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Modeling and control of a direct laser powder deposition process for Functionally Graded Materials (FGM) parts manufacturing
Journal of Materials Processing Technology 213 (2013) 685–692
Contents lists available at SciVerse ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Modeling and control of a direct laser powder deposition process for Functionally Graded Materials (FGM) parts manufacturing Pierre Muller ∗ , Pascal Mognol, Jean-Yves Hascoet Institut de Recherche en Communications et Cybernetique de Nantes (UMR CNRS 6597), Nantes, France
a r t i c l e
i n f o
Article history: Received 22 June 2012 Received in revised form 19 November 2012 Accepted 24 November 2012 Available online 4 December 2012 Keywords: Additive manufacturing FGM Heterogeneous objects Manufacturing strategy determination Modeling
a b s t r a c t Functionally Graded Materials (FGM) parts are heterogeneous objects with material composition and microstructure that change gradually into the parts. The distinctive feature of FGM structure gives the possibility of selecting the distribution of properties to achieve the desired functions. Today, multimaterial parts manufactured with additive manufacturing processes are not functional. To move from these samples to functional and complex parts, it is necessary to have an overall process control. This global approach requires a control of process parameters and an optimal manufacturing strategy. This paper presents a process modeling and a system control to manufacture FGM parts with a direct laser deposition system. This works enable to choose an adapted manufacturing strategy and control process parameters to obtain the required material distribution and the required geometry. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The concept of Functionally Graded Materials (FGM) has been proposed in 80s to develop materials capable of withstanding thermal and mechanical stresses in propulsion systems and space shuttle fuselage (Niino et al., 1987). FGM parts are heterogeneous objects with materials that change gradually into the parts (Qian and Dutta, 2003). The result is a variation in composition and structure gradually over volume which enables to choose the distribution of properties to achieve required functions (Ocylok et al., 2010). These multi-material parts offer great promise for aeronautical (Domack and Baughman, 2005) and biomedical (Pompe et al., 2003) applications because it is possible to change physical, chemical, biochemical or mechanical properties. Since the concept of FGM advent, some research studies was dedicated to manufacture these materials and a large variety of methods of production – gas phase, liquid phase and solid phase methods – has been developed (Kieback et al., 2003). Additive manufacturing processes are potentially suitable to manufacture FGM parts. Moreover they have the advantage to allowing the fabrication of morphologically complex parts by the addition of material
∗ Corresponding author at: IRCCyN/MO2P Team, 1 rue de la Noe, BP 92101, 44321 Nantes Cedex 03, France. Tel.: +33 0299055261; fax: +33 0299059328. E-mail addresses: [email protected] (P. Muller), [email protected] (P. Mognol), [email protected] (J.-Y. Hascoet). 0924-0136/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2012.11.020
which are fused with an energy source. Nowadays, with these processes, it is possible to obtain customized homogeneous parts from digital data with various materials: metals, ceramics and polymers (Bandyopadhyay et al., 2009). Although these processes seem adapted to produce FGM parts, the manufacturing of heterogeneous parts is limited to samples: parts are not functional, with simple morphology (Majumdar et al., 2009) and simple material distribution (Yakovlev et al., 2005). To move from these samples to functional parts a global approach was proposed (Mognol et al., 2011). It is achieved by a methodology which enables to move from the concept imagined by a designer to the manufacturing of the FGM part (Fig. 1(a)). This methodology includes a description of part – geometry and material distribution – and manufacturing process (Hascoet et al., 2011). From these descriptions, an appropriate manufacturing strategy is determined with the manufacturing process modeling and all the process parameters are controlled with the automatic generation of a Numerical Code (NC) program (Muller et al., 2012). The manufacturing strategy determination has an important influence in the manufacturing procedure. Methodological tools of manufacturing strategies determination or process planning have been developed for additive manufacturing processes. With some of them, it is possible to optimize the slicing procedure (Ruan et al., 2010), to choose the part orientation (Pandey et al., 2007), to adapt paths (Kao and Prinz, 1998) or to determine a process plan (Ren et al., 2010) but they do not take into account the multi-material aspect. Methodological tools which are appropriate to the fabrication of heterogeneous parts propose a discretization of parts into
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Fig. 2. FGM part description.
phenomena involved in the steps of description, process planning and manufacturing. An equivalent notation is used for the other data: data* for required data and data for those obtained from the simulation. 2.1. Part description
Fig. 1. (a) Numerical chain: from design to manufacturing and (b) direct laser powder deposition system.
