with those experimentally measured in the different cases.
517
2. Attenuation model development This section describes the bases of the proposed laser attenuation model. This model is based on a typical shadow model, which incorporates some general aspects allowing its use in industrial laser cladding operations. It is therefore a semi-empirical model that requires a previous characterization of the interaction between the laser and the material, for subsequently being generalized to a range of parameter combination of the process. The proposed model is based on the following assumptions: 1. The attenuation is proportional to the shadow generated by the particles of powder, i.e., its projected area at the plane of study. The shadow between particles is also neglected since it can be considered that the powder concentration is much lower than the gas volume. 2. Attenuation does not depend on the laser power. This assumption is only valid for low powers because if the power increases, particles could be partially evaporated varying their diameter. 3. Particles are considered spherical and their projection on the plane is approximated to a circle. The powder material used in laser cladding operations is obtained by gas atomization. Observing these particles under a microscope shows a quasi-spherical shape, so the error introduced by this assumption is minimal. 4. Previously developed and validated CFD model provides powder concentration in the different planes. Full description of this model can be found in Tabernero et al. (2010). 5. Material properties are considered to be independent of temperature maintaining constant density and particle size. 6. The attenuation generated by plasma formation or the scattering phenomenon is considered by introducing an experimental ˛ factor that depends on the material. 7. It is considered that the attenuation is produced after a plane in which the distribution profile of concentration is consolidated and takes a Gaussian form. This hypothesis has been previously validated by other works that have studied the phenomenon of attenuation suffered by the beam due to its interaction with the powder flow (Vetter et al., 1993). Taking into account these assumptions, it is proposed that the attenuation is proportional to the ratio between the projected area of the particles and the interaction area. In addition, the attenuation is also proportional to the interaction time between the particles and the laser beam (Eq. (1)):
Patt = Katt · Pi ,
where Katt = f
˛,
Sparticles Stotal
, tint
(1)
where Katt is the attenuation factor, dimensionless with values between 0 and 1, Sparticles is the area occupied by the particles per time unit [m2 /s], Stotal is the total area occupied by the laser beam [m2 ] and tint is the interaction time between beam and particle flow [s]. The material attenuation factor ˛ is dimensionless and it is obtained experimentally. This factor includes most of the physical phenomena that have been neglected in the model such as the scattering effect or the generation of plasma. The area occupied by the particles can be considered equal to the number of particles multiplied by its area (Eq. (2)): Sparticles = Nparticles · Aparticle
(2)
where Aparticles is the projection of a particle in the plane [m2 ] and Nparticles is the number of particles per unit time [s−1 ]. The number of particles is calculated as the concentration of particles multiplied by the area occupied and divided by the mass
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Fig. 1. Discretization of the material flow for a powder mass flow of 6.2 g/min.
of one particle. The mass of a particle can be estimated by its volume multiplied by density (Eq. (3)): [C] · Stotal [C] · Stotal = mparticle Vparticle ·
Nparticles =
(3) 3. Model resolution
where [C] is the mass flow of powder particles [kg/(m2 s)], mparticle is the mass of a particle [kg], Vparticle is the volume of a particle [m3 ] and is the density of the material used [kg/m3 ]. The interaction time between the beam and the particles can be considered as the thickness of the plane divided by the speed of the particles along the axis of the nozzle (Eq. (4)): tint =
z
vz
(4)
particles
where z is the layer thickness [m] and vz particles is the speed component in the nozzle axis [m/s]. Developing the attenuation factor expression leads to an expression similar to that obtained by Pinkerton (2007). Katt = ˛ ·
[C] · Aparticle Vparticle ·
·
z
vz
particle
=˛·
z 3 · [C] · (5) 4 · Rparticle · vz particle
Finally, since the flux model can provide both the concentration and speed of the particles they are all grouped in the term [C]F , directly obtained from the CFD model. Thus, the expression of attenuation factor to be used in the model (Eq. (6)): Katt = ˛ ·
3 · [C]F · z 4 · Rparticle ·
(6)
Therefore, the equation to be solved by the model is obtained from Eqs. (1) and (6):
I(x, y, z + z) = I(x, y, z) ·
3 · ˛(material) · CF (x, y, z) 1− · z 4 · Rp ·
(7) where I(x,y,z) is the power density [W/m2 ] in z plane and I(x,y,z + z) the intensity in the plane at z + z. Finally, this work has been carried out using a high power laser diode, which has a top-hat power distribution, defined by the following analytical expression (Eq. (8)): I(x, y, z) =
P 4lx · ly
×
erf
erf
l − 2x x √ 2 2a
ly − 2y √ 2 2a
+ erf
+ erf
Obviously, other types of laser can be modelled introducing different energy densities shapes, such as Gaussian or multimode energy densities.
