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\begin{document}

\title[Article Title]{Experimental and Computational Study on the Influence of
Recoater Geometry, Recoating Speed, and Layer Thickness on
Recoater Collision}

%%=============================================================%%
%% GivenName	-> \fnm{Joergen W.}
%% Particle	-> \spfx{van der} -> surname prefix
%% FamilyName	-> \sur{Ploeg}
%% Suffix	-> \sfx{IV}
%% \author*[1,2]{\fnm{Joergen W.} \spfx{van der} \sur{Ploeg} 
%%  \sfx{IV}}\email{iauthor@gmail.com}
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\author[1]{\fnm{Radek} \sur{Skácelík}}\email{radek.skacelik@fs.cvut.cz}

\author[2]{\fnm{Václav} \sur{Vrzal}}\email{vrzal@fzu.cz}
\equalcont{These authors contributed equally to this work.}

\author[1]{\fnm{Miroslav} \sur{Španiel}}\email{miroslav.spaniel@fs.cvut.cz}
\equalcont{These authors contributed equally to this work.}

\author*[1]{\fnm{Michal} \sur{Bartošák}}\email{michal.bartosak@fs.cvut.cz}
\equalcont{These authors contributed equally to this work.}

\affil*[1]{\orgdiv{Department of Mechanics, Biomechanics and Mechatronics, Faculty of Mechanical Engineering}, \orgname{Czech Technical University in Prague}, \orgaddress{\street{Technicka 4, Praha 6}, \city{Prague}, \postcode{16000}, \country{Czech Republic}}}

\affil[2]{\orgdiv{Institute of Physics}, \orgname{Czech Academy of Sciences}, \orgaddress{\street{Na Slovance 2}, \city{Prague}, \postcode{18221}, \country{Czech Republic}}}

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\abstract{Laser Powder Bed Fusion (LPBF) was used as a cost-effective, sustainable alternative to conventional subtractive methods. In this study, a finite element model was developed to investigate the effects of recoater geometry, recoating speed, and layer thickness on the mechanical performance of printed parts. The model incorporated a temperature-dependent elastic–plastic material law. Two blade types were were tested experimentally: a compliant rubber blade and a rigid ceramic blade. The experimental findings were used in the simulation as a print-failure criterion. The results validated the fixture-based measurements, demonstrating that the compliant blade did not impose significant mechanical stress on the printed part, even when the gap beneath the blade was fully closed. It was found that increasing the cooling time before depositing a new layer reduced the likelihood of build failure due to collisions between the sample and the recoater blade.}

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% \textbf{Results:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.
% 
% \textbf{Conclusion:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.}

\keywords{Finite element method, Laser powder bed fusion, Recoater, Additive manufacturing}

%%\pacs[JEL Classification]{D8, H51}

%%\pacs[MSC Classification]{35A01, 65L10, 65L12, 65L20, 65L70}

\maketitle

\section{Introduction}\label{sec1}

Metal additive manufacturing has emerged as a transformative approach to industrial production, enabling the fabrication of geometrically intricate components with high material efficiency and reduced lead times \cite{DUPLESSIS2022100918, HAMDI2025107402,LUO2025106561,REHAN2025104635,OBEIDI2022100473}. Among the available technologies, Laser Powder Bed Fusion (LPBF) stands out for its precision and suitability for high-performance applications \cite{PLOCHER2019108164,Yap,HERZOG2016371,CHOWDHURY20222109,DUPLESSIS2022100918}. In LPBF, a high-power laser selectively melts thin powder layers to build parts layer by layer \cite{DEBROY2018112}. Process stability, however, hinges not only on laser exposure but also on the quality and repeatability of powder spreading: powder flow behavior, recoater geometry and compliance, and build-induced distortion can reduce the effective recoating margin and trigger anomalies ranging from transient contact to full recoater crashes \cite{LE2021101890,CRAEGHS2010505}. Failure-focused studies further show that build interruptions, build height, scan strategy, and hatch spacing modulate defect morphology (lack-of-fusion vs. keyhole porosity) and shift failure locations under static and fatigue loading across alloys from Al-Si to Ti-6Al-4V \cite{Mahtabi2023_Interruption_EFA,Mahtabi2023_BuildHeight_EFA,Sarparast2024_Raster_EFA,Riju2024_Hatch_EFA,Li2024_AlSi_EFA,Risposi2025_Surface_EFA}. These trends motivate a closer examination of recoater-part interactions and the clearance available during spreading.

Recoater crashes generally originate from thermally driven distortions that raise the local build surface above the nominal powder layer, a condition that is especially likely in thin-walled or otherwise low-stiffness features \cite{Wu2020,Reijonen2024_IJAMT_Recoater}. When layer-wise vertical displacements exceed the available clearance, contact with the blade becomes likely and can jeopardize the ongoing layer \cite{CHAKRABORTY2022233}. Once contact is initiated, powder disturbance and blade dynamics can spread the effect laterally, so a localized protrusion may compromise adjacent regions of the layer \cite{LE2021101890}. Even brief planned or unplanned pauses may imprint weakness planes or porosity bands that subsequently bias crack initiation under static and fatigue loading \cite{Richardsen2023_BuildPause_EFA,Mahtabi2023_Interruption_EFA}. Energy input links consolidation quality with distortion and surface asperities: excessive values promote keyholing and swelling, whereas short scan tracks and moderate power reduce the probability of protrusions that trigger contact \cite{PROMOPPATUM2017262,Wang2013,WANG20131734,Yakout2017}. Choices in scan strategy, notably raster orientation and hatch spacing, further steer stress redistribution and defect pathways \cite{Sarparast2024_Raster_EFA,Riju2024_Hatch_EFA}. At elevated temperatures, thermo-mechanical response can amplify defect sensitivity in nickel-based systems \cite{Lu2025_GH3536_ThermoMech_EFA}. Beyond laser–material interaction, recoating hardware and kinematics also matter, since blade material and speed influence layer uniformity and the balance between inter-layer cooling and thermal accumulation \cite{LE2021101890,met12111782,Yuasa2021_IJAMT_PowderBed}. Altogether, these effects determine the effective clearance during spreading and, therefore, the likelihood of recoater–part contact.

Given the vast design and parameter space, physics-guided models are essential to rationalize thermal fields, distortion, and flaw formation and to translate process settings into quantitative risk indicators \cite{LIU2017351,Guo2013,huang,Babu2015}. In routine use, fast finite-element simulations provide layer-wise temperature histories and displacement fields at the part scale, while in-situ monitoring contributes complementary evidence of evolving surface condition and height variations; the two streams are increasingly combined for early deviation detection and process understanding across LPBF systems \cite{SIMPSON2017166,KNAPP2017390,MARTUKANITZ201452,Strano2013,Peralta2016,JARED2017141,DRUZGALSKI2020101169,Martin2019,Gaikwad01112020}. Commercial and research tools implement acceleration strategies (reduced domains, adaptive meshing, scan-path abstractions) to keep runtimes compatible with design iteration, yet reported predictions still vary across codes and machines and therefore require independent validation against targeted measurements before serving as acceptance checks \cite{PETER2020101531,ZHANG2019610,LUO2018318,Lee2018_IJAMT_PowderPacking}. Alongside these developments, comprehensive reviews of metal AM modelling and validation highlight the importance of calibrating thermal–mechanical responses and reporting uncertainty when models are used to support build decisions \cite{DebRoy2018_PMS_Review,Khorasani2020_IJAMT_Review}. In parallel, defect-aware frameworks connect surface condition and pore populations to performance, including surface-roughness-aware simulations, residual-stress models informed by surface treatments, and extreme-value statistics for pore distributions \cite{Cao2024_SP304L_EFA,Pal2024_SurfaceRoughness_EFA,Yang2025_EVA_EFA}. Mesoscale damage analyses coupled with tomography clarify how pore morphology and interactions govern damage evolution, while probabilistic approaches help prioritise risk-critical defect states for inspection and qualification \cite{Dastgerdi2025_Mesoscale_EFA,Centola2025_ProbML_EFA}. In this context, a build-level decision rule for recoater–part contact that operates on standard model outputs and is anchored in direct measurements of contact onset provides a practical bridge from modelling and monitoring to actionable pre-build screening.


