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\begin{frontmatter}

\title{Determination of optimal machining strategy using trochoid geometry for micro-channel machining method}

\author{Emre Günaydın$^*$}
\author{Babur Ozcelik}
\author{Emel Kuram}
\address{Gebze Technical University}
\cortext[]{\textbf{Email:} gunaydinemre@hotmail.com \textbf{Adress:} 41400 Gebze/KOCAELİ, Turkey \textbf{Tel:} +90-262-6051000 \textbf{Fax:} +90-262-6538490} 

\begin{abstract}

The milling of micro-channels is a critical step in many of today’s electronics. In this study, the most appropriate trochoid geometry and machining strategy was determined for the milling of micro-channels. For the milling of the channel, various cutting direction strategies were used and 26 different geometries were created to figure out the best strategies. Using simulation results on four machines, which have different control units, the best geometry and NC output format were determined from each group with reference to the processing times. Experiments were carried out with a tool having a diameter of 0.8 mm. This tool cut a total of 3 channels of 1.2 mm width, 1 mm depth and 10 mm length. The channels were cut on DIN 2738 (40 CrMnNiMo8-6) material to determine optimum geometry by using the 4 geometries selected from the groups according to the simulation results. In current study, force, tool wear, geometric accuracy and surface roughness were evaluated. After the investigation, the appropriate trochoid geometry and machining strategy were determined. As a result, a reduction of about 67.5\% was observed in the length of the tool path compared to the conventional method. In addition to the reduction in tool path length, the wear of the tool could be seen in the size of 20 $\mu$$m$*10 $\mu$$m$ when viewed from the tool face profile.

\end{abstract}

\begin{keyword}
Micro cutting \sep Tool path geometry \sep Cutting parameters \sep Tool wear \sep Surface roughness
\end{keyword}

\end{frontmatter}

%\linenumbers
\vspace*{-3mm}
\section{Introduction}

Today, the need for micro-milling has been increasing. When considering the importance of minimizing manufacturing time because of the competition in production, the need to improve micro-channel milling in manufacturing is critical, so;  a new strategy is required. Trochoid geometry and associated machining strategies used in many 2D and 3D CAM applications have advantages over conventional machining. These advantages include reduced cutting time, reduced tool wear and surface quality improvement. The basic principle of these strategies is that the cutting force is uniformly distributed through the tool helix while using the helix length as the depth of the tool. The heat generated and the adverse effects of the heat can be removed by cutting and easily removing the chip.
Although many studies have been seen in the literature as improved tool path strategy and tool path geometry in macro-milling, these studies are quite limited in micro-milling applications. As seen in previous studies, high investment costs, which are the requirements of high speed processing technology have limited the generalization of this method. Nevertheless, due to the advantages of high speed micro-milling applications, it is important to continue investigating options in this area. Kuram and Ozcelik \cite{makale_01} optimized the cutting parameters by Taguchi method during micro-milling of Ti6Al4V titanium alloy and Inconel 718 materials. They also examined the effects of tool path and machining parameters on micro-milling applications \cite{makale_02}. This study is quite important in the view of the effect of machining strategy and tool path geometry besides machining direction and cutting parameters. Zhenyu et al. \cite{makale_03} made tool path optimization for high speed machining of pocket milling applications. They minimized cutting force by smoothing the sharp corners of pockets milling applications. Zhao et al. \cite{makale_04} proposed smooth tool path geometries to remove instantaneous cutting force increases and the milling material remaining at sharp corners in pocket milling operations using big stepover. With this method, they minimized tool wear. In the study it was shown that machining strategy and tool paths geometry were quite effective on cutting force. Toh \cite{makale_05,makale_06} worked on the machining strategy and its effects on high speed machining of hard steels. With the alternative tool paths and machining strategies suitable for high speed machining technology, they minimized machining times for high volume machining. There is no study on high speed machining strategy in micro-milling applications. Toh \cite{makale_05,makale_06} reviewed the tool path strategy under three headings as 2D milling, entry and exit movements and improved tool life by minimizing the machining time. Similarly, in the study, tool passed through the input, 2D milling and output process in each cycle. For this reason, smooth transitions were preferred at points where input / output and tool path directions change. Jian-wei Ma et al. \cite{makale_07} planned tool path with constraint of cutting force fluctuation for curved surface machining. They reduced cutting time, cutting force fluctuation and improved machining quality and tool life directly by planning new tool path strategy in 3D surface machining on complex macro parts. Thus, that study shows us tool path planning and machining strategy importance. Litwinski et al. \cite{book_01} optimized burr formation and surface roughness by developing the strategy of tool path and optimized feedrate, depth of cut and cutting speed values using the Taguchi method in micro-milling applications. Down milling compared to up milling applications showed greater surface roughness values at the same feedrate, depth of cut and cutting speed. Burr formation decreased at higher cutting speeds, while higher feedrate and width of cut values increased. In down milling applications, they found more burr formation in the same feedrate and width of cut values than up milling applications. In the study, the effect of cutting strategies on the formation of burrs and surface roughness was observed. Kuram and Ozcelik \cite{makale_08} optimized the tool wear, cutting force and surface roughness by Taguchi method using AISI 304 in the experiments. They showed the effect of the feedrate on surface roughness and tool wear in micro-milling. Depending on the machining strategy and geometry of tool path, the feedrate of change was ignored. For this reason, the study focused on non-complicated geometries with smooth transitions that did not cause feedrate change when the tool path geometry was created.

