\chapter{Introduction and Problem Statement}\label{cha:intro}

A crankshaft's function within a motor is to combine the force of the firing cylinders and transform linear into rotational motion.
In essence crankshafts are a set of offset bearings and counterweights along a primary axis that terminates in a gearwheel.
Technologically they are at a unique intersection of requirements. 
They are mass produced to satisfy the consumer demand, but are also a crucial part of a vehicles power train and thus must not fail even after unfathomable numbers of revolutions under strongly oscillating force.

Calculating the projected lifetime of crankshafts is therefore of great importance for both quality control during production and for product development\autocite{webster2001residual}, where simulations are of great use here to test different designs without need for physical samples.
The properties of these digital models need to be consistent with the manufacturing processes that are being developed, so it is useful to have a simulation of said process that is as accurate as possible:

Shafts are forged from bar stock into their rough shape, then their bearing surfaces are machined slightly over-sized, oil channels are drilled, they are heat treated and finally ground to specification.
Of these steps, the heat treatment is the most crucial to correctly understand and model, since the steel's microstructure is severely affected by it, and thereby a great many of its material properties.

The surface hardening is accomplished inductive heat treatment, by which the shafts are rotated while several horse-shoe shaped inductors are lowered onto the bearing surfaces, whose coils cover a roughly \ang{120} section of each bearing.
The inductive surface hardening process itself has been in widespread use for crankshaft manufacture since the 1960s\autocite[ch. 1]{rudnev2017handbook}.
It's advantages over fuel-burning furnaces are plentiful: 

Heat can be generated internally without wasting energy on heating the environment.
For surface hardening in particular, the skin effect (see section~\ref{sec:sota_induction} can be leveraged by careful design of the induction coil geometry and choice of electromagnetic frequency\autocite[ch. 4]{rudnev2017handbook} to precisely shape the geometry of the heat treated zone.
This precision eliminates the need for bulky insulation of the heat treatment furnace and leads to am overall more efficient process. 
The needed electricity can be generated off-site by low-emission power plants, reducing the product carbon footprint of the vehicle. 
Lastly, target temperatures can be reached markedly faster which directly increases the possible production volume of a furnace.

However, with all these benefits come two main difficulties in transferring know-how from traditional heat treatment techniques:

Firstly, the faster heating of the material changes how the material's microstructure develops during the treatment\autocite{vieweg2018comparing, eggbauer2019situ}.  

Secondly, determining the influence of the inductor geometry on the resulting shape of heat treated volume is non-trivial. 
The heated zone is shaped by the geometry of the inductor and the frequency of the provided power but also by the material response to the electromagnetic field, which itself is not only specific to each material, but is also a temperature dependent property\autocite{kagimoto2010effect}.

While the former issue is one of gathering transferable know-how\autocite{vieweg2018comparing, jaszfi2019influence}, the second one has historically been simplifying a model's heating to the surface covered by the induction coil.
In recent years, however, simulation techniques and processor power have progressed to a point where inductor simulation can be used in iterative design studies for complex geometries \autocite{boadi2005designing}.

It was therefore the goal of this thesis develop a full \acrlong{fem} simulation chain of the inductive heat treatment process, combining electromagnetic simulations of the inductors' heat generation with thermophysical and material models to arrive at the distributions of material phases, hardness, and residual stress that are relevant to later life-cycle analysis of the heat treated parts.

To this end, two processes were chosen for modeling: 
Firstly a static treatment of a steel rod, conducted with a well instrumented scientific induction heating test rig, and secondly the first crank bearing of an automotive crankshaft hardened by an industrial hardening furnace.
For both materials, great care was taken in generating the material data, in describing the process parameters of the inductive heating, and finally in gathering validation data of the physical property distributions that were the goal of simulation.
A control script for non-linear magnetic materials was implemented in the numerical solver chosen for is endeavor, \emph{Abaqus CAE}\autocite{abaqus2021}, and a further simulation step was added to account for relaxation of residual stress samples to ensure that validation of the results was as accurate as possible.