The objective of this study is to develop a robust criterion for predicting recoater-part collisions in LPBF. The criterion was established experimentally from strain-gauge measurements on a dedicated test rig, yielding collision thresholds that are compared in simulation with model-predicted layer-wise vertical offsets. The effect of near-surface asperities is not evaluated explicitly by the model and is accounted for through these experimentally measured thresholds. The thresholds were then embedded in finite element simulations as a build-level acceptance check and applied across relevant settings and geometries. Predictions were compared with controlled printing outcomes and showed good agreement, demonstrating that experimentally measured collision thresholds can be integrated into numerical workflows and enable practical pre-build screening. The approach supports improved process reliability and a reduced risk of build failures in LPBF while remaining compatible with standard modeling outputs and routine reporting. This paper is organized as follows: Sections~\ref{Measurement setup} and~\ref{Experimental setup} describe the experimental methods and fixture design, Section~\ref{Numerical model} presents the FE model and the implementation of the criterion, Section~\ref{Results and discussion} reports and discusses the results, and Section~\ref{Conclusions} summarizes the main conclusions.

\section{Measurement and samples}
\label{Measurement setup}
In this work, experiments were performed on a Trumpf TruPrint 1000 printer. A schematic and figures of the device are shown in Fig.~\ref{schema}.


% v preambuli: \usepackage{subcaption} \usepackage{tikz} \usepackage{graphicx}
\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  % (a) Schematic
  \begin{subfigure}[t]{0.6\textwidth}
  \caption{}
    \begin{tikzpicture}
      \node[anchor=south west,inner sep=0] (imgA) at (0,0)
        {\includegraphics[width=\linewidth]{schema.png}};
      % normované souřadnice 0..1 přes rozměr imgA
      \begin{scope}[x={(imgA.south east)},y={(imgA.north west)}]
        \draw[{Latex[length=2mm]}-,thick] (0.36,0.72) -- (0.20,0.85)
          node[above left=2pt] {\small recoater};
        \draw[{Latex[length=2mm]}-,thick] (0.50,0.38) -- (0.35,0.09)
          node[below left=2pt] {\small build platform};
        \draw[{Latex[length=2mm]}-,thick] (0.53,0.65) -- (0.57,0.70)
          node[above right=2pt] {\small sensor placement};
      \end{scope}
    \end{tikzpicture}
    \label{schema}
  \end{subfigure}%
  %
  \begin{subfigure}[t]{0.38\textwidth}
  \caption{}
    \begin{tikzpicture}
      \node[anchor=south west,inner sep=0] (imgB) at (0,0)
        {\includegraphics[width=\linewidth]{pripravek.jpg}};
      \begin{scope}[x={(imgB.south east)},y={(imgB.north west)}]
        \draw[{Latex[length=2mm]}-,thick] (0.27,0.40) -- (0.60,0.20)
          node[right=2pt,fill=white] {\small strain gauge};
        \draw[{Latex[length=2mm]}-,thick,draw=white] (0.55,0.68) -- (0.65,0.78)
          node[right=2pt,fill=white] {\small GSV-6 unit};
        \draw[{Latex[length=2mm]}-,thick,draw=white] (0.30,0.79) -- (0.15,0.95)
          node[left=2pt,fill=white] {\small sample};
        \draw[{Latex[length=2mm]}-,thick,draw=white] (0.5,0.1) -- (0.05,0.25)
          node[pos=0.5, sloped, below =2pt,fill=white] {\small recoater direction};
      \end{scope}
    \end{tikzpicture}
    \label{fig:pripravek}
  \end{subfigure}

  \caption{Placement of the measurement setup in the Trumpf TruPrint 1000 machine: (a) schematic showing sensor placement, and (b) measurement setup with the GSV-6 unit.}
  \label{fig:measurement_setup}
\end{figure}

An assembly was positioned on the printer platform, which was equipped with full-bridge strain gauges. The orientation of the measuring assembly was aligned directly with the coating device. The position of the fixture on the platform was secured using dowel pins. The force gauges were placed symmetrically along an axis perpendicular to the movement direction of the coating equipment. The relative positions of the sample edges to the platform center are illustrated in Fig.~\ref{schema}.% obrazek tiskarny
The fixture was calibrated by applying a known force at the sample location and the resulting responses of the strain gauge were recorded. Measurements were carried out using a GSV6 measuring station \cite{gsv6bt_manual}, located in the printing area alongside the measuring set-up. The measuring station's sampling frequency was set to 2778 Hz, with a sensitivity of 1-2 mV/V.
%upnutí vzorku a poloha připravku na platformě

The samples were first additively manufactured and then placed in the measuring fixture, where they were clamped to the prismatic seating surfaces (Fig.~\ref{fig:pripravek}). During the measurement, additional layers were deposited onto the pre-printed part. The deposition on the top surface of the samples did not require support structures. The geometry of the individual samples is described later in this section. All samples were manufactured from 316L stainless steel (AISI~316L) and tested in the as-built (as-printed) condition, i.e., without any post-processing. The position of the sample within the measuring assembly was selected to ensure safe behavior in the event of inadvertent contact with the recoater blade. The measuring fixture was designed such that such contact induces a controlled deflection of the sample away from the blade, thereby clearing the recoater path and allowing the subsequent pass to proceed without damage to the machine or the measuring fixture. This was achieved by positioning the leading edge of the sample such that, in the event of deflection, the predicted trajectory of the sample remains outside the recoater travel path, preventing any intersection of the two trajectories. The LPBF printing parameters used for all samples are provided in Table~\ref{tab:lpbf_params_316L_core_amount}.


The alignment of the top layer of the sample after clamping in the fixture is ensured by applying 15 layers of printing. This process guarantees that the top layer is properly aligned and that the rotation of the part relative to the recoater is precisely at the desired angle.
Measurements were conducted on printed samples positioned within the measuring fixture. The strain gauge response was calibrated following the clamping of each new sample.

Two types of recoater blades were employed: a rubber blade and a ceramic blade. The blade geometries are shown in Fig.~\ref{fig:blades}. This configuration enabled the quantification of differences in recoating pressure between the rubber and ceramic recoaters.

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \makebox[0.63\textwidth][c]{%
    \begin{subfigure}[b]{0.25\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{keramickyBrit.png}
     \label{fig:ceramic_recoater_blade}
    \end{subfigure}%
    \begin{subfigure}[b]{0.38\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{gumaBrit.png}
     \label{fig:ruber_recoater_blade}
    \end{subfigure}%
  }

  \caption{}
  \label{fig:blades}
\end{figure}
Following the application of leveling layers, recoater crossings were measured with each new layer application. The thickness of these layers was systematically reduced from 20~\textmu m in increments of 2.5~\textmu m until reaching a thickness of 10~\textmu m. Subsequently, the value was further adjusted at a larger measurement range to 5~\textmu m. The measurement range established by the ceramic recoater was utilized as the nominal range for measurements conducted with the rubber recoater, where collisions with the part are less easily detectable. To mitigate measurement distortion caused by the application of thinner layers, an additional layer was consistently applied after the measurement layer, thereby restoring the total layer thickness to the nominal level. The procedure consisted of multi-layer powder recoating. The first deposited layer served as the measuring layer, whereas the subsequent layer(s) compensated for the difference between the measured layer thickness and the nominal layer thickness for which the process parameters were defined. Consequently, the process parameters were not influenced by variations in the thickness of the measuring layer.Within the measuring layer, the desired layer height was maintained by processing a fictitious body with predefined layer thicknesses. No actual printing of this body was performed, as the laser was kept deactivated; it was activated only for printing at the required nominal heights.