Current study consisted of 2 steps. The first step considered various examples of trochoid geometry. The geometries were divided into four different strategy groups and their NC outputs which can adapt to the 4 most common control units in the market. The minimum progress time was determined for the optimal trochoid geometric structures by simulation method in each strategy group. The second step considered the best trochoid geometric structure by examining the cutting force, coordinate measuring machine (CMM) measurement results, tool wear, burr formation, surface roughness values for cutting experiments on plastic mould steel DIN 2738 material. 

\section{Experimental Study}
\label{methodology}

This work was carried out in two stages, namely simulation and experimental: Determination of the most suitable geometry by simulation and specification of the optimum among these geometries by cutting experiments. The flow chart of the work is given in Figure \ref{fig_1_flowchart}.

\begin{figure}[H]
	\centering	
	\subfigure{
	\includegraphics[width=0.6\textwidth]{figures/fig_1_flowchart.jpg}
	}
	\vspace*{-3mm}
	\caption{Flowchart}
\label{fig_1_flowchart}       
\end{figure}

\subsection{Simulation Study}
\label{simulationStudy}

In this section, high speed machining methods with conventional machining method were evaluated in terms of cutting length of tool path in micro-channel milling applications. Tool path cutting length includes channel depth, width and length, tool diameter, stepover and depth of cut parameters.
In the conventional machining method, tool completes the profile cycle after moving on the Z axis as depth of cut as value and the process is completed when the channel height is complete. For the final depth of cut is equal to the values of the others, the value obtained by dividing the depth of the channel height by the depth of cut must be rounded to the upper integer and the new depth of cut must be recalculated according to the obtained new Z pass.

In the high speed machining method, the tool can cut at the helical length. In cases where the depth of the channel is greater than the helical height of the tool, the depth of cut should not exceed the helical length. In this case, Z down pass must be rounded to the upper integer after obtained and depth of cut must be recalculated.