Once the expression of the attenuation model is obtained it is solved by using an algorithm implemented in Matlab© 6.8. In order to do this, the powder flow is analyzed in different planes perpendicular to the nozzle axis. Laser cladding process results are optimum if the laser beam is focused onto the substrate; therefore, the discretization of the powder flow should be performed from the substrate surface up to the consolidation plane of powder flow. Thus, for a conventional coaxial nozzle like the one used in this work, the discretization should be performed from the substrate up to about 5 mm in height. Each of these planes is discretized with a mesh of 0.1 mm × 0.1 mm, in order to obtain the necessary resolution (Fig. 1). The model resolution algorithm is shown in Fig. 2, where it can be seen that the energy of each point is calculated by multiplying the energy that reaches each plane by the attenuation factor calculated with the process parameters and the information coming from the concentration model. Thus, the algorithm allows to estimate the energy radiated to the focal plane and Eq. (9) calculates the attenuation of the laser beam due to the interaction with the flow of powder: Att =
P − P att 0 P0
Once the model and the resolution algorithm are raised, three alternatives have been developed taking into account different aspects of the process: 1. Model 1 (M1 ): Particle size is considered constant using an average diameter, moreover, the beam divergence has been neglected, i.e., a cylindrical beam is considered.
l + 2x x √ 2 2a
ly + 2y √ 2 2a
(9)
(8) Fig. 2. Resolution algorithm for the attenuation model.
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Fig. 3. Sketch of the experimental setup.
2. Model 2 (M2 ): Variable particle size is introduced using an experimentally adjusted Rosin–Rammler distribution (Tabernero et al., 2010). In this case the attenuation factor is considered as a summatory of attenuation factors. These are obtained by Eq. (6) for each diameter and multiplied by the corresponding weight within the range of particle size (Eq. (10)):
Katt = ˛ ·
n
w i
i=0
100
·
3 · [C]F · z 4 · Rparticlei ·
4. Experimental setup The attenuation measurement is carried out using a similar setup to that presented by Picasso and Rappaz (1994). Additionally, an aluminum protective plate has been added. This plate determines accurately the plane where the attenuation measuring is being carried out (Fig. 3). The experimental setup consists of the following elements (Fig. 4):
(10)
3. Model 3 (M3 ): Besides the variable particle size, the beam divergence is introduced by its analytic expression. So, attenuated power is calculated for each plane and distributed on the next one by Eq. (8), in order to obtain these values, lx and ly are reduced depending on the angle of beam divergence. The beam divergence value is usually provided by the manufacturer or it is possible to be obtained experimentally by laser calibration.
1. Protection plate: It is an aluminum disk located just above the power meter and allows to set the measuring plane. The protection plate has a central hole through which the powder flow crosses. It is a 10 mm diameter hole, allowing a minimum loss of powder. 2. Main cross-jet: This element deflects the powder flow in order to stop the interaction with the beam. So, it is possible to measure the energy attenuation on the measuring plane, fixed by the protection plate. The cross-jet injects compressed air at 6 bar.
Fig. 4. Experimental setup for the attenuation measuring.
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the real value of the attenuation suffered by the beam for each mass flow using Eq. (9).
5. Results
Fig. 5. Graph of power evolution in an attenuation measurement.