The geometry is described by a domain D∗P ⊂ R3 corresponding to the part (Fig. 2). The part is made with two basic materials A and B. The function M* (x, y, z) represents the material composition in the space R3 , it corresponds to the volume concentration of material A: M ∗ (x, y, z) : D∗P → [0; 1]
areas with homogeneous material (Shin and Dutta, 2002) or do not propose path generation (Zhou, 2004). For a manufacturing with a continuous approach of material distribution, the selection of a manufacturing strategy has a direct influence on the control of the powder distribution system. This is why a manufacturing process modeling is necessary to choose a strategy and control the commands of the system. This paper presents a modeling of the direct laser powder deposition process which includes all the steps of the manufacturing procedure, in particular the step concerning the operation of the powder distribution system. A test-part was manufactured, analyzed and discussed in comparison with the model result. Moreover, the method of manufacturing strategy determination and the system control are described. The direct laser powder deposition system which will be considered and used for this study is the CLAD® system. This system is based on the three dimensions layer by layer deposition of laser melted powders to build the profile of the requested part (Fig. 1(b)). Powders are injected into a high power laser beam. The energy input is partly used to melt both powders and the surface of the substrate. This system consists of a coaxial powder feed system and a fiber laser mounted on a five axis machine. The powders are supplied by two powder feeders, argon gas is used to prevent the melt pool form oxidizing throughout fabrication. 2. Modeling: mathematical data and relationships The control of the powder flow rates is decisive to ensure the fabrication of a part in compliance with the desired material distribution. The modification of the flow rates is made by the command of the powder distribution system. The differences which may exist between the theoretical distribution and the deposed material are particularly due to the system dynamic behavior. As the powder flow rates are directly determined by the manufacturing strategy, it is essential to choose an adapted strategy. Our model was developed in order to be able to choose an adapted strategy and to control the system commands. A selection of strategies is made and strategies are simulated and compared with performances indexes. It is why the model is based on the comparison between the required material distribution, noted M* , and the one obtained from the simulation, noted M. For that, mathematical data are used to describe
(1)
2.2. Path description The path is described by a curve C∗P . The orientation, the height and the width of the bead are expressed in each point of the curve (Fig. 3). The material function in each points depends on the theoretical material function. 2.3. NC program The Numerical Control (NC) program generate temporal commands, the mathematical data of its model are consequently temporally expressed. For this, the machine axis (Fig. 1(b)), laser, gas and powder flow rates orders are expressed in each point of the curve C∗P then they are temporally expressed. The axes are determined according to the curve C∗P and the orientation of the bead. The laser power and the axis speed depend on the height and the width of the bead. The gas flow rates in the pipes are chosen constant to formed an adapted cone of powder at the nozzle outlet. The volume flow rates of the powder feeders A∗ and B∗ (Fig. 4) are modified according to the value of the material function, the control laws chosen are linear, for example: A∗ = M ∗ × max
(2)
Given that max is the volume flow rate of powder determined to manufacture a bead with only one basic material and with the process parameters previously chosen. 2.4. Process operation The system do not always have the desired behavior in particular due to the dynamic behavior of its components.
Fig. 3. Path description and bead parameters.
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Table 1 Chemical composition (wt.%).
Fig. 4. Powder and gas flow rates.
The process used has maximum feed rates for each axis, maximum variations of these feed rates given by accelerations for each axis and maximum variations of these accelerations given by jerks for each axis (Erkorkmaz and Altintas, 2001). In view of the values of these parameters for the process used and the commands of the feed-rates, the outputs and the inputs concerning the axes are considered equivalent. Moreover, the outputs and the inputs concerning the laser and the gas are considered equivalent. One of the major differences between inputs and outputs concerns the volume flow rates of powder A and B . It is why, except for the powder distribution system, the components are considered perfect. The modeling of the powder distribution system has been experimentally obtained with an indirect calibration approach to quantify the imperfect output of this system (Section 3). 2.5. Bead deposition Geometrical characteristics and localization of the bead are considered similar to the specifications of the path description. Concerning the material, the ratio of the powder A in the bead to the powder A in the nozzle outlet is equal to the ratio of the powder B in the bead to the powder B in the nozzle outlet. M 1−M = A B
(3)
2.6. Manufactured part The thermo-mechanical phenomena are not taken into account at this time, the part does not deform. The model of the manufactured domain is equivalent to the model of the theoretical domain. In a first approach, thermo-metallurgical and mechanometallurgical phenomena are not taken into account, there is no material diffusion and material blending in the weld pool:
∀(x, y, z) ∈ DP , M(x, y, z) = M(˜x, y˜ , z˜ )
(4)
Given that (˜x, y˜ , z˜ ) are the coordinates of the point of the bead curve CP with the smallest distance with the point of coordinates (x, y, z). 3. Modeling of the powder distribution system with an indirect calibration approach 3.1. Motivation To model the process operation it is necessary to study the powder distribution system behavior (Section 2.4). This system consists of two powder containers which feed the nozzle by pipes. Powders
Material
C
Co
Cr
Fe
Mn
Mo
Ni
Si
W
316L Stellite 6
0.03 1.2
– 60
17 29
64 2
2 –
3 –
12 2
1 1
– 4.8
particles are moved from containers to pipes by turning plates. The powder flow rates are modified by controlling the speed of rotation of these distribution plates. A difference exists between the powder flow rates at the container outlets and the powder flow rates commanded due to the dynamic behavior of the distribution plates. Moreover the powder at the nozzle outlet will be deposited after going through the pipes. The powder distribution system is considered as a dynamic system and a calibration is necessary to quantify the imperfect output of the powder distribution system. To do that, an indirect approach is proposed because the implementation of a flow meter is difficult. The experiments were conducted with only one powder feeder to determine the output of the powder distribution system. Finally, we use this model to manufacture FGM parts considering that the two powder feeders have a similar behavior. 3.2. Experimental procedure The experiments were conducted with the CLAD® process. Commercially stainless steel 316L powder with particle size between 45 and 90 m was used in this study (Table 1). The test-parts were manufactured on a 3 mm thick steel substrate. The test-parts were deposited using one powder feeder contained elemental 316L powder. The deposition of beads – 0.8 mm thickness – were achieved by controlling the flow rate of powder A∗ (Fig. 5(a)). The beads were deposited with several functions A∗ (t) (Fig. 5(b)). The machine axis speed – 900 mm min−1 – and the laser power – 256 W – were chosen and considered constant throughout manufacturing. To compare with the powder flow rate command, the bead height was measured with an optical three dimensional micro coordinate system for form and roughness measurement (Fig. 5(c)). The bead height was obtained all 0.02 mm. A moving average of the results was made to determine the transfer functions which represent the process operation (Fig. 5(d)). This moving average was made on a set of 200 points – 2 mm – and it enables to mitigate the height variations due to the irregularity of the bead. 3.3. Results The first test part was manufactured with a step signal of powder flow rate: from a minimal powder flow rate A∗ = 0 to a maximum powder flow rate A∗ = max (Fig. 5(b)). From the results of the first test-part, it is possible to model the imperfection of the powder feeding system by a delay 1 = 6.2 s – mainly due to the transfer of the powder from container to nozzle in the pipes – and a first-order transfer function with time constant 2 = 10 s (Fig. 6(a)). The second test part was manufactured with a step signal of powder flow rate: from a maximal powder flow rate A∗ = max to a minimal powder flow rate A∗ = 0. From the results of this second test-part, it is possible to model the imperfection of the powder feeding system by a delay 3 = 1 = 6.2 s and a first-order transfer function with time constant 4 = 2 s (Fig. 6(b)). The time characteristic of this transfer function is different from the time constant of the first test-part. This difference is explained by a different behavior of the distribution plate during acceleration and deceleration. These two models are used to represent the process operation of the powder distribution system considering that the two powder feeders have a similar behavior. The first model is used when
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Fig. 5. Test description: (a) test-part description, (b) input signal: powder flow rate, (c) bead height, and (d) moving average of the bead height.
