% !TeX root = ../dissertation.tex

\chapter{Process Characterization}
\label{cha:process_char}

Induction heating, despite all its positive aspects, is a difficult process to control due to it's multi-physical nature.

Annika Eggbauer described in her PhD\cite{eggbauer2018inductive} the influence of heating speed on the resulting quenched microstructure, on top of austenitization temperature, hold time, and quenching parameters.
This influence of the full heating curve compounds with the fact that every the heat generation of an induction setup are unique to each pairing of material and inductor geometry.


\section{Rod Hardening Process}

As such, heavy instrumentation would be required to collect adequate physical data as input for a full process simulation:
Precise voltage or current measurements for the electromagnetic simulation of heat generation, as well as detailed temperature measurements at several key points of the volume to easily verify the simulation.
Many industrial induction ovens are however not instrumented beyond a power meter, and even that will not record information about the transformer's efficiency and output waveform.

For this reason, the \gls{mcl} commissioned an induction heating teat rig equipped with a bank of thermocouple endpoints.
This machine (shown in figure~\ref{fig:mcl-test-rig}) is equipped with a \emph{ThermProTEC MS 30} series LC oscillator, capable of \SIrange{10}{40}{\kilo\Hz} in frequency and \SIrange{10}{50}{\kilo\W} in power.
It can be run in constant-voltage, constant-current, and constant-power mode.
The sample can be rotated and the coil can be moved along its axis to emulate continuous induction heating.  
The induction coil is water-cooled and fixed via a face plate that allows different coil geometries to be mounted, alongside a circular quenching nozzle (see figure~\ref{fig:test-rig-coil}).

\begin{figure}[htbp]
    \centering
    \begin{tabular}{cc}
         \subfloat[Full view\label{fig:mcl-test-rig}]{\includegraphics[width=0.45\linewidth]{Abbildungen/mcl-test-rig.png}}
         &\quad        
         \subfloat[Induction coil assembly\label{fig:test-rig-coil}]{\includegraphics[width=0.45\linewidth]{Abbildungen/test-rig-rogowski.png}}
    \end{tabular}
    \caption{\acrshort{mcl} induction heating test rig (model HU-VH300-MS30, manufactured by Ideal
Thermal Processes GmbH (ITP), Oberkirch, Germany).}poe
    
\end{figure}


A series of induction experiments was conducted by our research group to obtain data on an arbitrary induction hardening procedure, whose temperature curve imitated that of the industrial process experienced by the crankshafts in the following section. 
These experiments on rod samples done on the \gls{mcl} in-house induction test rig were well instrumented and published under J\'aszfi \emph{et al.}\cite{jaszfi2019influence, jaszfi2022indirect, jaszfi2022residual}. 

To summarize, the induction test rig was configured to approximate a linear temperature increase up to the assumed maximum of \qty{1050}{\degreeCelsius} which was held for \qty{10}{\s}, after which quenching fluid was injected in between the induction coil to achieve a cooling coefficient of $\lambda = 0.01$ or \qtyrange{800}{500}{\degreeCelsius} in \qty{1}{\s}.

The rod samples measured \qty{22}{\mm} in diameter and \qty{300}{\mm} in length. They had holes drilled for thermocouples at center height of the coil at \qtylist{0.5;10.5}{\mm} depth, and voltage and current were measured directly by the machine.

\begin{figure}[htbp]
    \centering
    \includegraphics[height=7cm]{Abbildungen/IBA_data.png}
    \caption{Machine protocol of induction heating experiment.}
    \label{fig:test-rig-curve}
\end{figure}

While the machine itself recorded the heating process (see figure~\ref{fig:test-rig-curve}), some caveats apply to collected data.
Firstly, it is evident that the resolution of the measurements is lacking; \
secondly, the electrical data was measured before the transformer.
This meant that they could not be directly used as simulation inputs since the transformer was outside the scope of simulation for this thesis.