\begin{table}[t]
  \setlength{\tabcolsep}{4pt}
  \small
  \centering
  \caption{LPBF process parameters for AISI~316L (as-built). Layer height $t=\SI{20}{\micro\metre}$ for all builds.}
  \label{tab:lpbf_params_316L_core_amount}
%  \sisetup{round-mode=places, round-precision=0, zero-fill=false}
  \begin{tabular}{
      S[table-format=3]   % P (W) integers
      S[table-format=4]   % v (mm/s) integers
      S[table-format=3]   % h (µm) integers
      S[table-format=2]   % t (µm) integers
      l                   % strategy text
    }
    \toprule
    {$P$~(W)} & {$v$~(mm/s)} & {$h$~(\si{\micro\metre})} & {$t$~(\si{\micro\metre})} & {Strategy} \\
    \midrule
    200 & 800 & 90 & 20 & chessboard (\ang{90}) \\
    \bottomrule
  \end{tabular}
\end{table}

The sample geometries were designed to capture the broadest possible range of factors affecting the force exerted on the part during recoating. For collision detection, the nominal frictional interaction with the top surface must be established first; therefore, an L-shaped geometry was selected. Owing to the extended traversal distance over the L-shaped feature, the recoater remains in contact with the part for a longer time interval, enabling stable measurements even at higher recoating velocities. Accordingly, for the L-shaped specimen (Fig.~\ref{fig:Lshape}), the recoating speed was varied while the nominal layer thickness was kept constant. For both recoater types, the recoating speed was increased in 10~mm/s increments from 20 to 200~mm/s, and ten recoating passes were recorded at each speed. This geometry provides a constant-dimension top-surface region over which the nominal frictional response can be determined.


\begin{figure}[ht]
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering
  \makebox[0.96\textwidth][c]{%
    \begin{subfigure}[t]{0.32\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{E90.png}
      \label{fig:45}
    \end{subfigure}%
    %
    \begin{subfigure}[t]{0.32\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{3x3.png}
     \label{fig:3x3}
    \end{subfigure}%
    %
    \begin{subfigure}[t]{0.32\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{L.png}
      \label{fig:Lshape}
    \end{subfigure}%
  }

  \caption{Samples with modified edge (dimensions in mm): (a) 45 degrees edge sample (E90); (b) 3×3 sample; (c) L-shape sample.}
  \label{fig:dva_obrazky}
\end{figure}
To recognize the effect of the magnitude of the force on the size of the face area, T-shaped solids with graduated contact edge widths of 3, 6, 24, and 48 mm were chosen (Fig.~\ref{fig:3x3} and \ref{fig:Tshape}). Their orientation was selected to be parallel to the recoater blade, which is assumed to be the worst possible alignment of the part relative to the recoater's direction of motion.
\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \makebox[0.97\textwidth][c]{%
    \begin{subfigure}[t]{0.23\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{T6.png}
      \label{fig:t6}
    \end{subfigure}%
    %
    \begin{subfigure}[t]{0.32\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{T24.png}
     \label{fig:t24}
    \end{subfigure}%
    %
    \begin{subfigure}[t]{0.42\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{T48.png}
      \label{fig:t48}
    \end{subfigure}%
  }

  \caption{Samples with perpendicular leading edge (dimensions in mm): (a) sample type T6; (b) sample type T24; (c) sample type T48.}
  \label{fig:Tshape}
\end{figure}
To compare the effect of the rotation of the contact area, a specimen with edges oriented at 45 degrees (Fig.~\ref{fig:45}) to the plane of the recoater was chosen. The total width of the specimen is 6 mm, allowing for a comparison of the rotational effect with the same face of the part.


The subsequent set of samples comprises those with cylindrical contact surfaces. These specimens are fabricated as half-cylinders, featuring a 6mm flat region at the posterior. This design facilitates the detection of changes in friction on the upper surface and assesses the impact of increasing contact area on the resulting force. The specimens were produced in diameters of 6, 12, and 24 mm (Fig.~\ref{fig:Dsamp}).
\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \makebox[0.97\textwidth][c]{%
    \begin{subfigure}[t]{0.23\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{D6.png}
      \label{fig:d6}
    \end{subfigure}%
    %
    \begin{subfigure}[t]{0.32\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{D12.png}
      \label{fig:d12}
    \end{subfigure}%
    %
    \begin{subfigure}[t]{0.42\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{D24.png}
      \label{fig:d24}
    \end{subfigure}%
  }

  \caption{Samples with cylindrical leading edge (dimensions in mm): (a) sample type D6; (b) sample type D12; (c) sample type D24.}
  \label{fig:Dsamp}
\end{figure}

\section{Validation Experiment}\label{Experimental setup}
The experimental measurement results are used in the mathematical simulation as a print failure criterion. This criterion is expressed as the size of the gap between the coating device and the printed part. This gap is evaluated at the time corresponding to the passage of the coating device.
This time is determined by knowing the length of the coating and printing time loop for each layer.

The samples on which the criterion is tested have a constant cross section throughout their height. This means that the length of the time loop does not change and is constant throughout the printing process. This time loop consists of the time of the laser welding and the deposition of the new powder layer, in addition to the stabilization cooling time. This stabilization artificially extends the print loop time to prevent overheating of the printed sample. Placing this cooling delay within the print cycle allows the coating device to pass through different sample temperatures while maintaining the same print parameters.

The tested samples are thin sheets with a uniform width of 6 mm, corresponding to the width of the samples used in the previous section. The thickness of each sample is graded from 0.25 mm in increments of 0.05 mm up to 0.9 mm (Fig.~\ref{fig:usporadaniPlatformy}). The samples of the same thickness are arranged so that their position relative to the width of the applicator blade allows evaluating the influence of sample placement within the build area. Three rows of samples were selected to account for the time interval between consecutive passes of the applicator blade across the rows. This arrangement is illustrated in Fig.~\ref{fig:usporadaniPlatformy}, where the numbering of the samples corresponds to their thickness, with the highest numbers indicating the thinnest samples.
\begin{figure}[H]
    \centering
    \includegraphics[scale=0.45]{platformaUsporadani.png}
    \caption{Sample arrangement on the 3D printer build platform.}
    \label{fig:usporadaniPlatformy}
\end{figure}

The calculation was performed using the OOFem program in which two types of time distributions of the printing loop were simulated. In one case, the cooling delay time was placed at the end of the printing cycle, i.e. after a new layer of powder was applied. In the second case, the delay was placed prior to the application of the new layer of powder.

\section{Numerical model}\label{Numerical model}
To be able to effectively predict the risk of collision between the coating device and the printed model, it was necessary for computational power reasons to use a simplified computational model that does not take into account the individual laser motion paths. This simplification uses modified layers to represent the behavior of the printed layers. This makes it possible to compute the whole body at once. The balance of time and energy is applied depending on the number of layers and is performed according to \cite{ZHANG2019610}. This allows us to calculate the temperature and material response.

\subsection{Thermal heat transfer analysis}
The governing equations for the transient heat conduction problem are given as:
\begin{equation}
    \rho c_p \frac{\partial T}{\partial t} =  \frac{\partial}{\partial x} \left( k \frac{\partial T}{\partial x} \right) + \frac{\partial}{\partial y} \left( k \frac{\partial T}{\partial y} \right) + \frac{\partial}{\partial z} \left( k \frac{\partial T}{\partial z} \right) + Q
\end{equation}
\begin{equation*}
T(x;t) = T_p \text{ on } \varGamma_D
\end{equation*}
\begin{equation*}
k \frac{\partial T}{\partial x} = h(T(x;t)-T_\infty) \text{ on } \varGamma_h,_x
\end{equation*}
where \(\rho\) denotes density, \(C_p\) represents thermal capacity and \(k\) signifies thermal conductivity. Heat generated by plastic deformation is excluded from the calculation. \(\varGamma_D\) indicates a Dirichlet boundary condition with a prescribed temperature \(T_p\). \(Q\) represents the heat source and \(\varGamma_{h,x}\) denotes the Robinson boundary condition for the x direction of the heat flux, where \(h\) is the heat transfer coefficient and \(T_\infty\) is the ambient temperature. This principle is similarly applicable to the other two directions.
\subsubsection{Heat source}
To expedite the simulation process for the entire component, the laser's movement across the surface is simplified by uniformly heating the entire volume of the top layer during the laser's application time in the given area of the layer. The size of the volumetric heat source is determined by the power and motion parameters of the laser.\cite{LI2016171} %odkaz na parametry tisku
The heating and cooling time are controlled by the internal time step of the layer. The energy balance following the use of a mesh size larger than the thickness of the layer is identical to the procedure in \cite{ZHANG2019610}. The size of the thermal source is then represented in the simulation as a \(Q_v\) volume heat source.
\begin{equation}
    Q_v = \frac{P\cdot A}{L\cdot l\cdot h}
    \label{eq:energie}
\end{equation}
where P is the power of the laser beam, A is the absorption of the heat source and \(L\),\(l\),\(h\) are the dimensions of the mesh.