the powder flow rate decreases and the second is used when the powder flow rate increases. 4. Manufacturing and analysis of a FGM test-part 4.1. Experimental procedure The experiments were conducted with the CLAD® process. Commercially stainless steel 316L powder with particle size between 45 and 90 m and chromium cobalt alloy with particle size between 50 and 120 m were used in this study (Table 1). In a first approach, knowing that the particle size of the powders used are almost similar, the influence of the particle size is not taken into account. The test-parts were manufactured on a 5 mm thick steel substrate. They were deposited using the two powder feeders, while the first contained elemental 316L powder (A), the second contained elemental Stellite 6 powder (B). The composition of the deposited powder was achieved by controlling the powder flow rates from each feeders A∗ and B∗ . Samples are thin walls – 15 mm height, 90 mm length and 0.8 mm thickness – with a material gradient perpendicular to the substrate (z-axis) (Fig. 7). The deposition started with only the powder feeder containing 316L powder. After 1 mm, the flow rate of the first powder feeder was reduced and the flow rate of the second powder feeder was increased by the same
Fig. 6. Bead height and transfer function: (a) switch on and (b) switch off.
Fig. 7. Test description.
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proportion. The deposition finished with only the second powder feeder. The machine axis speed – 900 mm min−1 – and the laser power – 256 W – were chosen and considered constant throughout the manufacturing. The parts were polished and analyzed. The composition along material gradient was characterized with scanning electron microscope (SEM) and energy-dispersive X-ray spectroscopy (EDS). 4.2. Manufacturing simulation The manufacturing of the test-part was simulated with the model (Section 2) and the transfer functions (Section 3). The geometry of the test part was described by a domain D∗P ⊂ R3 . The material distribution was described in this domain by a function M* (x, y, z):
∀(x, y, z) ∈ D∗P , M ∗ (x, y, z) =
⎧ 1 if z ≤ 1. ⎪ ⎪ ⎨ 14 − z 13 ⎪ ⎪ ⎩ 0
if 1 < z ≤ 13.
(5)
Fig. 8. Powder flow rates (command and simulation).
if 14 < z.
The path was described given that nozzle was moved with a back and forth motion. The orientation, the height – 0.25 mm – and the width – 0.8 mm – of bead were defined constant in each point of the curve. All the process parameters were temporally expressed from the mathematical data of the path description. The commands A∗ and B∗ are determined from the expected material function (Eqs. (2) and (5)). The powder flow rates A and B are then deducted by simulation using the transfer functions (Fig. 6). The results are represented as functions of the manufacturing time (Fig. 8), knowing that the manufacturing time is determined from the machine axis speed and the path geometry. 4.3. Analysis The samples without pore and crack were obtained using the CLAD® process (Fig. 9). All the powder particles were melted.
Fig. 9. FGM test-part and microstructure.
The composition analyses were made all 0.5 mm on all elements present in 316L and Stellite 6. The comparison with results of simulation was made on four elements: chromium, cobalt, iron and nickel (Fig. 10).
Fig. 10. Chemical composition (wt.%) (y = 20 mm): (a) Chromium, (b) Cobalt, (c) Iron, and (d) Nickel.
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Fig. 12. Example: part description.
Fig. 11. Material function (simulated and measured).
Concerning the results of the simulation, concentrations of elements were determined from the simulated powder flow rates at the nozzle outlet A and B , for example: %Fe =
A A %Fe316L + 1 − A + B A + B
%FeStellite6
(6)
The material distribution of the test-part was determined with the chromium, cobalt, iron and nickel volume concentrations, which are representative of the presence of 316L and Stellite 6.
1 %316L = 4
×
5.2. Process control description
%Co − %CoStellite6 %Cr − %CrStellite6 + %Cr316L − %CrStellite6 %Co316L − %CoStellite6
%Fe − %FeStellite6 %Ni − %NiStellite6 + %Fe316L − %FeStellite6 %Ni316L − %NiStellite6
In view of powder distribution system operation, a powder flow rates control may be required in some cases. This control is proposed before the step of NC program generation. To illustrate this proposition, the system control is made to manufacture a test-part with an important difference between the simulated material distribution and the requested material distribution (Fig. 12). The manufacturing of the part was simulated. The geometry and the material distribution were described (Section 4.2). The path was described given that the nozzle is moved with a back and forth motion. The orientation vector, the height and the width of the bead were considered constant in each point of the curve. All the process parameters were temporally expressed from the mathematical data of the path description and the process operation modeling was made with transfer functions. The powder flow rates A and B are determined, they give a picture of the deposited material and the error over time (Fig. 13).
(7)
There is a good correlation between the simulated and the deposited material distributions (Fig. 11). The 316L concentration decreases continuously similarly to the simulated concentration. Although the results are satisfactory, we notice that simulated material distribution is close to the command. Other test-parts will have to be manufactured to validate the model. These test-parts will bring up a clear difference between the simulated and the requested material distributions. 5. Process control 5.1. Motivation
The first control concerns the delay. To make this control, the powder flow rates commands are advanced by a period of d = 1 = 3 = 6.2 s (Section 3.3). Using this first control, it is possible to cancel the impact of the delay (Fig. 14). In some cases this control may be sufficient to obtain a part in compliance with the desired material distribution. In other cases an additional control can mitigate the impacts of the powders distribution plates dynamic behavior. The second control is a predictive closed-loop control. It is based on the powder distribution system modeling without delay (Fig. 15). Signals are introduced in a closed-loop virtual system including a controller. The signals used to generate the NC program – noted A∗∗ and B∗∗ – are taken at the output of the controller and advanced to cancel the delay. The purpose of the controllers is to reduce the errors A∗ − A and B∗ − B . The two controllers – one concerning powder A and one concerning powder B – are chosen equivalent. They are
To ensure the fabrication of a part in compliance with the desired material distribution, it is necessary to manufacture with: A∗
A∗
+ B∗
=
A A + B
(8)
To ensure the fabrication of a part in compliance with the desired geometry, it is necessary to manufacture the bead with the powder flow rates determined for the formation of a bead with required dimensions taking into account other parameters: A + B = max
(9)
To ensure the fabrication of a part in compliance with the desired material distribution and the geometry, it is necessary to manufacture the bead with:
(8) (9)
⇔
A∗ = A B∗ = B
(10) Fig. 13. Material function without control.