3. Secondary cross-jet: The air flow generated by this cross-jet avoids that surrounding powder will be deposited on the power meter. 4. Power meter Coherent PM3K-100: It is a thermopile type sensor that measures instantaneous power radiated by the laser with a measuring uncertainty of ±5% (±1% according to the calibration certificate). 5. Coax-8 coaxial nozzle developed by Alotec and IWS Fraunhoffer center. It is an industrial coaxial nozzle responsible of creating the powder flow. 6. Protective window: It is an optically neutral glass that is transparent to the wavelength of the laser. Protective windows practically do not absorb energy from the laser beam, but protects the power meter from powder projections. Therefore, this setup allows energy attenuation measurements due to the interaction between the beam and the injected powder, without considering other factors. Fig. 5 shows the evolution of the laser power. First, the power is stabilized at the nominal power (Pi ), then the powder material is injected and the measured power drops until posterior stabilization. In this way, it is possible to calculate
The adjustment and model validation tests have been performed on two different materials: a tool steel usually used for die and moulds (AISI D2), and a nickel-based superalloy mainly used in the aeronautical sector (Inconel© 718). For the aeronautical material, two particle diameter distributions have been included in order to verify the validity of the model for different particle sizes (Table 1). Before adjusting and validating the model, some tests have been carried out using different values of the laser power in order to verify the assumption No.2. It can be observed in Table 2 that the measured attenuation for the studied powers possesses a low standard deviation in most cases. Thus, initially a series of tests have been carried out in order to characterize the ˛ parameter for each material and for each version of the model (Table 3). All tests were carried out at constant power (1000 W) and repeated three times in order to avoid measurement errors. In all cases the variation between measurements was less than 1%. It can be observed from the results how the material attenuation factor (˛) is dependent, as expected, on the type of material and on its range of particle size. In addition, these results allow the study of the relevance of the different improvements added to the model. It can be observed how for the AISI D2, introducing a variable particle size significantly changes the value of material attenuation factor, whereas for the Inconel© 718 this value is practically constant. Therefore, it can be concluded that adjustment parameter for Inconel© 718 depends more on the nature of the material than the size of particle or the beams divergence. Once the model has been adjusted for the studied materials, validation tests have been carried out for different mass flow rates in order to compare the attenuation estimated by the model with the experimentally measured values (Table 4). It can be observed that the average error does not exceed 10% of the measured values and the maximum error reaches a 17% value. Therefore, it can be concluded that the presented model allows an estimation of the
Table 1 Composition and particle size of the used materials.
AISI D2 Inconel© 718
Al
C
Cr
Fe
Mn
Mo
Ni
Nb
Si
Ti
V
Particle size
– 0.2–0.8
1.55 0.08
11.8 17–21
Bal. 17
0.4 0.35
0.8 2.8–3.3
– 50–55
– 4.75–5.5
0.3 0.35
– 0.65–1.15
0.8 –
−150 + 45 m −110 + 40 m −160 + 80 m
Table 2 Values of measuring deviation for different powers. P (W)
Att (%)
Att (%)
150.2 300.0 460.2 615.0
36.5 75.0 115.7 155.8
19.6 20.0 20.1 20.2
20.0
0.29
188.9 390.0 590.9 778.5
145.4 300.0 457.0 599.9
43.5 90.0 133.9 178.6
23.0 23.1 22.7 22.9
22.9
0.19
189.8 383.0 583.0 783.0
156.6 316.0 480.0 639.0
33.2 67.0 103.0 144.0
17.5 17.5 17.7 18.4
17.8
0.43
Power (W) Theoretical
Initial
Attenuated
AISI D2 (−150 + 45 m)
200 400 600 800
186.7 375.0 575.9 770.8
Inco 718 (−110 + 40 m)
200 400 600 800
Inco 718 (−160 + 80 m)
200 400 600 800
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Table 3 Characterization tests of ˛ parameter. AISI D2 (−150 + 45 m)
Flow (g/min)
Attenuation (%)
Inco 718 (−110 + 40 m) ˛
Model
Real