In the classical method, the Z down pass and the stepover in the high speed process were considered to be $0.05 mm$ for a channel with a depth of $1 mm$ and a length of $10 mm$, the tool path lengths will be calculated as $456 mm$ in the conventional method and $142mm$ in high speed method with trochodial geometry. It is clear that with this calculation method the trochodial method has a tool path which is \%70 shorter than the conventional machining methods. Reducing the tool path length not only reduces the machining times, but also the tool wear goes down to a minimum value. In the trochoid method, the micro-tool moves through the channel with a stepover at the depth of cut up to the helical height of tool. An example is shown from tool paths developed in Figure \ref{fig_2_hst_strategies}. In this study, tool path was studied under four main headings.

\begin{figure}[H]
	\centering	
	\subfigure{
	\includegraphics[width=0.75\textwidth]{figures/fig_2_hst_strategies.jpg}
	}
	\vspace*{-3mm}
	\caption{High speed tool path strategies.}
\label{fig_2_hst_strategies}       
\end{figure}

According to high speed manufacturing approach geometry groups were created. The geometries of these groups are as shown in figure \ref{fig_3_toolpath_geo}. In the simulation study, the aim was to determine the best NC output format and geometric structure examples that can adapt to all control units. In the simulation experiments, the mean processing times of 26 geometries separated by 4 groups in 10 CNC machines, which have different control units, were determined. The effective feedrate of each geometry was evaluated by calculating the feedrate over the average processing times. The optimum geometry was selected from each group in reference to these values. By evaluating the most suitable geometries selected from each group with different NC output format, the trochoid geometry most suitable for common control units was determined.

\begin{figure}[H]
	\centering	
	\subfigure{
	\includegraphics[width=0.90\textwidth]{figures/fig_3_toolpath_geo.jpg}
	}
	\vspace*{-3mm}
	\caption{A) Geometries used up or down milling strategy that do not clean micro-channel walls. B) Geometries used up or down milling strategy that clean micro-channel walls C) Geometries used zig-zag milling strategy that do not clean micro-channel walls D) Geometries used zig-zag milling strategy that clean micro-channel walls}
\label{fig_3_toolpath_geo}       
\end{figure}

Geometry groups

\begin{itemize}
    \item [-] Groups A in which geometries used up or down milling strategy that do not clean micro-channel walls.
    \item [-] Groups B in which geometries used up or down milling strategy that clean micro-channel walls.  
    \item [-] Groups C in which geometries used zig-zag milling strategy that do not clean micro-channel walls.
    \item [-] Groups D in which geometries used zig-zag milling strategy that clean micro-channel walls.
\end{itemize}


\subsection{Experimental Study on Micro-Cutting}
\label{experimentalStudyMicroCutting}

In the cutting experiments, 3 channels were milled on DIN 2738 materials in 10X10X10 mm dimensions with a width of $1.2mm$ and a depth of $1 mm$. Deckel Maho DMU 60P 5.5 axis vertical machine with Union Tool C-Ces2008 which diameter $0.8 mm$ with $2$ flutes was used (Figure \ref{fig_4_exp_setup}). The geometry of the tool used and cutting parameters are shown in Table \ref{cuttingParameterValues}. A new tool was used for each test. The tool used in the experiments is as shown in Figure \ref{fig_5_sem}. In the experiments, run out values were determined between 3-4 $\mu$$m$. The workpiece material used in the experiments are $1,2738$ $40CrMnNiMo8-6$.

\begin{figure*}[]
	\centering	
	\subfigure{
	\includegraphics[width=0.95\textwidth]{figures/fig_4_exp_setup.png}
	}
	\vspace*{-3mm}
	\caption{Experimental setup}
\label{fig_4_exp_setup}       
\end{figure*}