Layer-wise deposition is modeled using the concept of birth-and-death elements. In this technique, the model of the printed part is initially in the base state, which effectively represents the 'death state.' This state is simulated by assigning near-zero stiffness to the corresponding elements, rendering them inactive in the mechanical and thermal analysis until they are "born" during the simulation. As the printing process progresses, elements are sequentially activated to reflect the deposition of the material.
\subsection{Structural analysis}
Quasi-static mechanical analysis is used to evaluate the mechanical response, including residual distortion and thermal stresses of the simulated part. The thermal history obtained from the preceding thermal analysis is applied as an external load and boundary condition to the model. The governing equation is
\begin{equation}
\nabla \cdot \sigma + \mathbf{b} = 0 \quad (r\in\Omega)
\end{equation}
where $\Omega$ is the computational domain, $\mathbf{b}$ is the body force per unit volume, and $\sigma$ is the Cauchy stress tensor. A temperature-dependent elastic–plastic constitutive model with isotropic hardening is employed. The total small strain $\epsilon$ is additively decomposed as
\begin{equation}
\epsilon = \epsilon^e + \epsilon^p + \epsilon^{th}, \qquad
\epsilon^{th}(T) = \Big(\int_{T_{ref}}^{T}\alpha_e(\theta)\,\mathrm{d}\theta\Big) I
\end{equation}
where superscripts $e$, $p$, $th$ denote elastic, plastic, and thermal parts, respectively; $\alpha_e(T)$ is the coefficient of thermal expansion, $T$ the instantaneous temperature, $T_{ref}$ the reference temperature, and $I$ the second-order identity. The elastic response follows Hooke’s law with temperature-dependent stiffness
\begin{equation}
\sigma = D(T):\epsilon^e \qquad 
D(T) \equiv D\!\big(E(T),\nu(T)\big)
\end{equation}
with $E(T)$, $\nu(T)$ (if available), and $\alpha_e(T)$ taken in tabulated form (Table~\ref{tab:temp_dependent_props}) and evaluated by piecewise-linear interpolation between temperatures.

Plastic behavior is modeled by the von Mises yield criterion with isotropic hardening. The yield function is
\begin{equation}
f(\sigma,\bar{\epsilon}^p;T) = \sigma_{eq} - \sigma_y(\bar{\epsilon}^p,T) \le 0, \qquad
\sigma_{eq} = \sqrt{\tfrac{3}{2}\,s:s}, \qquad
s = \sigma - \tfrac{1}{3}\mathrm{tr}(\sigma)\,I
\end{equation}
and the associated flow rule governs plastic strain evolution,
\begin{equation}
\dot{\epsilon}^p = \dot{\lambda}\,\frac{\partial f}{\partial \sigma}, \qquad
\dot{\lambda} \ge 0, \qquad f \le 0, \qquad \dot{\lambda}\,f = 0
\end{equation}
The temperature-dependent yield stress $\sigma_y(\bar{\epsilon}^p,T)$ is introduced as tabulated values derived from high-temperature tensile tests of LPBF 316L stainless steel \cite{Dryepondt2021,Dudziak2023,Sprengel2021} and is used at the same temperature points as the other properties in Table~\ref{tab:temp_dependent_props}. Unless additional hardening data are specified, a perfectly plastic post-yield response is assumed ($H(T)=0$).

\subsection{Numerical implementation}
Figure~\ref{fig:mesh} shows the finite-element voxel mesh and the applied boundary conditions used in the analyses. The base element size was selected such that at least three elements spanned the thickness of the test samples, despite their small thickness. Each sample was simulated independently, and the computational domain was extended by the height of the build platform on which the sample was placed. A systematic three-step mesh convergence study was conducted to assess the sensitivity of the results to mesh resolution. Element sizes of 0.1, 0.075, and 0.05~mm were evaluated, and the monitored output quantities, including the maximum top-layer temperature and the corresponding deformation magnitude, exhibited negligible variation between the two finest meshes. Based on this assessment, the selected mesh resolution was considered sufficient to ensure mesh-independent results. Temperature calibration was performed on the top surface layer in a manner consistent with the approach reported in~\cite{ZHANG2019610}..%tady to ještě opravit
\begin{figure}[H]
    \centering
    \begin{tikzpicture}
        % Vložení obrázku
        \node[anchor=south west,inner sep=0] (image) at (0,0) 
            {\includegraphics[scale=0.3]{mesh.png}};
        
        % Vložení legendy a šipky
        \begin{scope}[x={(image.south east)},y={(image.north west)}]
            % Legenda v pravém dolním rohu
        \node[fill=white,opacity=0.8,text opacity=1] at (1.5,0.9)
            {\begin{minipage}{8cm}
                \small \textbf{Boundary conditions:} \\
                \textcolor{black}{Top surface - Heat source, \\\hspace*{5.8em} Heat radiation and convection } \\
                 \textcolor{black}{Side of sample - Convection to the powder} \\
                 \textcolor{black}{Base - Heat conduction} \\
            \end{minipage}};
            
            % Šipka od legendy k bodu v obrázku
            \draw[->,line width=0.5pt , red] (0.8,0.96) -- (0.55,0.91);
            \draw[->,line width=0.5pt , red] (0.8,0.84) -- (0.55,0.8);
            \draw[->,line width=0.5pt , red] (0.8,0.84) -- (0.55,0.3);
            \draw[->,line width=0.5pt , red] (0.85,0.78) -- (0.7,0.1);
        \end{scope}
    \end{tikzpicture}
    \caption{Computational finite-element mesh and applied boundary conditions.}
    \label{fig:mesh}
\end{figure}
The simulations were carried out for three sample geometries located closest to the recoating device (positions A14, A7, and A1 in Fig.~\ref{fig:usporadaniPlatformy}). Each model consisted of approximately 176{,}000 voxel elements in the base configuration. The simulation time for the largest sample was approximately 1.2~h on a workstation equipped with an Intel Core i7-9700K processor and 64~GB of RAM. Thermomechanical analyses were performed using the OOFem finite-element solver.

In the present study, the material was assumed to be isotropic and homogeneous. Temperature-dependent material properties of solid AISI~316L were adopted from the literature~\cite{FOROOZMEHR2016255,Hodge2014} and are summarized in Table~\ref{tab:temp_dependent_props}.
\begin{table}[t]
  \centering
  \small
  \caption{Temperature-dependent properties of AISI~316L: Young's modulus $E$, coefficient of thermal expansion (CTE), specific heat $c_p$, thermal conductivity $k$, and yield stress $\sigma_y$. Elastic, thermal and plastic data are taken from \cite{FOROOZMEHR2016255,Hodge2014,Dryepondt2021,Dudziak2023,Sprengel2021}.}
  \label{tab:temp_dependent_props}
  \begin{tabular}{
      S[table-format=4.0]   % Temperature (K)
      S[table-format=3.1]   % E (GPa)
      S[table-format=2.2]   % CTE (µm/mK)
      S[table-format=4.0]   % cp (J/kgK)
      S[table-format=2.2]   % k (W/mK)
      S[table-format=3.0]   % sigma_y (MPa)
    }
    \toprule
    {Temperature (\si{\kelvin})} &
    {$E$ (\si{\giga\pascal})} &
    {CTE (\si{\micro\metre\per\metre\per\kelvin})} &
    {$c_p$ (\si{\joule\per\kilogram\per\kelvin})} &
    {$k$ (\si{\watt\per\metre\per\kelvin})} &
    {$\sigma_y$ (\si{\mega\pascal})} \\
    \midrule
    273  & 200.8 & 15.07 & 440 & 12.76 & 600 \\
    432  & 188.9 & 16.09 & 510 & 14.94 & 540 \\
    590  & 176.3 & 16.96 & 545 & 17.18 & 480 \\
    749  & 163.1 & 17.70 & 560 & 19.30 & 430 \\
    907  & 149.1 & 18.29 & 585 & 21.48 & 360 \\
    1066 & 134.6 & 18.74 & 620 & 23.66 & 180 \\
    1224 & 119.3 & 19.05 & 650 & 25.84 & 120 \\
    1383 & 103.4 & 19.21 & 680 & 28.02 & 120 \\
    1541 &  86.8 & 19.23 & 713 & 30.20 & 120 \\
    1700 &  69.5 & 19.23 & 744 & 32.38 & 120 \\
    \bottomrule
  \end{tabular}
\end{table}
\section{Results and discussion}\label{Results and discussion}
\subsection{Measurement results}
Measurement in the printing chamber on the L-type sample (Fig.~\ref{fig:Lshape}) revealed that at a nominal layer height of 20~µm, the difference in the type of applicator blades was negligible.Within the investigated range of powder deposition speeds, the median force values at individual recoater speeds fall within the scatter of the measured data and do not exhibit a dependence on the deposition speed (Figs.~\ref{fig:rychGuma} and \ref{fig:rychKerm}).

