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Title:
NUMERICAL PROCESS SIMULATION OF ADDITIVE MANUFACTURING
Document Type and Number:
WIPO Patent Application WO/2019/070125
Kind Code:
A1
Abstract:
Numerical process simulation of additive manufacturing to predict, prevent, or compensate for adverse AM process effects, wherein computational simulation of the process steps executed during additive manufacturing is carried out with parallel computing using several computing devices. The simulation result of the individual process steps, in particular the calculation of the process response of the part or structure due to a newly printed or added layer, is computed completely independently and in parallel with the simulation of the other process steps. The distortion (and overall state) of the part or structure after a number of process steps is computed as the superposition of the distortion (state) of the individual process steps.

Inventors:
MUNRO DIRK (NL)
Application Number:
PCT/NL2018/050659
Publication Date:
April 11, 2019
Filing Date:
October 05, 2018
Export Citation:
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Assignee:
UNIV DELFT TECH (NL)
International Classes:
G06F17/50; B33Y50/02
Other References:
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CALCULIX DOCUMENTATION, VERSION 2.12, GUIDO DHONDT AND KLAUS WITTIG, 2017
Attorney, Agent or Firm:
VAN BREDA, Jacques (NL)
Download PDF:
Claims:
CLAIMS

1. Numerical process simulation of additive manufacturing to predict, prevent, or compensate for adverse AM process effects, wherein computational simulation of the process steps executed during additive manufacturing is carried out, charac- terized in that the simulation of the process steps executed during additive manufacturing is carried out with parallel computing using several computing devices.

2. Numerical process simulation of additive manufacturing according to claim 1, characterized in that the simulation result of the individual process steps of the part or structure due to a newly printed added layer, is computed independently and in parallel with the simulation of the other process steps.

3. Numerical process simulation of additive manufacturing according to claim 1 or 2, characterized in that the compu- tation of the cumulation of the process steps of a part or structure resulting from the AM process is executed as the superposition or summation of all separately calculated process responses due to each individual process step.

4. Numerical process simulation of additive manufac- turing according to any one of claims 1 - 3, characterized in that after each independent static equilibrium incremental process step computation, the deformations present in the part of the reference configuration which is not yet deposited (or solidified) are recorded.

5. Numerical process simulation of additive manufacturing according to claim 4, characterized in that after a process step of interest the so far accumulated initial deformation increments are superimposed to render an eventual equilibrium state .

Description:
Numerical process simulation of additive manufacturing

The invention relates to numerical process simulation of additive manufacturing to predict, prevent, or compensate for adverse AM process effects, wherein computational simulation of the process steps executed during additive manufacturing is carried out.

Additive manufacturing (AM) (or "3D printing') is a manufacturing technique which relies on building a part or structure bit by bit, from the bottom up, according to a series of time-dependent process steps. A process step is typically defined as each time a new "layer' is printed on top of the previous "layers 1 , eventually making up the complete part or structure. The part need not necessarily be seen as being composed of "layers': it might as well be seen to be composed of individual "blocks ' .

Building a part or structure with an AM process causes residual stresses in the part or structure, and the part or structure distorts. Therefore, design tolerances may be vio- lated. In practice, a multitude of slightly different versions of the part or structure may have to be fabricated by the said process in order to tune the shape of the part or structure and the process parameters, by trial and error, in an attempt to reduce the aforementioned phenomena to acceptable levels. In order to avoid these expensive and labour intensive trial and error procedures, numerical process simulation is resorted to.

Numerical process simulation is used to predict, prevent, or compensate for the adverse AM process effects, and avoid the need to actually build the physical part or structure on a trial-and-error basis. The issue is that AM processes are inherently transient by nature, involving hundreds or thousands of individual process steps (i.e., hundreds or thousands of printed " layers'). Therefore, sequential computational simulation of the process steps is extremely involved and slow, often requiring more time and effort to conduct the computations than the time required to build the physical part. This severely inhibits the design and development of parts and structures in the AM sector.

From a design-engineer's point of view, the main ad- vantage of AM is the liberty afforded in the (quick) realization of complex and efficient parts and structures-by exploiting, potentially, computational design-optimization techniques—with less assembly time and more flexible functional integrations. AM manufacturing techniques operate on a range of materials.

Especially metal AM is notorious for defects, dimen ¬ sional inaccuracy, and difficulties in micro-structural control. Megahed et al. [13] classify existing metal AM processes based on the manner in which the material is deposited prior to fu ¬ sion, referring to powder-bed, blown-powder, and wire-feed pro- cesses. The predominant metal AM technology is selective laser melting (SLM) , a powder bed process [14-18]. In general, metal AM technology is characterized by a localized heat (energy) input directed in such a way as to (at least partially) melt and fuse the deposited material with the existing structure. The phase changes and temperature gradients cause residual stress and part distortion [13, 15, 16] .