% Please add the following required packages to your document preamble:
% \usepackage{graphicx}
\begin{table}[]
\centering
\caption{Cutting parameter values}
\label{cuttingParameterValues}
\resizebox{0.65\columnwidth}{!}{%
\begin{tabular}{|l|l|}
\hline
\textbf{Name of cutting parameters} & \textbf{Value}   \\ \hline
Tool diameter                       & 0.8 mm           \\ \hline
Channel width/Tool diameter ratio   & 1.5              \\ \hline
Number of cutting flute             & 2                \\ \hline
Flute length of tool                & 1.2 mm           \\ \hline
Stepover                            & 0.075 mm         \\ \hline
Feed rate per teeth                 & 0.006 mm/teeth   \\ \hline
Cutting speed                       & 37.5 m/min       \\ \hline
Spindle speed                       & 14914.77 rev/min \\ \hline
Feedrate                           & 178.97 mm/min    \\ \hline
\end{tabular}%
}
\end{table}


\begin{figure}[t]
	\centering	
	\subfigure{
	\includegraphics[width=0.75\textwidth]{figures/fig_5_sem.jpg}
	}
	\vspace*{-3mm}
	\caption{SEM view of 800 $\mu$$m$ diameter two-flutes end mill.}
\label{fig_5_sem}       
\end{figure}



\subsection{Measurements}
\label{measurements}

In this study, the processing times were evaluated during the simulation experiment. In the cutting experiment, cutting force, surface roughness values, dimension and geometric accuracy, tool wear and burr formation were evaluated. In the experiment, the effects of different geometry and machining strategies were observed by keeping the cutting parameters constant. Scanning electron microscope (SEM, JEOL JSM-6510LV) was used for tool wear measurements. Fx and Fy cutting forces were measured with a Kistler 9275B type dynamometer and analysed with Dynoware software. The resultant force was calculated by taking the analytical average of the two forces. Geometric accuracy was evaluated with PC-DMIS Pro 2013 software and DEA Global CMM. In the measurements, a 0.5 mm diameter Renishaw probe was connected to the ProbTesaStar-SM 7.5 head with a TP200 device. The workpiece was examined with a Nikon ECLIPSE LV100 microscope at a magnification of 100 times in the measurement of surface and burr formation. Surface roughness measurements were conducted via Mitutoyo Surf Test 301 tester. Calibration was done just before measurements. The average surface roughness (Ra) parameter was evaluated for surface roughness measurements. The measurement was repeated 10 times and the average value was taken. Surface roughness measurements were evaluated as the bottom surface and right-left vertical walls.


\section{Experimental Results }
\label{experimentalResults}

Experimental results were presented in this section.

\vspace*{-5mm}
\subsection{Experimental Results on Simulation }
\label{experimentalResultsOnSimulation}

The best geometry from each group of geometries shown above (in Figure \ref{fig_3_toolpath_geo}) was determined by observing the reaction of the control units and cutting times. At this point, the objective is to specify the NC output format and processing strategy that can adapt to common control units. Developed geometry and NC output formats have been evaluated together because the developed geometry is expressed by NC codes in the control unit. 5 different NC output format obtained from each geometry were evaluated in various control units. The optimal NC output format is the geometry that has the minimum number of NC block and is created by geometric parts of equal length. It is difficult to conduct micro precision movements for control units. For this reason, the geometry of one cycle tool path should be created with a minimum number of elements which are equal length. When the number of NC blocks defining the tool paths increases, it is seen that the control units try to process each block one by one and therefore cannot reach the desired feedrate and cause discontinuous cutting.

\begin{figure}[t]
	\centering	
	\subfigure{
	\includegraphics[width=0.95\textwidth]{figures/fig_6_feedrate_effect.jpg}
	}
	\vspace*{-3mm}
	\caption{Effective feedrate values of trochoid geometries in shown figure \ref{fig_3_toolpath_geo} }
\label{fig_6_feedrate_effect}       
\end{figure}


In this study, the influence of tool path geometry and machining strategy on performance can be seen in the micro-milling applications. The cutting parameters used in the experiments are shown in Table \ref{cuttingParameterValues}. The change of geometry used in experiment and active feedrate value is shown in Figure \ref{fig_6_feedrate_effect}. Figure shows the average feedrate values for each geometry shown in Figure \ref{fig_3_toolpath_geo}. When the four different groups were evaluated with their cutting time and the response of the control units, the best geometries were determined from each group. Figure \ref{fig_7_geo_exp_setup} shows the best trochoid geometries selected from each group.



