A machine learning-based digital twin of the manufacturing process: metal powder-bed fusion case

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I. INTRODUCTION
Additive manufacturing is increasingly used for serial production and holds great promises to revolutionize the traditional manufacturing system by enabling new higher-level performance parts and totally unique business models such as distributed manufacturing. In metal powder bed fusion (PBF), the high scrap rate has a substantial impact on the cost and therefore the adoption of additive manufacturing. Multiple software solutions based on finite element approaches have emerged to address some of these issues. These technologies are aiming at optimizing the build preparation including the support and the part orientation to minimize the distortions.
Nonetheless, other challenges leading to scrap cannot be solved on the component level but are a consequence of a sub-optimal vector and process parameters selection. The combination of short scanning vectors and overhang areas can lead to the increase of the meltpool size yielding an accumulation of material that is at the origin of multiple recoating collisions. Further, these overheated zones are usually resulting in inconsistent microstructures and properties due to the different thermal history. To the knowledge of the authors no one has solved this problem for PBF previously. While the thermal history in small excerpts induced by a laser propagating through the part can be simulated using finite element approach, the large spread in spatial and time scales renders it an impossible task to simulate a whole part on the scale of the melt pool dimensions.
Leveraging synthetic data obtained from appropriate FEM simulations for a machine learning model can help to overcome this problem [3]. In [4,5] the authors show how the calculation of the thermal history in a direct energy deposition (DED) process can be applied to a whole part using machine learning.
In section 2, the novel machine learning framework is introduced providing detailed elements on the architecture of the solution. Then, the validation approach of the methodology and specifically how the physics-based synthetic data are verified is outlined. A use case is described based on a complex aerospace geometry made of Inconel 718. Finally, we conclude our results and provide a hint about how such a framework could be extended from its actual process planning usage to a future self-healing use case.

II. MATERIALS AND METHODS
The intelligent path analyzer approach reported here can be divided into two major parts: the training part and the simulation part (see Fig. 1). Key starting point to perform a thermal simulation of the full powder bed fusion process to print a part -including the exact and complete exposure path -is to overcome the well-known problem of the spread of spatial and times scales when applying a finite -element based method (FEM). A common approach is to separate thermal simulations according to its scales as follows [6]: Here, the reference temperature T 0 is obtained from a macro-scale simulation of the complete workpiece as the long-time temperature, averaged over a layer after the exposure [7]. The fastchanging part T fast is the short time behavior induced by the local propagation of the laser following the set exposure path. Combined, they provide the full thermal transient. The macro scale simulation can be applied to a whole part to print and is the starting point of the simulation procedure (see right-hand side of Fig. 1). However, a thermal model needs to be set up to obtain the fast changing part based on the concrete exposure path provided by the build processor.
This renders a training procedure necessary to obtain the thermal model (see left-hand side of In order to calibrate the span of criticality with respect to local overheating, a set of simple specimens provoking a range of overheating are printed and accordingly to those results the relevant thresholds for criticality are set. This is the second part of the calibration procedure ensuring the correctness of the simulation of the intelligent path analyzer.

III. RESULTS
The described algorithm is seamlessly integrated as AM Path Optimizer in the NX AM build This proves the successful avoidance of the overheating effect. Whereas for the results depicted in Fig. 3 delay times have been introduced in order to correct local overheating, the thermal information obtained in the described method allows to implement a much more sophisticated corrective strategy combining an optimization approach with heuristics for the improved design of exposure strategies that SIEMENS have experimented on other use cases.

IV. DISCUSSION
We have introduced a new digital twin of the manufacturing process for metal powder bed fusion. This digital twin can simulate the transient temperature at each point and thus detect issues such as overheating. The framework is based on a machine learning algorithm trained on experimentally validated, synthetic data obtained from a finite element approach. The algorithm considers the scan strategy, the laser parameters, the materials properties and the part geometry.
With this framework we have introduced a first machine learning based digital twin of the powder bed fusion process used as a robust tool to perform predictive and corrective process planning and speed up of the computation compared to finite element approach with a factor of 10 7 without parallelization. Future work consists in using a similar framework trained on in-process monitoring data, thus achieving in process, corrective, or self-healing capabilities, where up-front simulation and in-process data stimulate each other.