The properties of the deposited material and the action by which it is bonded or fused—in terms of thermofluid effects- determine the mechanical properties of the consequential struc- ture [14, 19-21]. Megahed et al. [13] highlight the multiphysics character of the process, and the fact that the small time and length scales associated with the heat source have to be accounted for (in comparison with the macroscopic scale of the part) . In varying degrees, the aforementioned phenomena contrib- ute to undesirable surface finishes and material properties, dimensional inaccuracy, degraded performance, and premature failure of the part in service. In short, violation of design tolerances. In the extreme, the part or structure may distort excessively and fail during the build, and thereby cause failure (typically obstruction) of the AM machine [22, 23] .

The complexities which per se accompany the strengths of AM implicate computational simulation in an attempt to predict, control, and potentially exploit the (undesirable) side- effects of the process [7] . If computational simulation is not available, costly and time-consuming physical trial-and-error experiments have to be resorted to [24-26] . Simulation technology permits a designer to compensate a priori for the process responses with design modifications [27], design-optimization of the part with respect to the process [28] , or optimization of the process itself as a function of the process parameters [16] .

Due to the predominance of thermomechanical effects, one branch of fast AM process simulation is focused on the efficient calculation of the thermal history of the build. Depending on the particular thermomechanical coupling—typically one-way— the temperature histories form the input to a macroscale mechan- ical analysis in order to predict residual stress fields and part distortion. Zeng and co-workers [29, 30] employ a dynamically meshed finite element (FE) model to reduce the number of degrees of freedom (and thereby reduce the computational burden) [29, 30].

Yang et al. [31] also manage to decouple (to some extent) the FE discretization from the accuracy of the thermal history calculation. To reduce computation time, cheap analytical solutions of the steep thermal gradients in and around the heat source are superimposed on a relatively course FE mesh

[31].

Both approaches [29-31] permit the simulation of specific scanning paths and patterns in SLM. However, Heigel et al.

[32] point out that a measurement-based convection model may be necessary in order to predict accurate thermal histories in metal AM. Moreover, Ghosh and Choi [19] advocate modelling of the phase transformation kinetics in laser-aided metal AM in order to calculate accurate residual stress distributions. Similarly, Mukherjee et al . [33] propose a transient heat transfer and fluid-flow SLM model—in order to simulate, in particular, the convective thermal interactions associated with the melt- pool—combined with a thermomechanical analysis to determine accurate macroscale stress and distortion. Yet, the computation of only the transient thermofluid fields in the equivalent of a 5- layer build (using an adaptive FE mesh) , requires about 5 hours of wall-clock time on a contemporary hardware platform (the simulation requires about 30 hours using a conventional ''brute- force' FE mesh) [34] .

With an eye on the computational burden, Neugebauer and co-workers [27, 35] develop a hierarchical multiscale computa- tional procedure (for SLM) whereby a generic microscale heat source model is mapped to a layer-wise hatching model, serving as input to a ^lumped' mechanical layer equivalent (MLE) analysis. Li et al. [36] adopt much the same approach. To the end of fast computation of the mechanical process responses, the sub- macroscale models are used to predetermine a so-called inherent strain, accompanying each layer in the MLE. Reportedly, calculation time is reduced by two or more orders of magnitude if the sub-macroscale phenomena are predetermined and averaged ('lumped') in this way.

The proposed method according to the invention takes the form of a set of software routines which permits the calculation of the effects due to building a part or structure with an AM process in a substantially reduced amount of time compared to state of the art methods.

In the method of the invention computational simulation of the process steps executed during additive manufacturing is carried out with parallel computing using several computing devices. The decrease in simulation time that can be achieved is dependent on the amount of parallel computation devices that are used. The method relies on the insight that a linear formulation of the transient AM process is satisfactory for accurately modelling the AM process. This permits the computation of the final distortion of the part or structure as the superposition (summation) of the process response due to each individual process step, simulated/computed independently. The implication of this is that the result of the individual process steps i.e., the distortion of the structure due to a newly printed "layer' is computed completely independently and in parallel (instead of sequentially) . This reduces the amount of time required to conduct the simulation from days, weeks or months, to a number of minutes.

The method of the invention does not rely on any particular programming language. It is for instance possible that the software routines which exploit the method are coded in a combination of Fortran, C, Python and Linux bash scripting.

Furthermore the software is not platform specific, and trivially portable to other platforms. It does not rely on a graphical user interface (although it could) , and it requires no other products or applications.

In a current implementation a free and open source fi- nite element simulation package called " Calculix&#8217 ; is used to simulate the individual process steps (in parallel) . Note however that the method is independent of the software used to simulate the individual process steps of the AM process.

Calculix is free software; it can be redistributed and/or modified under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or any later version.

In Figure 1 flowcharts of the prior art conventional (sequential) AM process simulation (left) and the parallel process-step AM simulation (right) is given. Throughout, to compute static equilibrium is meant to imply that a set of equations of the form

is assembled and solved.