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Fig. 14. Material function with compensation of the delay. Fig. 17. Influence of the parameters on the error.
Fig. 15. Virtual closed-loop control.
proportional-plus-integral controller (PI). They are defined by a transfer function: C(s) =
A∗∗ (s)
A∗ (s) − A (s)
= Kc × 1 +
1 c s
(11)
These controller – with Kc = 1 and c = 0.1 – are applied. The error is greatly reduced and nearly deleted with the coefficients chosen (Fig. 16). 5.3. Controllers parameters The PI controllers have two parameters Kc and c . These parameters have an influence on the final error and the signal form. By increasing the coefficient Kc and decreasing the coefficient c the error average decreases (Fig. 17). Beyond some limits, this effect is less important but high frequency fluctuations become significant. A control with a very important coefficient Kc enables to reduce strongly the error but the signals that are imposed on the distribution plates are not suitable. In this case high frequency fluctuations become too significant for the mechanism (Fig. 18). The coefficients should be chosen to ensure a final part in compliance with the desired geometry and the desired material
Fig. 18. Material function with control (Kc = 20 and c = 0.1).
distribution and to generate signals that are adapted to the system. In this example, the choice Kc = 1 and c = 0.1 is a good compromise between a very low error and signals that are adapted to the system. 5.4. Conclusion A comparison was made between the results obtained without control, with only a compensation of the delay and with a control (Kc = 20 and c = 0.1). To do that, the cartographies of performance index Imat were determined for these three cases (Fig. 19). The performance index represents, in each point of the domain D∗P , the global error concerning the material distribution. It is equal to one when the difference is null: Imat (x, y, z) = 1 − |M ∗ (x, y, z) − M(x, y, z)|
Fig. 16. Material function with control (Kc = 1 and c = 0.1).
(12)
Fig. 19. Performance index cartographies: (a) without control, (b) with compensation of the delay, and (c) with control.
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The manufacturing of this test-part in compliance with the desired material distribution can be achieved through a two-step procedure. This procedure is made before the step of NC program generation. First, signals are controlled by using a virtual closed-loop control based on the system modeling and a PI controller. Second, signals are advanced to compensate the delay. The coefficients selected should be established to ensure manufacture of the part with specification. The controllers coefficients are adapted according to the tolerance of the material function. 6. Conclusion and objectives for further research In this paper a modeling and a control of a direct laser powder deposition process for FGM parts manufacturing is exposed. The modeling takes into account all the steps of the manufacturing procedure, from the part description to the manufactured part. To model the process operation, experiments were conducted and two transfer functions are used to describe it. With this modeling it is possible to find an appropriate manufacturing strategy with the comparison between some strategies. Moreover, it is possible to control the signals used by the NC controller. The control is made before the step of NC program generation in two stages. First, the signals are control with a virtual closed-loop controls and a PI controller. Second, the delay is compensated. Further research will be conducted to manufacture functional FGM parts. The modeling will be used to compare manufacturing strategies to produce parts with complex material distribution. The choice of an adapted manufacturing strategy will be made by taking into account the possibility or not to correct signals. Acknowledgements This work was carried out within the context of the working group Manufacturing 21 which gathers about twenty French laboratories. The topics approached are: the modeling of the manufacturing process, the virtual machining and the emergence of new manufacturing methods. References Bandyopadhyay, A., Krishna, B., Xue, W., Bose, S., 2009. Application of laser engineered net shaping (LENS) to manufacture porous and functionally graded structures for load bearing implants. Journal of Materials Science 20, 29–34.