M1 : Constant powder size
3.5 4.5 5.5 6.5 7.5
0.96 1.50 1.72 2.13 2.09
6.09 8.13 10.26 11.65 13.56
6.3 5.4 5.9 5.5 6.5
M2 : Variable powder size
3.5 4.5 5.5 6.5 7.5
0.79 1.23 1.41 1.75 1.72
6.09 8.13 10.26 11.65 13.56
7.7 6.6 7.3 6.7 7.9
M3 : Variable size and beam divergence
3.5 4.5 5.5 6.5 7.5
0.77 1.20 1.38 1.70 1.67
6.09 8.13 10.26 11.65 13.56
7.9 6.8 7.4 6.9 8.1
˛ ¯
Inco 718 (−160 + 80 m) ˛
Attenuation (%) Model
Real
5.9
1.54 1.77 2.35 2.67 3.02
6.15 7.61 9.38 10.55 11.64
4.0 4.3 4.0 4.0 3.9
7.2
1.50 1.73 2.29 2.61 2.95
6.15 7.61 9.38 10.55 11.64
4.1 4.4 4.1 4.0 4.0
7.4
1.44 1.68 2.21 2.52 2.84
6.15 7.61 9.38 10.55 11.64
4.3 4.5 4.3 4.2 4.1
˛ ¯
Attenuation (%)
˛
˛ ¯
Model
Real
4.0
0.43 0.57 0.70 0.94 0.94
4.4 6.32 7.07 7.81 9.33
10.2 11.1 10.1 8.3 9.9
9.9
4.1
0.43 0.58 0.70 0.95 0.95
4.4 6.32 7.07 7.81 9.33
10.2 10.9 10.1 8.2 9.8
9.9
4.3
0.42 0.56 0.68 0.92 0.96
4.4 6.32 7.07 7.81 9.33
10.5 11.3 10.4 8.5 9.7
10.1
Table 4 Validation tests of the model. Flow (g/min)
AISI D2 (−150 + 45 m) Attenuation (%)
|err| (%)
Model
Real
M1
4 5 6 7 8
6.72 8.21 8.74 10.83 11.82
6.79 8.71 10.2 12.56 13.39
1.0 5.7 14.3 13.8 11.7
M2
4 5 6 7 8
6.71 8.22 8.75 10.82 12.83
6.79 8.71 10.2 12.56 13.39
1.2 5.6 14.2 13.9 4.2
M3
4 5 6 7 8
6.74 8.09 8.68 11.02 12.58
6.79 8.71 10.2 12.56 13.39
0.7 7.1 14.9 12.3 6.0
Inco 718 (−110 + 40 m) |err| (%)
Attenuation (%)
|err| (%)
Model
Real
9.30
6.96 11.18 9.36 12.71 13.58
6.5 9.67 11.24 12.22 13.74
7.1 15.6 16.7 4.0 1.2
8.81
6.96 8.17 9.37 12.73 13.60
6.5 9.67 11.24 12.22 13.74
7.1 15.5 16.6 4.2 1.0
8.21
6.71 8.50 12.75 13.21 13.40
6.5 9.67 11.24 12.22 13.74
3.2 12.1 13.4 8.1 2.5
Inco 718 (−160 + 80 m) |err| (%)
Attenuation (%)
|err| (%)
|err| (%)
Model
Real
8.92
4.70 6.54 6.60 8.73 11.47
4.92 6.22 7.19 9.84 10.3
4.5 5.1 8.2 11.3 11.4
8.05
8.88
4.69 5.88 6.58 8.71 11.45
4.92 6.22 7.19 9.04 10.3
4.7 5.5 8.5 3.7 11.2
6.69
7.87
4.64 5.83 6.52 9.43 11.37
4.92 6.22 7.19 9.04 10.3
5.7 6.3 9.3 4.3 10.4
7.20
Fig. 6. Images of the interaction zone obtained with a thermographic camera for a 6.3 g/min mass flow: (a) 200 W and (b) 400 W.
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attenuation suffered by the beam due to its interaction with the particle flow. Finally, it can be observed both in the adjustment and validation tests how a smaller particle size produces higher attenuation. This fact has been predicted by the model (Eq. (6)), and it can be verified by the images provided by a IR camera. Fig. 6 shows how, for a fixed mass flow, if a smaller average particle size is used, the radiated energy by the heated powder flow is higher, i.e., the powder flow absorbs more energy from the laser beam and the attenuation generated is higher. 6. Conclusions This paper presents a model that estimates the attenuation suffered by the laser beam due to the interaction with the powder flow during the laser cladding process. The model is based on the shadow generated by the powder particles on the beam and uses the concentration obtained by a CFD model. Three versions of the model have been developed: the first one uses a constant particle size and the beam divergence is neglected. In the second version a variable particle size is introduced using an experimentally measured Rosin–Rammler distribution. Finally, the beam divergence has been introduced in order to obtain a more realistic model. The model has been adjusted and validated for two different materials and two ranges of particle size. The estimate average error in respect to the measured attenuation does not exceed 10%. The model also estimates a higher value of attenuation for a smaller particle size, a fact that has been shown both experimentally and by using images provided by an IR camera. Therefore, it can be concluded that the model presented could be considered a useful tool for estimating the attenuation suffered by the beam due to the interaction with the flow of powder material, i.e., for estimating the real energy that radiates the substrate surface and generates the melt pool. Acknowledgement The authors wish to thank the Spanish Ministry of Science and Innovation for financial support provided through the SURFACER project (Ref: DPI2010-20317-C02-01).
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