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  % 1. řádek (0.375 + 0.38)
  \makebox[\textwidth][c]{%
    \begin{subfigure}[b]{0.375\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{rychlost_keramika.png}
      \label{fig:rychGuma}
    \end{subfigure}%
    \hspace{0.02\textwidth}%
    \begin{subfigure}[b]{0.38\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{rychlost_guma.png}
      \label{fig:rychKerm}
    \end{subfigure}%
  }

  \vspace{0.75\baselineskip}

  % 2. řádek (0.38 + 0.3)
  \makebox[\textwidth][c]{%
    \begin{subfigure}[b]{0.38\textwidth} 
    \caption{}
      \includegraphics[width=\linewidth]{guma2.png}
      \label{fig:GumaPrub}
    \end{subfigure}%
    \hspace{0.02\textwidth}%
    \begin{subfigure}[b]{0.3\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{otlak.jpg}
      \label{fig:otlak}
    \end{subfigure}%
  }

  \caption{Recoater–specimen interaction under variable recoating speeds:
  (a) force response to rubber recoater velocity; (b) force response to ceramic recoater velocity;
  (c) recoater force response to layer thickness variation; (d) imprint of the specimen on the rubber blade edge.}
  \label{fig:rychlostiAGuma}
\end{figure}
 
To validate this result, the layer height was reduced in the case of the rubber blade (Fig.~\ref{fig:GumaPrub}) in such a way that the sample was first enclosed and subsequently pushed out of the powder bed by a thickness equivalent to two nominal layer heights. Even this did not lead to an increase in the load variation measured on the sample. A significant trace was observed on the surface of the applicator blade, corresponding to the width of the measured sample (Fig.~\ref{fig:otlak}). The measurements indicate that variations in layer thickness with the rubber blade do not increase the load acting on the sample, but instead lead to increased wear of the applicator blade.


Measurements performed with the rigid ceramic recoater blade showed that the magnitude of the force acting on the sample during recoating varies with the clearance between the sample and the blade under conditions of reduced nominal layer height. As shown in (Fig.~\ref{fig:prubeh}), the interaction between the blade and the measured sample can be observed. This interaction can be divided into the following phases: powder accumulation and traversal of the sample’s leading edge, traversal across the sample surface, and subsequent elastic rebound with overshoot. This segmentation of the measured response shows that the highest load occurs during traversal of the sample’s leading edge. This may be caused by the adhesion of loose powder grains to the contours of the printed sample or by the attachment of droplets ejected from the melt pool onto the surface of the printed part.

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

\begin{subfigure}[b]{0.49\textwidth}
  \caption{}
  \centering

  \begin{tikzpicture}
    \node[anchor=south west, inner sep=0] (img) at (0,0)
      {\includegraphics[width=\linewidth]{graf_response.png}};

    % zajistí, že se velikost tikzpicture = velikost obrázku
    \path[use as bounding box] (img.south west) rectangle (img.north east);

    \begin{scope}[x={(img.south east)}, y={(img.north west)}]
      % všechno uřízni na (0..1, 0..1), aby nic "netrčelo" ven
      \clip (0,0) rectangle (1,1);

      % ŠIPKA 1 (šikmá) + popis
      \draw[-{Latex[length=2mm]}, black, line width=0.6pt]
        (0.570,0.85) -- (0.5,0.85)
        node[pos=0.0, right=5.5pt, fill=white, inner sep=0.1pt] {\small Powder build-up};

      % ŠIPKA 2 (šikmá) + popis
      \draw[{Latex[length=2mm]}-, black, line width=0.6pt]
        (0.60,0.32) -- (0.7,0.73)
        node[pos=1, right=1.5pt, fill=white, inner sep=0.1pt] {\small rebound};
    \end{scope}
  \end{tikzpicture}

  \label{fig:prubeh}
\end{subfigure}%
  %
  \begin{subfigure}[b]{0.49\textwidth}
   \caption{}
    \includegraphics[width=\linewidth]{graf_relax.png}
   \label{fig:relaxace}
  \end{subfigure}

  \caption{Recoating force behavior over time: (a) force evolution during recoater pass across the sample; (b) measured force reduction over time due to repeated recoater traversal.}
  \label{fig:zatez}
\end{figure}

This assumption is based on the observation that repeated passes of the recoating system over a single layer resulted in a reduction of the peak measured response. With each pass, a gradual relaxation of the measured values was observed (Fig.~\ref{fig:relaxace}), which was attributed to the progressive abrasion of adhered satellite powder grains by the blade. A subsequent inspection of the blade ruled out any change in response due to blade damage.


From the perspective of applying the measurements in simulations, it is necessary first to determine the minimum layer thickness at which a significant increase in stress on the printed part occurs. The variation in measured values for individual samples is visualized in groups categorized by the height of the measured layer. Although the response differs for each pass, the value acting on the sample at the front edge, where the maximum occurs, is critical for our purposes. Therefore, in the following graphs (Fig.~\ref{fig:ceramicBlade}), the measurements will be evaluated as the values at the front edge for each sample.
\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  % 1. řádek — válcová čela: D6, D12, D24
  \makebox[\textwidth][c]{%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{rozptyl_d6.png}
      \label{fig:disp_d6}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{rozptyl_d12.png}
      \label{fig:disp_d12}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{rozptyl_d24222.png}
     \label{fig:disp_d24}
    \end{subfigure}%
  }

  \vspace{0.6\baselineskip}

  % 2. řádek — kolmá čela: T6, T24, T48
  \makebox[\textwidth][c]{%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{rozptyl_t6.png}
      \label{fig:disp_t6}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{rozptyl_T24.png}
      \label{fig:disp_t24}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{rozptyl_T48.png}
      \label{fig:disp_t48}
    \end{subfigure}%
  }

  \vspace{0.6\baselineskip}

  % 3. řádek — 3x3 a 45°
  \makebox[\textwidth][c]{%
    \begin{subfigure}[b]{0.327\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{rozptyl_3x3.png}
     \label{fig:disp_3x3}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{rozptyl_E90.png}
      \label{fig:disp_e90}
    \end{subfigure}%
  }

  \caption{Specimens with varied leading-edge geometries:
  (a) 6\,mm cylindrical leading face; (b) 12\,mm cylindrical leading face; (c) 24\,mm cylindrical leading face;
  (d) 6\,mm perpendicular leading edge; (e) 24\,mm perpendicular leading edge; (f) 48\,mm perpendicular leading edge;
  (g) 3\,mm perpendicular leading edge; (h) 45° leading edge.}
  \label{fig:ceramicBlade}
\end{figure}

Across the investigated sample geometries, an increase in the applied force was observed when the effective deposited layer thickness approached approximately 15~$\mu$m, corresponding to a reduction of about 5~$\mu$m relative to the nominal layer height. Layer thicknesses below this value can be considered a safe operating regime, in which surface irregularities generated during printing can be accommodated without a pronounced interaction with the recoater blade. Owing to the discrete nature of the measurement method, the exact onset of contact cannot be resolved with higher precision; consequently, some samples exhibit a noticeable increase in front-edge loading at an effective layer thickness of approximately 15~$\mu$m, whereas for others this increase becomes apparent only after this value is exceeded.