Domack, M., Baughman, J., 2005. Development of nickel-titanium graded composition components. Rapid Prototyping Journal 11, 41–51. Erkorkmaz, K., Altintas, Y., 2001. High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. International Journal of Machine Tools & Manufacture 41, 1323–1345. Hascoet, J., Muller, P., Mognol, P., 2011. Manufacturing of complex parts with continuous functionally graded materials (FGM). In: Proceedings of the Twenty Second Annual International Solid Freeform Fabrication Symposium, Austin, U.S.A. Kao, J., Prinz, F., 1998. Optimal motion planning for deposition in layered manufacturing. In: Design Engineering Technical Conferences, Atlanta, U.S.A, pp. 13–16. Kieback, B., Neubrand, A., Riedel, H., 2003. Processing techniques for functionally graded materials. Materials Science and Engine A 362, 81–106. Majumdar, J., Manna, I., Kumar, A., Bhargava, P., Nath, A., 2009. Direct laser cladding of Co on Ti–6Al–4V with a compositionally graded interface. Journal of Materials Processing Technology 209, 2237–2243. Mognol, P., Muller, P., Hascoet, J., 2011. A novel approach to produce functionally graded materials for additive manufacturing. In: Proceedings of the Conference on Advanced Research in Virtual and Rapid Prototyping, Leiria, Portugal, pp. 473–478. Muller, P., Mognol, P., Hascoet, J., 2012. Functionally Graded Material (FGM) parts: from design to the manufacturing simulation. In: Proceedings of the Eleventh Biennal Conference On Engineering Systems Design and Analysis, ASME, Nantes, France. Niino, M., Suzuki, A., Hirai, T., Watanabe, R., Hirano, T., Kuroishi, N., 1987. Method of producing a functionally gradient material. Ausz. Eur. Patentanmeld. I 3, 1555. Ocylok, S., Weisheit, A., Kelbassa, I., 2010. Functionally graded multi-layers by laser cladding for increased wear and corrosion protection. Physics Procedia 5, 359–367. Pandey, P., Venkatareddy, N., Dhande, S., 2007. Part deposition orientation studies in layered manufacturing. Journal of Materials Processing Technology 185, 125–131. Pompe, W., Worch, H., Epple, M., Friess, W., Gelinsky, M., Greil, P., Hempel, U., Scharnweber, D., Schulte, K., 2003. Functionally graded materials for biomedical applications. Materials Science and Engine A 362, 40–60. Qian, X., Dutta, D., 2003. Design of heterogeneous turbine blade. Computer-Aided Design 35, 319–329. Ren, L., Sparks, T., Ruan, J., Liou, F., 2010. Integrated Process Planning for a Multiaxis Hybrid Manufacturing System. Journal of Manufacturing Science and Engineering 132. Ruan, J., Tang, L., Liou, F., Landers, R., 2010. Direct three-dimensional layer metal deposition. Journal of Manufacturing Science and Engineering 132, 064502-1–064502-6. Shin, K., Dutta, D., 2002. Process-planning for layered manufacturing of heterogeneous objects using direct metal deposition. Journal of Computing and Information Science in Engineering 2, 330–344. Yakovlev, A., Trunova, E., Grevey, D., Pilloz, M., Smurov, I., 2005. Laser-assisted direct manufacturing of functionally graded 3D objects. Surface and Coatings Technology 190, 15–24. Zhou, M., 2004. Modeling and processing of functionally graded materials for rapid prototyping. Journal of Materials Processing Technology 146, 396–402.
Contents lists available at SciVerse ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Modeling and control of a direct laser powder deposition process for Functionally Graded Materials (FGM) parts manufacturing Pierre Muller ∗ , Pascal Mognol, Jean-Yves Hascoet Institut de Recherche en Communications et Cybernetique de Nantes (UMR CNRS 6597), Nantes, France
a r t i c l e
i n f o
Article history: Received 22 June 2012 Received in revised form 19 November 2012 Accepted 24 November 2012 Available online 4 December 2012 Keywords: Additive manufacturing FGM Heterogeneous objects Manufacturing strategy determination Modeling
a b s t r a c t Functionally Graded Materials (FGM) parts are heterogeneous objects with material composition and microstructure that change gradually into the parts. The distinctive feature of FGM structure gives the possibility of selecting the distribution of properties to achieve the desired functions. Today, multimaterial parts manufactured with additive manufacturing processes are not functional. To move from these samples to functional and complex parts, it is necessary to have an overall process control. This global approach requires a control of process parameters and an optimal manufacturing strategy. This paper presents a process modeling and a system control to manufacture FGM parts with a direct laser deposition system. This works enable to choose an adapted manufacturing strategy and control process parameters to obtain the required material distribution and the required geometry. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The concept of Functionally Graded Materials (FGM) has been proposed in 80s to develop materials capable of withstanding thermal and mechanical stresses in propulsion systems and space shuttle fuselage (Niino et al., 1987). FGM parts are heterogeneous objects with materials that change gradually into the parts (Qian and Dutta, 2003). The result is a variation in composition and structure gradually over volume which enables to choose the distribution of properties to achieve required functions (Ocylok et al., 2010). These multi-material parts offer great promise for aeronautical (Domack and Baughman, 2005) and biomedical (Pompe et al., 2003) applications because it is possible to change physical, chemical, biochemical or mechanical properties. Since the concept of FGM advent, some research studies was dedicated to manufacture these materials and a large variety of methods of production – gas phase, liquid phase and solid phase methods – has been developed (Kieback et al., 2003). Additive manufacturing processes are potentially suitable to manufacture FGM parts. Moreover they have the advantage to allowing the fabrication of morphologically complex parts by the addition of material
∗ Corresponding author at: IRCCyN/MO2P Team, 1 rue de la Noe, BP 92101, 44321 Nantes Cedex 03, France. Tel.: +33 0299055261; fax: +33 0299059328. E-mail addresses: [email protected] (P. Muller), [email protected] (P. Mognol), [email protected] (J.-Y. Hascoet). 0924-0136/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2012.11.020
which are fused with an energy source. Nowadays, with these processes, it is possible to obtain customized homogeneous parts from digital data with various materials: metals, ceramics and polymers (Bandyopadhyay et al., 2009). Although these processes seem adapted to produce FGM parts, the manufacturing of heterogeneous parts is limited to samples: parts are not functional, with simple morphology (Majumdar et al., 2009) and simple material distribution (Yakovlev et al., 2005). To move from these samples to functional parts a global approach was proposed (Mognol et al., 2011). It is achieved by a methodology which enables to move from the concept imagined by a designer to the manufacturing of the FGM part (Fig. 1(a)). This methodology includes a description of part – geometry and material distribution – and manufacturing process (Hascoet et al., 2011). From these descriptions, an appropriate manufacturing strategy is determined with the manufacturing process modeling and all the process parameters are controlled with the automatic generation of a Numerical Code (NC) program (Muller et al., 2012). The manufacturing strategy determination has an important influence in the manufacturing procedure. Methodological tools of manufacturing strategies determination or process planning have been developed for additive manufacturing processes. With some of them, it is possible to optimize the slicing procedure (Ruan et al., 2010), to choose the part orientation (Pandey et al., 2007), to adapt paths (Kao and Prinz, 1998) or to determine a process plan (Ren et al., 2010) but they do not take into account the multi-material aspect. Methodological tools which are appropriate to the fabrication of heterogeneous parts propose a discretization of parts into
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Fig. 2. FGM part description.
phenomena involved in the steps of description, process planning and manufacturing. An equivalent notation is used for the other data: data* for required data and data for those obtained from the simulation. 2.1. Part description
Fig. 1. (a) Numerical chain: from design to manufacturing and (b) direct laser powder deposition system.