The following description is exemplary and not restric- tive for the appended claims, which indeed do not comprise any of the limitations set forth in the following example. To avoid any doubt it is explicitly remarked that the invention is not confined to isotropic inelastic deformation increments, and the following example is merely a simple representation setting forth the principles of the invention.

In the following example the processed material is taken to be isotropic, with for instance a constant Young' s modulus of 125 GPa and a Poisson ratio of .333. Of course these values are completely arbitrary, and do not influence the manner of computation according to the invention, nor the time required to conduct the computation.

Each process step is taken to cause an isotropic increment in the inelastic deformation components associated with the new part of the configuration (the new layer or block in that step), with the principal components prescribed at Δε^ Ρ)ί = - 0.005. This value is taken to be representative of a thermal contraction from the melting temperature of the material to the temperature of the build chamber.

In general, after each independent static equilibrium increment computation, the deformations present in the part of the reference configuration which is not yet deposited (or solidified) are recorded — this does not, however, involve a static equilibrium computation. Subsequently, the accumulated initial deformation increments are superimposed to render the equilibrium state after a process step of interest (after the build, for example) .

The final equilibrium state is the starting point for the modelling of the ^posterior' nonlinear elastoplastic material law, to the end of accurate stress predictions.

The static equilibrium increment may be written in terms of the (newly extended) system-level stiffness matrix

ΚΔΰ = Δ (1) and the increment in the equivalent nodal loads; that is

K = D r [0]SD[0], and Δ? ¾ = Ϊ> Γ [0]8Δ£ 4 , respectively.

The initial deformations ° required to fit the new part of the configuration to the old part in a stress-free man- ner, have dropped out for the representation of the current state of the configuration: a static increment is computed with respect to a stress-free reference configuration. Inelastic deformation increments in either or both the pre-existing or new part of the configuration Δ έ are taken to be representative of thermal deformations, or predetermined inherent deformations.

The linear formulation of the AM process model permits quick and easy computation of the equilibrium state of the configuration. The incremental conditions for static equilibrium after each process step and the quantities required in the defi- nition of the material law, render the relative increment in the state of the configuration according to equation (1) computable completely independent. The implication is that the static equilibrium increment generated by each and every process step in the linear AM simulation may be computed independently and in parallel.

Next the speed-up in wall-clock time will be discussed which may be achieved by exploiting parallel process-step com- putability in the linear regime as employed in the invention. For the sake of brevity, only a layer-wise version of the AM process model is considered. It is obvious that the necessity of employing the known Newton' s method in every step of a prior art sequential, nonlinear elastoplastic simulation is much more time-consuming than the linear case appended with an elastoplastic step according to the invention. The wall-clock times required to simulate the linear part of the layer-wise AM builds are measured and summarised in Table 1. Table 1: Problem sizes for wall-clock time measurements of par ¬ allel process-step computation and superposition.

Per Layer Total

Layers Elements dofs Elements dofs

10 100 363 1000 3993

20 400 1323 8000 27783

30 900 2883 27000 89373

40 1600 5043 64000 206763

50 2500 7803 125000 397953

60 3600 11163 216000 680943

70 4900 15123 343000 1073733

80 6400 19683 512000 1594323

90 8100 24843 729000 2260713

100 10000 30603 1000000 3090903

The wall-clock time measurements show that process-step parallelization is an simple avenue for computation of AM pro- cess simulations in a reasonable amount of wall-clock time.

Moreover, process-step parallel computation illustrates rather nicely the nature of AM process simulation in the linear regime.

The structural configurations range from small — 10 layers made-up of 1000 elements in total — to large— refined to 100 layers, made-up of 1,000,000 elements in total. The wall- lock times required using a 4-core laptop architecture (i7- 4770HQ CPU 2.20GHz, 7.7GB RAM), considering the 10-50 layer AM builds, are plotted in Figure 2a. Using more than one core, the parallel process-steps are arranged in such a way that each core is tasked with roughly an equal computational burden (in terms of the sizes of the configurations corresponding to each process-step increment) . Using 2 cores, wall-clock time is halved, approximately. Using 3 and 4 cores, wall-clock time is reduced further, although the relative speed-up diminishes due to the increased levels of data handling and cross-core communication.

The wall-clock times achieved on a computational cluster, applying 10-50 cores on the 50-100 layer builds, are shown in Figure 2b. The same wall-clock time scaling as in the small- scale (laptop) setting is observed. For both the small- and large-scale implementations a modified version of CalculiX [46] (a free and open-source FE analysis code) is used. Although the invention has been discussed in the foregoing with reference to an exemplary embodiment of the apparatus of the invention, the invention is not restricted to this particular embodiment which can be varied in many ways without de- parting from the invention. The discussed exemplary embodiment shall therefore not be used to construe the appended claims strictly in accordance therewith. On the contrary the embodiment is merely intended to explain the wording of the appended claims without intent to limit the claims to this exemplary embodiment. The scope of protection of the invention shall therefore be construed in accordance with the appended claims only, wherein a possible ambiguity in the wording of the claims shall be resolved using this exemplary embodiment. References

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