Measurements performed on samples with an identical front-face width of 6~mm but differing geometries did not indicate a systematic dependence of the measured force magnitude on the sample shape (Fig.~\ref{fig:porovnani6}). Under identical layer-thickness conditions, the measured force values were comparable and remained within the scatter of the experimental data, suggesting a limited influence of sample geometry on the applied force within the investigated parameter range. The effect of the leading-edge geometry can be observed for samples with a front face perpendicular to the recoating direction only up to the moment of initial contact between the blade and the sample (Fig.~\ref{fig:prubehKolma}). Once contact is established, direct loading transmitted through the contact edge becomes the dominant interaction mechanism.
\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \makebox[\textwidth][c]{%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=1.0\linewidth]{porovnani_t6_d6_E90_5.png}
      \label{fig:thick_5}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
     \caption{}
      \includegraphics[width=1.0\linewidth]{porovnani_t6_d6_E90_10.png}
     \label{fig:thick_10}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
     \caption{}
      \includegraphics[width=1.0\linewidth]{porovnani_t6_d6_E90_12.5.png}
     \label{fig:thick_12_5}
    \end{subfigure}%
  }

  \vspace{0.6\baselineskip}

  \makebox[\textwidth][c]{%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=1.0\linewidth]{porovnani_t6_d6_E90_15.png}
      \label{fig:thick_15}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=1.0\linewidth]{porovnani_t6_d6_E90_17.5.png}
      \label{fig:thick_17_5}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=1.0\linewidth]{porovnani_t6_d6_E90_20.png}
      \label{fig:thick_20}
    \end{subfigure}%
  }

  \caption{Effect of layer thickness on recoating force across different leading-edge geometries:
  (a) $5\,\mu$m; (b) $10\,\mu$m; (c) $12.5\,\mu$m; (d) $15\,\mu$m; (e) $17.5\,\mu$m; (f) $20\,\mu$m.}
  \label{fig:porovnani6}
\end{figure}

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \makebox[\textwidth][c]{%
    \begin{subfigure}[b]{0.327\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{porovnani_t6_t24_t48_20.png}
     \label{fig:w_20}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{porovnani_t6_T24_T48_17.5.png}
     \label{fig:w_17_5}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{porovnani_t6_T24_T48_15.png}
      \label{fig:w_15}
    \end{subfigure}%
  }

  \vspace{0.6\baselineskip}

  \makebox[\textwidth][c]{%
    \begin{subfigure}[b]{0.327\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{porovnani_t6_T24_T48_12.5.png}
     \label{fig:w_12_5}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{porovnani_t6_T24_T48_10.png}
     \label{fig:w_10}
    \end{subfigure}%
    \begin{subfigure}[b]{0.327\textwidth}
    \caption{}
      \includegraphics[width=\linewidth]{porovnani_t6_t24_t48_5.png}
      \label{fig:w_5}
    \end{subfigure}%
  }

\caption{Influence of varying sample width on recoating force at different layer thicknesses:
  (a) $20\,\mu$m; (b) $17.5\,\mu$m; (c) $15\,\mu$m; (d) $12.5\,\mu$m; (e) $10\,\mu$m; (f) $5\,\mu$m.}
  \label{fig:prubehKolma}
\end{figure}
\subsection{Numerical simulation results}
Measurements performed on samples clamped in the fixture indicate an increased likelihood of interaction with the recoating system when the total clearance between the sample and the blade approaches approximately 15~$\mu$m. In the simulation framework, this condition is expressed in terms of the maximum recoater gap reduction, and it is employed as a process-dependent criterion for the evaluation of the simulation results. For the simulated samples, temperature and deformation responses were evaluated as the average values at four nodal points located at the center of the top layer of the simulated mesh.

Temperature-field results for sample A14 are shown in (Fig.~\ref{fig:temp_fields_A14}). The temporal evolution of the maximum top-surface temperature for all three simulated samples is presented in Fig.~\ref{fig:surface_temp}, referenced to the time instant of recoater blade traversal. For all simulated samples, a rapid increase in the maximum top-surface temperature was observed, followed by a gradual stabilization with increasing distance of the top layer from the build platform. This transition is attributed to enhanced heat dissipation into the build platform in its immediate vicinity, where the platform forms part of the thermally active zone. With increasing distance from the platform, the influence of this heat sink diminishes, resulting in a reduced heat removal rate from the top layer and a stabilization of the temperature increase for samples with a constant cross section. This behavior was observed consistently across all simulated samples. Differences in cross-sectional geometry had only a limited effect on the temperature evolution, as the temperature values remained nearly identical at different sample heights due to the small variations in the thickness of the individual sample geometries.

The deformation in the printing direction (Figs.~\ref{fig:gap_reduction} and \ref{fig:deformaceVzorekKonec}) is evaluated as the difference between the deformation magnitude immediately before the deposition of a new layer and the deformation state corresponding to the traversal of the recoating system. This approach filters out the influence of the gradual temperature increase occurring toward the end of the process cycle and prevents cumulative deformation effects across successive layers. The evaluation is based on the assumption that the difference between the nominal and the actual layer height evolves as a result of thermal loading, with the magnitude of the layer-thickness reduction described by the maximum recoater gap reduction between the applicator blade and the top layer. The values presented in the corresponding graphs represent the maximum values evaluated within the top layer of the sample. With each newly deposited layer, this difference is reset during the recoating process at the expense of the newly added material. The temporal evolution of the deformation response and the associated recoater gap reduction is illustrated by the histories shown in (Figs.~\ref{fig:gap_reduction} and \ref{fig:deformaceVzorekKonec}). The corresponding spatial and temporal distributions along the sample geometry are further depicted in (Fig.~\ref{fig:riskFem}), which show the same sample evaluated under two different recoating strategies.

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \begin{subfigure}[b]{0.7\textwidth}
   \caption{}
    \includegraphics[width=1.0\linewidth]{teplotyOld.PNG}
   \label{fig:teplotaStareho}
  \end{subfigure}

  \vspace{0.6\baselineskip}

  \begin{subfigure}[b]{0.7\textwidth}
  \caption{}
    \includegraphics[width=1.0\linewidth]{teplotyNew.PNG}
    \label{fig:teplotaNoveho}
  \end{subfigure}

  \caption{Temperature-field results for sample A14 at different build heights. The individual images correspond to results evaluated at 2~mm height increments and are referenced to the time instant of recoater blade traversal:
  (a) original printing cycle interval; (b) modified printing cycle interval.}
  \label{fig:temp_fields_A14}
\end{figure}

The simulation results indicate that the temperature of the part at the moment of layer deposition is strongly influenced by the distance between the top layer and the build platform surface (Fig.~\ref{fig:gap_reduction}). This effect is most pronounced within the first 10~mm of the build height, where the platform forms part of the thermally active zone and acts as an effective heat sink. In this region, the sample exhibits pronounced temperature fluctuations due to the direct influence of the heat source. The highest temperature increase occurs within the initial 10~mm of the sample height, followed by a gradual stabilization for samples with a constant cross section. This stabilization takes place at a height where the thermally active zone no longer directly interacts with the build platform and a consistent internal time step is established within the printed part of uniform cross section.