The geometry is described by a domain D∗P ⊂ R3 corresponding to the part (Fig. 2). The part is made with two basic materials A and B. The function M* (x, y, z) represents the material composition in the space R3 , it corresponds to the volume concentration of material A: M ∗ (x, y, z) : D∗P → [0; 1]
areas with homogeneous material (Shin and Dutta, 2002) or do not propose path generation (Zhou, 2004). For a manufacturing with a continuous approach of material distribution, the selection of a manufacturing strategy has a direct influence on the control of the powder distribution system. This is why a manufacturing process modeling is necessary to choose a strategy and control the commands of the system. This paper presents a modeling of the direct laser powder deposition process which includes all the steps of the manufacturing procedure, in particular the step concerning the operation of the powder distribution system. A test-part was manufactured, analyzed and discussed in comparison with the model result. Moreover, the method of manufacturing strategy determination and the system control are described. The direct laser powder deposition system which will be considered and used for this study is the CLAD® system. This system is based on the three dimensions layer by layer deposition of laser melted powders to build the profile of the requested part (Fig. 1(b)). Powders are injected into a high power laser beam. The energy input is partly used to melt both powders and the surface of the substrate. This system consists of a coaxial powder feed system and a fiber laser mounted on a five axis machine. The powders are supplied by two powder feeders, argon gas is used to prevent the melt pool form oxidizing throughout fabrication. 2. Modeling: mathematical data and relationships The control of the powder flow rates is decisive to ensure the fabrication of a part in compliance with the desired material distribution. The modification of the flow rates is made by the command of the powder distribution system. The differences which may exist between the theoretical distribution and the deposed material are particularly due to the system dynamic behavior. As the powder flow rates are directly determined by the manufacturing strategy, it is essential to choose an adapted strategy. Our model was developed in order to be able to choose an adapted strategy and to control the system commands. A selection of strategies is made and strategies are simulated and compared with performances indexes. It is why the model is based on the comparison between the required material distribution, noted M* , and the one obtained from the simulation, noted M. For that, mathematical data are used to describe
(1)
2.2. Path description The path is described by a curve C∗P . The orientation, the height and the width of the bead are expressed in each point of the curve (Fig. 3). The material function in each points depends on the theoretical material function. 2.3. NC program The Numerical Control (NC) program generate temporal commands, the mathematical data of its model are consequently temporally expressed. For this, the machine axis (Fig. 1(b)), laser, gas and powder flow rates orders are expressed in each point of the curve C∗P then they are temporally expressed. The axes are determined according to the curve C∗P and the orientation of the bead. The laser power and the axis speed depend on the height and the width of the bead. The gas flow rates in the pipes are chosen constant to formed an adapted cone of powder at the nozzle outlet. The volume flow rates of the powder feeders A∗ and B∗ (Fig. 4) are modified according to the value of the material function, the control laws chosen are linear, for example: A∗ = M ∗ × max
(2)
Given that max is the volume flow rate of powder determined to manufacture a bead with only one basic material and with the process parameters previously chosen. 2.4. Process operation The system do not always have the desired behavior in particular due to the dynamic behavior of its components.
Fig. 3. Path description and bead parameters.
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Table 1 Chemical composition (wt.%).
Fig. 4. Powder and gas flow rates.
The process used has maximum feed rates for each axis, maximum variations of these feed rates given by accelerations for each axis and maximum variations of these accelerations given by jerks for each axis (Erkorkmaz and Altintas, 2001). In view of the values of these parameters for the process used and the commands of the feed-rates, the outputs and the inputs concerning the axes are considered equivalent. Moreover, the outputs and the inputs concerning the laser and the gas are considered equivalent. One of the major differences between inputs and outputs concerns the volume flow rates of powder A and B . It is why, except for the powder distribution system, the components are considered perfect. The modeling of the powder distribution system has been experimentally obtained with an indirect calibration approach to quantify the imperfect output of this system (Section 3). 2.5. Bead deposition Geometrical characteristics and localization of the bead are considered similar to the specifications of the path description. Concerning the material, the ratio of the powder A in the bead to the powder A in the nozzle outlet is equal to the ratio of the powder B in the bead to the powder B in the nozzle outlet. M 1−M = A B
(3)
2.6. Manufactured part The thermo-mechanical phenomena are not taken into account at this time, the part does not deform. The model of the manufactured domain is equivalent to the model of the theoretical domain. In a first approach, thermo-metallurgical and mechanometallurgical phenomena are not taken into account, there is no material diffusion and material blending in the weld pool:
∀(x, y, z) ∈ DP , M(x, y, z) = M(˜x, y˜ , z˜ )
(4)
Given that (˜x, y˜ , z˜ ) are the coordinates of the point of the bead curve CP with the smallest distance with the point of coordinates (x, y, z). 3. Modeling of the powder distribution system with an indirect calibration approach 3.1. Motivation To model the process operation it is necessary to study the powder distribution system behavior (Section 2.4). This system consists of two powder containers which feed the nozzle by pipes. Powders
Material
C
Co
Cr
Fe
Mn
Mo
Ni
Si
W
316L Stellite 6
0.03 1.2
– 60
17 29
64 2
2 –
3 –
12 2
1 1
– 4.8