To alleviate this, the electrical power was measured directly across the coil was measured by a digital oscilloscope \emph{Picoscope 3404D MSO}, with a set of Rogowski coils\autocite[175]{tumanski2011handbook} used to convert current to a voltage.

\begin{figure}[htbp]
    \centering
    \label{fig:rogoswki-coils-rod}
\end{figure}

This gave better data, was well as the opportunity to graph the electrical wave shape as supplied by the transformer.
Figure~\ref{fig:rogowski-data-rod} corroborated the power curve of the machine, but multiplied by a factor of \num{18}, somewhat lower than the reported transformation factor of the machine's transformer.

\begin{figure}[htbp]
    \centering
    \subfloat[Current flow\label{fig:current-rod}]{\includegraphics[width=6cm]{Abbildungen/IBA_current_comparison.png}}
    \qquad
    \subfloat[Single wave at $t=\qty{6}{\sec}$??\label{fig:waveshape-rod}]{\includegraphics[width=6cm]{Abbildungen/IBA_waveform.png}}
    \caption{Process data of 50CrMo4 rod being heated in the \acrshort{mcl} test rig using a helical induction coil.}
    \label{fig:rogowski-data-rod}
\end{figure}

The current data used as simulation input was then reduced to a set of num?? interpolation points to increase calculation stability.


\section{Crankshaft Hardening Process}

The crankshaft production line at the BMW Motoren Werk in Steyr, Austria, was a system constructed by \emph{SMS-Elotherm GmbH} that was powered by a transformer bank and run in a constant voltage regimen.
It behaved like many industrial machines, in that it did have a controlling computer that showed the electrical characteristics of each heating cycle while they were happening and cold even plot those as needed, but it did not have the option to export that data in a table format for process control. 

The same methodology of a voltage measurement across inductor contacts and a Rogowski coil for current data was applied with the added challenge of said inductor moving along with the eccentric crank bearing during rotational induction heating (see figure~\ref{fig:produciton-setup}.

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.66\linewidth]{Abbildungen/crank-rogowski.png}
    \caption{Experimental setup at the crankshaft hardening line.}
    \label{fig:produciton-setup}
\end{figure}

\begin{figure}[htbp]
    \centering
    \subfloat[Power flow\label{fig:current-crank}]{\includegraphics[width=0.45\linewidth]{Abbildungen/elotherm-hl1.png}}
    \quad
    \subfloat[Normalized single wave at $t=\qty{1}{\sec}$\label{fig:waveshape-crank}]{\includegraphics[width=0.45\linewidth]{Abbildungen/Elotherm_sine.png}}
    \caption{Process data of C38p crankshaft bearing being heated by a \ang{120} arc shaped inductor at the BMW production line. As per publication~\ref{apx:pub1}, the slight over regulation of the waveform can be ignored during simulation.}
    \label{fig:rogowski-data-crank}
\end{figure}

For the simulation, the electrical current data was again simplified.
the fluctuating current was set to switch between two set levels of \qtyrange{00}{00}{A} with a timing of \qty{00}{\s} high and \qty{00}{\s} low. 

\section{Signal Quality}

As seen in figures~\ref{fig:waveshape-rod} and~\ref{fig:waveshape-crank}, the electrical signal driving  the inductors of this thesis are not sinusoidal. 
This presents a problem for the harmonic solution of the electromagnetic field problem (discussed in section~\ref{sub:sota-fem-em}):
While the principle of \emph{superposition} states that different subharmonic components can be summed up to solve an arbitrary oscillation\autocite{??}, this stops being the case when materials respond in a non-linear fashion\autocite{??}.
Harmonic solutions with non-linear materials therefore must therefore assume a simple sinusoidal electric input, which will lead to some systemic error of the simulation.
Publication~\ref{apx:pub1} presents the \acrfull{thd} as a method of characterizing the deviation of input signals from a sinus wave, based on the amplitudes of the Fourier transformation:

\begin{equation}
\label{eq:thd}
    \textrm{THD} = \frac{\sqrt{\sum_{k=2}^{N} I_k^2}}{I_1}
\end{equation}

Resulting in a \acrshort{thd} of \num{0.19} for the induction test rig, and \num{0.10} for the industrial furnace.

Publication~\ref{apx:pub1} further demonstrates a positive linear correlation between the \acrshort{thd} of an input signal and the Joule heating it induces through a coil.
This influence will later be considered when estimating the efficiency coefficients for the \acrshort{fem} simulation of the coil setups.