The thermal state of the part at the moment of layer deposition can be directly related to the evaluated recoater gap reduction (Figs.~\ref{fig:gap_reduction} and~\ref{fig:riskOld}). Based on this representation, the simulation predicts that a gap closure of approximately 5~µm, corresponding to an effective deposited layer thickness of about 15~µm, is exceeded at a sample height of approximately 8.6~mm. At this height, the simulation indicates the onset of interaction between the recoating device and the printed part.
\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \begin{subfigure}[b]{0.49\textwidth}
  \caption{}
    \includegraphics[width=\linewidth]{porovnani_hodnot2.png}
    \label{fig:gap_reduction}
  \end{subfigure}%
  %
  \begin{subfigure}[b]{0.49\textwidth}
  \caption{}
    \includegraphics[width=\linewidth]{porovnani_hodnotTepMax.png}
    \label{fig:surface_temp}
  \end{subfigure}

  \caption{Original printing cycle interval:
  (a) recoater gap reduction; (b) recoating surface temperature.}
  \label{fig:Modified2}
\end{figure}
When the recoating cycle and the thermal stabilization period were adjusted, the simulation showed a pronounced reduction in the temperature of the part at the moment of layer deposition (Fig.~\ref{fig:teplotaKonecVzorek}). This reduction in temperature resulted in a corresponding decrease in deformation (Figs.~\ref{fig:deformaceVzorekKonec} and~\ref{fig:riskUprav}), which would otherwise contribute to an increased risk of recoater–part interaction and instability of the deposited layer height. Based on the applied evaluation criterion, the results of the adjusted simulation do not indicate any recoater blade collision with the printed samples.
\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \makebox[0.63\textwidth][c]{%
    \begin{subfigure}[b]{0.29\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{riskUpraveny.png}
     \label{fig:riskUprav}
    \end{subfigure}%
%    \begin{subfigure}[b]{0.15\textwidth}
%     \caption{}
%      \includegraphics[width=\linewidth]{bar.png}
%     \label{fig:ruber_recoater_blade}
%    \end{subfigure}%
    \begin{subfigure}[b]{0.3\textwidth}
     \caption{}
      \includegraphics[width=\linewidth]{riskOld.png}
     \label{fig:riskOld}
    \end{subfigure}%
    \begin{subfigure}[b]{0.155\textwidth}
%     \caption{}
      \includegraphics[width=\linewidth]{bar.png}
%     \label{fig:ruber_recoater_blade}
    \end{subfigure}%
  }

  \caption{Temporal evolution of recoater gap reduction along the sample geometry from numerical simulation:
(a) modified recoating cycle,
(b) original recoating cycle resulting in recoater–part collision.
}
  \label{fig:gapFem}
\end{figure}

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \begin{subfigure}[b]{0.49\textwidth}
  \caption{}
    \includegraphics[width=\linewidth]{porovnani_hodnot.png}
    \label{fig:deformaceVzorekKonec}
  \end{subfigure}%
  %
  \begin{subfigure}[b]{0.49\textwidth}
  \caption{}
    \includegraphics[width=\linewidth]{porovnani_hodnotTepEnd.png}
    \label{fig:teplotaKonecVzorek}
  \end{subfigure}

  \caption{Modified printing cycle interval:
  (a) recoater gap reduction; (b) recoating surface temperature.}
  \label{fig:Modified3}
\end{figure}
\subsection{Experiment results}

The evaluation of the experimental print was carried out by identifying traces of sample deflection. These traces are visible to the naked eye on compliant geometries, such as printed samples. Upon contact with the recoater blade, the sample deflects, manifesting itself as a significant surface offset on the geometry. These offsets were subsequently located and their positions were measured relative to the platform surface.


To validate the interaction of the recoater blade with the selected sample geometry, printing was initially performed with a layer height of 15~$\mu$m. The laser power was reduced to maintain a consistent energy input into the material according to equation~(\ref{eq:energie}). During this print, contact between the recoater blade and the printed samples was audible within the first few dozen layers. These interactions culminated in permanent deflection of samples C4 and B14 (Fig.~\ref{fig:tisk15}). The remaining samples, due to increasing and repeated interaction with the recoater blade, lost the ability to retain newly deposited powder layers as a result of sample oscillation. This phenomenon gradually led to discontinuities in the printing process across all samples, ultimately resulting in complete build failure. The print was terminated once disconnected fragments of printed metal became visible in the powder bed.


\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \begin{subfigure}[b]{0.78\textwidth}
  \caption{}
    \begin{tikzpicture}
      \node[anchor=south west,inner sep=0] (img) at (0,0)
        {\includegraphics[width=\linewidth]{schema_shake.png}};
      % normalized coords: (0,0)=bottom-left, (1,1)=top-right
      \begin{scope}[x={(img.south east)},y={(img.north west)}]
        \node[callout box,anchor=east] (labA) at (0.38,0.72) {Recoater collision};
        \draw[callout arrow] (labA.east) -- (0.45,0.62);

        \node[callout box,anchor=west] (labA2) at (0.70,0.95) {Disturbed powder layer};
%        \draw[callout arrow] (labA2.west) -- (0.56,0.38);
      \end{scope}
    \end{tikzpicture}
    \label{fig:mechanismusZtratyKontinuity}
  \end{subfigure}

  \vspace{0.6\baselineskip}
  
  \begin{subfigure}[b]{0.78\textwidth}
   \caption{}
   \centering
    \begin{tikzpicture}
      \node[anchor=south west,inner sep=0] (img) at (0,0)
        {\includegraphics[width=0.7\linewidth]{prasek.png}};
      \begin{scope}[x={(img.south east)},y={(img.north west)}]
        \node[callout box,anchor=west,align=left,draw=black] (labB) at (0.62,0.85)
          {Powder bed defect\\after recoater impact};
        \draw[callout arrow, draw=red] (labB.west) -- (0.42,0.48);
      \end{scope}
    \end{tikzpicture}
   \label{fig:prasek}
  \end{subfigure}

  \caption{Damage to powder bed integrity due to part collisions and vibrations:
  (a) schematic illustration of powder layer disruption during LPBF caused by recoater collision;
  (b) visual documentation of a powder bed defect initiated by recoater impact during laser-based powder fusion.}
  \label{fig:kolize}
\end{figure}
The first signs of sample deflection were observed for sample A10 (Fig.~\ref{fig:tisk15}(a)), where an initial surface offset caused by permanent displacement from the original position was identified on the rear side of the sample at a height of 4.27~mm. Although audible contacts between the recoater blade and the samples occurred from the early stages of the build, the first visually identifiable permanent deflection was detected only after a certain build height had been reached. This behavior can be attributed to the influence of the build platform, which directly affects the thermally active zone in this region, as well as to the stiffness of the samples themselves, which, despite their small thickness, are able to elastically recover from contact-induced deflection during the initial stages of the build. In the case of samples B14, C4, B5, and A1–A3, the deflection was so severe that the print could not continue onto subsequent layers. It is likely that mechanical jamming occurred, resulting in complete bending of the sample. Samples 1–9 in rows A and B exhibited an increased number of fully disconnected layers, with characteristic surface offsets caused by strong collisions with the recoater blade. In row C, this phenomenon affected samples 1–6 (Fig.~\ref{fig:tisk15}(b)). The effect was also visible during printing through the observation window of the build chamber (Fig.~\ref{fig:prasek}). Such collisions manifested as damage to the integrity of the powder bed (Fig.~\ref{fig:mechanismusZtratyKontinuity}). Frequent repetition of this phenomenon led to the breakdown of newly printed layers, ultimately resulting in print termination at a height of 7.52~mm.

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \begin{subfigure}[b]{0.78\textwidth}
  \caption{}
    \includegraphics[width=\linewidth]{zadniStrana15.jpg}
    \label{fig:rear_15}
  \end{subfigure}

  \vspace{0.6\baselineskip}

  \begin{subfigure}[b]{0.78\textwidth}
    \caption{}
    \includegraphics[width=\linewidth]{predniStrana15.jpg}
  \label{fig:front_15}
  \end{subfigure}

  \caption{Samples printed with a reduced nominal layer height of 15~$\mu$m:
  (a) rear sides of the samples showing visible offset ridges caused by deflected parts;
  (b) front sides with clearly visible print discontinuities.}
  \label{fig:tisk15}
\end{figure}


Samples printed with the unmodified recoating loop show signs of contact with the ceramic blade of the recoating system (Fig.~\ref{fig:tisk20crash}). The first collision traces appeared on sample A7 at a height of 9.63~mm. Subsequently, deflection marks began to appear on all samples. A higher frequency of deflection traces was observed in row A, which is located closest to the recoating system. Samples 9 and 10 from row A lost the ability to maintain continuous printing, with this failure occurring at a height of 10.58~mm. The announced defects were also observed in other samples above this level in all rows (Fig.~\ref{fig:tisk20crash}).