particles are moved from containers to pipes by turning plates. The powder flow rates are modified by controlling the speed of rotation of these distribution plates. A difference exists between the powder flow rates at the container outlets and the powder flow rates commanded due to the dynamic behavior of the distribution plates. Moreover the powder at the nozzle outlet will be deposited after going through the pipes. The powder distribution system is considered as a dynamic system and a calibration is necessary to quantify the imperfect output of the powder distribution system. To do that, an indirect approach is proposed because the implementation of a flow meter is difficult. The experiments were conducted with only one powder feeder to determine the output of the powder distribution system. Finally, we use this model to manufacture FGM parts considering that the two powder feeders have a similar behavior. 3.2. Experimental procedure The experiments were conducted with the CLAD® process. Commercially stainless steel 316L powder with particle size between 45 and 90 m was used in this study (Table 1). The test-parts were manufactured on a 3 mm thick steel substrate. The test-parts were deposited using one powder feeder contained elemental 316L powder. The deposition of beads – 0.8 mm thickness – were achieved by controlling the flow rate of powder A∗ (Fig. 5(a)). The beads were deposited with several functions A∗ (t) (Fig. 5(b)). The machine axis speed – 900 mm min−1 – and the laser power – 256 W – were chosen and considered constant throughout manufacturing. To compare with the powder flow rate command, the bead height was measured with an optical three dimensional micro coordinate system for form and roughness measurement (Fig. 5(c)). The bead height was obtained all 0.02 mm. A moving average of the results was made to determine the transfer functions which represent the process operation (Fig. 5(d)). This moving average was made on a set of 200 points – 2 mm – and it enables to mitigate the height variations due to the irregularity of the bead. 3.3. Results The first test part was manufactured with a step signal of powder flow rate: from a minimal powder flow rate A∗ = 0 to a maximum powder flow rate A∗ = max (Fig. 5(b)). From the results of the first test-part, it is possible to model the imperfection of the powder feeding system by a delay 1 = 6.2 s – mainly due to the transfer of the powder from container to nozzle in the pipes – and a first-order transfer function with time constant 2 = 10 s (Fig. 6(a)). The second test part was manufactured with a step signal of powder flow rate: from a maximal powder flow rate A∗ = max to a minimal powder flow rate A∗ = 0. From the results of this second test-part, it is possible to model the imperfection of the powder feeding system by a delay 3 = 1 = 6.2 s and a first-order transfer function with time constant 4 = 2 s (Fig. 6(b)). The time characteristic of this transfer function is different from the time constant of the first test-part. This difference is explained by a different behavior of the distribution plate during acceleration and deceleration. These two models are used to represent the process operation of the powder distribution system considering that the two powder feeders have a similar behavior. The first model is used when
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Fig. 5. Test description: (a) test-part description, (b) input signal: powder flow rate, (c) bead height, and (d) moving average of the bead height.
the powder flow rate decreases and the second is used when the powder flow rate increases. 4. Manufacturing and analysis of a FGM test-part 4.1. Experimental procedure The experiments were conducted with the CLAD® process. Commercially stainless steel 316L powder with particle size between 45 and 90 m and chromium cobalt alloy with particle size between 50 and 120 m were used in this study (Table 1). In a first approach, knowing that the particle size of the powders used are almost similar, the influence of the particle size is not taken into account. The test-parts were manufactured on a 5 mm thick steel substrate. They were deposited using the two powder feeders, while the first contained elemental 316L powder (A), the second contained elemental Stellite 6 powder (B). The composition of the deposited powder was achieved by controlling the powder flow rates from each feeders A∗ and B∗ . Samples are thin walls – 15 mm height, 90 mm length and 0.8 mm thickness – with a material gradient perpendicular to the substrate (z-axis) (Fig. 7). The deposition started with only the powder feeder containing 316L powder. After 1 mm, the flow rate of the first powder feeder was reduced and the flow rate of the second powder feeder was increased by the same
Fig. 6. Bead height and transfer function: (a) switch on and (b) switch off.
Fig. 7. Test description.
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proportion. The deposition finished with only the second powder feeder. The machine axis speed – 900 mm min−1 – and the laser power – 256 W – were chosen and considered constant throughout the manufacturing. The parts were polished and analyzed. The composition along material gradient was characterized with scanning electron microscope (SEM) and energy-dispersive X-ray spectroscopy (EDS). 4.2. Manufacturing simulation The manufacturing of the test-part was simulated with the model (Section 2) and the transfer functions (Section 3). The geometry of the test part was described by a domain D∗P ⊂ R3 . The material distribution was described in this domain by a function M* (x, y, z):
∀(x, y, z) ∈ D∗P , M ∗ (x, y, z) =
⎧ 1 if z ≤ 1. ⎪ ⎪ ⎨ 14 − z 13 ⎪ ⎪ ⎩ 0
if 1 < z ≤ 13.
(5)
Fig. 8. Powder flow rates (command and simulation).
if 14 < z.
The path was described given that nozzle was moved with a back and forth motion. The orientation, the height – 0.25 mm – and the width – 0.8 mm – of bead were defined constant in each point of the curve. All the process parameters were temporally expressed from the mathematical data of the path description. The commands A∗ and B∗ are determined from the expected material function (Eqs. (2) and (5)). The powder flow rates A and B are then deducted by simulation using the transfer functions (Fig. 6). The results are represented as functions of the manufacturing time (Fig. 8), knowing that the manufacturing time is determined from the machine axis speed and the path geometry. 4.3. Analysis The samples without pore and crack were obtained using the CLAD® process (Fig. 9). All the powder particles were melted.
Fig. 9. FGM test-part and microstructure.
The composition analyses were made all 0.5 mm on all elements present in 316L and Stellite 6. The comparison with results of simulation was made on four elements: chromium, cobalt, iron and nickel (Fig. 10).
Fig. 10. Chemical composition (wt.%) (y = 20 mm): (a) Chromium, (b) Cobalt, (c) Iron, and (d) Nickel.
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Fig. 12. Example: part description.
Fig. 11. Material function (simulated and measured).
Concerning the results of the simulation, concentrations of elements were determined from the simulated powder flow rates at the nozzle outlet A and B , for example: %Fe =
A A %Fe316L + 1 − A + B A + B
%FeStellite6
(6)
The material distribution of the test-part was determined with the chromium, cobalt, iron and nickel volume concentrations, which are representative of the presence of 316L and Stellite 6.
1 %316L = 4
×
5.2. Process control description
%Co − %CoStellite6 %Cr − %CrStellite6 + %Cr316L − %CrStellite6 %Co316L − %CoStellite6
%Fe − %FeStellite6 %Ni − %NiStellite6 + %Fe316L − %FeStellite6 %Ni316L − %NiStellite6
In view of powder distribution system operation, a powder flow rates control may be required in some cases. This control is proposed before the step of NC program generation. To illustrate this proposition, the system control is made to manufacture a test-part with an important difference between the simulated material distribution and the requested material distribution (Fig. 12). The manufacturing of the part was simulated. The geometry and the material distribution were described (Section 4.2). The path was described given that the nozzle is moved with a back and forth motion. The orientation vector, the height and the width of the bead were considered constant in each point of the curve. All the process parameters were temporally expressed from the mathematical data of the path description and the process operation modeling was made with transfer functions. The powder flow rates A and B are determined, they give a picture of the deposited material and the error over time (Fig. 13).
(7)
There is a good correlation between the simulated and the deposited material distributions (Fig. 11). The 316L concentration decreases continuously similarly to the simulated concentration. Although the results are satisfactory, we notice that simulated material distribution is close to the command. Other test-parts will have to be manufactured to validate the model. These test-parts will bring up a clear difference between the simulated and the requested material distributions. 5. Process control 5.1. Motivation
The first control concerns the delay. To make this control, the powder flow rates commands are advanced by a period of d = 1 = 3 = 6.2 s (Section 3.3). Using this first control, it is possible to cancel the impact of the delay (Fig. 14). In some cases this control may be sufficient to obtain a part in compliance with the desired material distribution. In other cases an additional control can mitigate the impacts of the powders distribution plates dynamic behavior. The second control is a predictive closed-loop control. It is based on the powder distribution system modeling without delay (Fig. 15). Signals are introduced in a closed-loop virtual system including a controller. The signals used to generate the NC program – noted A∗∗ and B∗∗ – are taken at the output of the controller and advanced to cancel the delay. The purpose of the controllers is to reduce the errors A∗ − A and B∗ − B . The two controllers – one concerning powder A and one concerning powder B – are chosen equivalent. They are
To ensure the fabrication of a part in compliance with the desired material distribution, it is necessary to manufacture with: A∗
A∗
+ B∗
=
A A + B
(8)
To ensure the fabrication of a part in compliance with the desired geometry, it is necessary to manufacture the bead with the powder flow rates determined for the formation of a bead with required dimensions taking into account other parameters: A + B = max
(9)
To ensure the fabrication of a part in compliance with the desired material distribution and the geometry, it is necessary to manufacture the bead with:
(8) (9)
⇔
A∗ = A B∗ = B
(10) Fig. 13. Material function without control.
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Fig. 14. Material function with compensation of the delay. Fig. 17. Influence of the parameters on the error.
Fig. 15. Virtual closed-loop control.
proportional-plus-integral controller (PI). They are defined by a transfer function: C(s) =
A∗∗ (s)
A∗ (s) − A (s)
= Kc × 1 +
1 c s
(11)
These controller – with Kc = 1 and c = 0.1 – are applied. The error is greatly reduced and nearly deleted with the coefficients chosen (Fig. 16). 5.3. Controllers parameters The PI controllers have two parameters Kc and c . These parameters have an influence on the final error and the signal form. By increasing the coefficient Kc and decreasing the coefficient c the error average decreases (Fig. 17). Beyond some limits, this effect is less important but high frequency fluctuations become significant. A control with a very important coefficient Kc enables to reduce strongly the error but the signals that are imposed on the distribution plates are not suitable. In this case high frequency fluctuations become too significant for the mechanism (Fig. 18). The coefficients should be chosen to ensure a final part in compliance with the desired geometry and the desired material
Fig. 18. Material function with control (Kc = 20 and c = 0.1).
distribution and to generate signals that are adapted to the system. In this example, the choice Kc = 1 and c = 0.1 is a good compromise between a very low error and signals that are adapted to the system. 5.4. Conclusion A comparison was made between the results obtained without control, with only a compensation of the delay and with a control (Kc = 20 and c = 0.1). To do that, the cartographies of performance index Imat were determined for these three cases (Fig. 19). The performance index represents, in each point of the domain D∗P , the global error concerning the material distribution. It is equal to one when the difference is null: Imat (x, y, z) = 1 − |M ∗ (x, y, z) − M(x, y, z)|
Fig. 16. Material function with control (Kc = 1 and c = 0.1).
(12)
Fig. 19. Performance index cartographies: (a) without control, (b) with compensation of the delay, and (c) with control.
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The manufacturing of this test-part in compliance with the desired material distribution can be achieved through a two-step procedure. This procedure is made before the step of NC program generation. First, signals are controlled by using a virtual closed-loop control based on the system modeling and a PI controller. Second, signals are advanced to compensate the delay. The coefficients selected should be established to ensure manufacture of the part with specification. The controllers coefficients are adapted according to the tolerance of the material function. 6. Conclusion and objectives for further research In this paper a modeling and a control of a direct laser powder deposition process for FGM parts manufacturing is exposed. The modeling takes into account all the steps of the manufacturing procedure, from the part description to the manufactured part. To model the process operation, experiments were conducted and two transfer functions are used to describe it. With this modeling it is possible to find an appropriate manufacturing strategy with the comparison between some strategies. Moreover, it is possible to control the signals used by the NC controller. The control is made before the step of NC program generation in two stages. First, the signals are control with a virtual closed-loop controls and a PI controller. Second, the delay is compensated. Further research will be conducted to manufacture functional FGM parts. The modeling will be used to compare manufacturing strategies to produce parts with complex material distribution. The choice of an adapted manufacturing strategy will be made by taking into account the possibility or not to correct signals. Acknowledgements This work was carried out within the context of the working group Manufacturing 21 which gathers about twenty French laboratories. The topics approached are: the modeling of the manufacturing process, the virtual machining and the emergence of new manufacturing methods. References Bandyopadhyay, A., Krishna, B., Xue, W., Bose, S., 2009. Application of laser engineered net shaping (LENS) to manufacture porous and functionally graded structures for load bearing implants. Journal of Materials Science 20, 29–34.
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