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \begin{subfigure}[b]{0.68\textwidth}
   \caption{}
    \includegraphics[width=\linewidth]{normalZadek.jpg}
   \label{fig:rear_20}
  \end{subfigure}

  \vspace{0.6\baselineskip}

  \begin{subfigure}[b]{0.68\textwidth}
  \caption{}
    \includegraphics[width=\linewidth]{normalPredek.jpg}
    \label{fig:front_20}
  \end{subfigure}

  \caption{Specimens printed with a nominal layer thickness of 20~$\mu$m:
  (a) rear sides of the specimens showing rebound marks from displaced parts;
  (b) front side showing a visible print discontinuity.}
  \label{fig:tisk20crash}
\end{figure}

Printing with a modified timing of layer deposition and an extended stabilization period for part cooling was completed without any signs of collision across all samples, regardless of their position (Fig.~\ref{fig:tisk20fullMod}). Therefore, it can be concluded that the prolonged cooling time prior to the deposition of a new layer contributed to reducing the risk of build failure due to collisions between the sample and the recoater blade.

The printing results are consistent with the simulation results, where the original recoating cycle configuration predicted a collision at a level comparable to that observed in the experiment. Printing with the modified timing of the recoating cycle did not result in any collisions, as predicted.

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  \begin{subfigure}[b]{0.78\textwidth}
  \caption{}
    \includegraphics[width=\linewidth]{optZadek.jpg}
    \label{fig:rear_20_opt}
  \end{subfigure}

  \vspace{0.6\baselineskip}

  \begin{subfigure}[b]{0.78\textwidth}
  \caption{}
    \includegraphics[width=\linewidth]{optPredek.jpg}
    \label{fig:front_20_opt}
  \end{subfigure}

  \caption{Specimens printed with a nominal layer thickness of 20~$\mu$m and extended cooling time before recoating:
  (a) rear sides of the specimens without visible rebound marks;
  (b) front side without visible print discontinuity.}
  \label{fig:tisk20fullMod}
\end{figure}

To confirm that interaction with the recoater blade is the primary factor influencing print failure, the experiment using the original recoating cycle configuration was repeated—this time with a compliant rubber blade. The print was carried out to the same height as in previous tests (20~mm). After successfully reaching 20~mm, the stabilization delay was shortened from 15~s to 7~s. This change manifested on the sample surfaces (Fig.~\ref{fig:tiskguma}(a), above the green line) as a gradual shift in surface coloration, caused by insufficient heat dissipation and rising part temperature.
At a height of 60~mm, the integrity of the rubber blade was inspected (Fig.~\ref{fig:tiskguma}(a), red line). This inspection resulted in a temporary drop in sample temperature and a corresponding surface offset indicating resumed layer bonding. Continued printing confirmed the trend of surface discoloration due to inadequate cooling during the shortened cycle time.
The print was terminated at a height of 100~mm, where noticeable protrusion of the samples from the powder bed was observed (Fig.~\ref{fig:tiskguma}(b)). This condition is attributed to insufficient cooling time at the melt zone, leading to a gradual temperature increase throughout the part. These findings confirmed that the rubber recoater blade, even when significantly raised above the nominal layer thickness, did not induce increased mechanical loading. Only sample B14 exhibited a similar failure mechanism to that observed with the ceramic blade at a height of 93~mm (Fig.~\ref{fig:tiskguma}(c–d)). The outcome of this print validated the fixture-based measurements, showing that the compliant blade does not impose mechanical stress on the printed part—even when the gap beneath the blade is fully closed.

\begin{figure}
  \captionsetup[subfigure]{singlelinecheck=false,skip=0pt,font=large}
  \centering

  % stejné sloupce 0.48\textwidth, obrázky uvnitř mají pevnou výšku i šířku
  \begin{subfigure}[t]{0.48\textwidth}
   \caption{}
    \includegraphics[width=\linewidth,height=65mm,width=70mm]{gumaTisk.jpg}
   \label{fig:rubber_fronts}
  \end{subfigure}%
  \begin{subfigure}[t]{0.48\textwidth}
   \caption{}
    \includegraphics[width=\linewidth,width=70mm,height=65mm]{vystouple.jpg}
   \label{fig:rubber_protrusion}
  \end{subfigure}

  \vspace{0.6\baselineskip}

  \begin{subfigure}[t]{0.48\textwidth}
  \caption{}
    \includegraphics[width=\linewidth,width=70mm,height=65mm]{gumaPred.jpg}
    \label{fig:rubber_14B_front}
  \end{subfigure}%
  \begin{subfigure}[t]{0.48\textwidth}
   \caption{}
    \includegraphics[width=\linewidth,width=70mm,height=65mm]{gumaZad.jpg}
   \label{fig:rubber_14B_rear}
  \end{subfigure}

  \caption{Specimens printed with a nominal layer thickness of 20~$\mu$m using a rubber blade:
  (a) front sides of the specimens with a green line indicating the height of other specimens and a red line marking the blade inspection point;
  (b) protrusion of specimens from the powder bed at a specimen height of 100~mm;
  (c–d) discontinuity observed in specimen 14B.}
  \label{fig:tiskguma}
\end{figure}


\section*{Conclusions}\label{Conclusions}
This work examined recoater–part interactions in LPBF of 316L stainless steel by combining the fixture-based measurements with a temperature-dependent elastic–plastic finite element model. Experimentally determined collision thresholds were embedded in the simulations and applied as a build-level acceptance check. The main findings and implications for pre-build screening and process reliability are summarised below:

\begin{itemize}[leftmargin=*]
  \item A practically applicable criterion for predicting recoater–part collisions in LPBF was developed. It compares simulated layer-wise vertical offsets and near-surface asperities with an experimentally calibrated threshold, enabling a pre-build acceptance check instead of trial-and-error.

  \item Collision thresholds were established on a dedicated fixture using strain-gauge measurements. The procedure imposed controlled overheight and contact conditions and produced repeatable signals for two blade types (a compliant rubber blade and a rigid ceramic blade), which form the basis for calibration.

  \item The calibrated thresholds were implemented in a finite element model with a temperature-dependent elastic–plastic constitutive law. Standard model outputs (vertical displacement fields and simple surface-elevation proxies) are sufficient to evaluate the criterion consistently across geometries without bespoke post-processing.

  \item Model predictions were compared with controlled printing trials and showed good agreement within the experimental scatter. The check correctly identified collision-prone configurations and did not flag cases that printed successfully, supporting the use of the measured thresholds within numerical workflows.

  \item The procedure relies only on standard FE outputs and can be inserted into build preparation as a simple screening step. In practice, it quickly rules out settings with limited recoating margin and makes better use of machine time; detailed modelling of powder flow and blade deformation is left for future work.
\end{itemize}
Overall, the calibrated criterion provided a practical acceptance check that agreed with controlled printing trials and required only standard FE outputs. The results point to actionable levers for practitioners, notably the use of compliant blades when clearance is marginal and extending inter-layer cooling for tall, low-stiffness features. While developed and validated for the present machine and setup, the workflow is readily transferable via the same calibration procedure and can be integrated into routine design for additive manufacturing and qualification practices.
\section*{Declarations}

\subsection*{Funding}
This work was supported by the Czech Science Foundation (GA\v{C}R) Grant No.\ 24-11308S.

\subsection*{Conflicts of interest/Competing interests}
The authors declare that they have no competing interests.

\subsection*{Availability of data and materials}
Data of this study can be accessed in Zenodo (DOI: \url{https://doi.org/10.5281/zenodo.17391766}).

\subsection*{Authors' contributions}
Radek Sk\'acel\'ik: Writing -- Original Draft, Writing -- Review \& Editing, Conceptualization, Investigation, Methodology, Visualization.
V\'aclav Vrzal: Resources, Investigation.
Miroslav \v{S}paniel: Supervision, Writing -- Review \& Editing.
Michal Barto\v{s}\'ak: Writing -- Original Draft, Writing -- Review \& Editing, Project administration, Supervision, Investigation.






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