\subsection{ Result of Cutting Experiment  }
\label{resultOfCuttingExperiment}

In the first experiments, the most appropriate geometry from each group was selected through simulation from 26 different geometries which have different machining strategies consisting of 4 groups. These 4 geometries were evaluated together with the effects of cutting direction by making the two geometries having the one-way cutting strategy compatible with the down and up milling. The geometries of the other two groups are geometries suitable for the up-down milling strategy in each cycle.

\begin{figure}[t]
	\centering	
	\subfigure{
	\includegraphics[width=0.65\textwidth]{figures/fig_7_geo_exp_setup.jpg}
	}
	\vspace*{-3mm}
	\caption{Experiment geometries}
\label{fig_7_geo_exp_setup}       
\end{figure}

By cutting experiments, cutting force, tool wear, surface roughness, dimensional accuracy of the part, surface quality and burr formation were evaluated and one of the best was determined in four group of strategies after trochoid geometries and their NC outputs were obtained with simulation experiment. In the simulation section, all the geometries shown in Figure \ref{fig_3_toolpath_geo} were considered, with variations in feedrate using different CNC machines. Due to the complexity of certain geometries, many CNC control units and mechanisms face challenges in achieving precise feedrate values, especially when dealing with small tool path features such as those with a radius below $0.1mm$. As a result, the best four geometries were selected during this observation stage. So, cutting experiments were performed trochoid geometries shown in Figure \ref{fig_7_geo_exp_setup}.


\vspace*{-5mm}
\subsubsection{ Result of Cutting Force  }
\label{resultOfCUttingForce}


The cutting force values obtained from the cutting experiments are shown in Figure \ref{fig_8_cutting_force}.

\begin{figure}[H]
	\centering	
	\subfigure{
	\includegraphics[width=0.95\textwidth]{figures/fig_8_cutting_force.jpg}
	}
	\vspace*{-3mm}
	\caption{Results of cutting force values according to experiment geometries}
\label{fig_8_cutting_force}       
\end{figure}


When the up and down milling forces were evaluated for geometry, a 6\% increase was observed between A1 down milling and A1 up milling. This reduction in cutting force under the same cutting conditions showed the effect of the cutting direction on the force. Pathak BN et al. \cite{makale_10} studied the effects of cutting parameters on cutting force and surface roughness. The lowest cutting force of $137 N$ was found at the highest cutting speed of $500m/min$ and the lowest feedrate of $0.10 mm/rev$. In addition, build-up edge (BUE) was observed at the lowest cutting speeds $200 m/min$ and at high feedrate values $0.30 mm/rev$ \cite{makale_10}.

Xuewei Zhang et al. \cite{makale_11,makale_12} predicted cutting forces and tool deflection in micro-end milling by considering tool run-out which includes axial and tilt offset, the trochoidal trajectory of tooth and variable entry and exit angles of the tool. They used cutting speed of $7.85-18.85 m/min$, radial depth of cut of $0.25-0.50 mm$ and axial depth of cut of $0.15-0.2 mm$ in their cutting experiment with $0.5 mm$ end mill tool. They obtained maximum cutting force as a $4.5 N$ and deflection $20$ $\mu$$m$. In this study maximum cutting force was seen $146 N$ without deflection. This is an advantage of the machining strategy used in this study.

When comparing geometry A and geometry B, it was observed that the cutting force increased by approximately $12\%$ for both down milling and up milling. The results indicate that cleaning the vertical walls of the channel in each cycle had a noticeable impact on increasing the cutting force. In fact, this effect was twice as significant as the effect of the machining direction. When comparing geometry A and geometry C, both of which involve moving without cleaning the channel walls, it was observed that up-down milling (experiment 5) resulted in a higher cutting force compared to down and up milling (experiments 1 and 2). Specifically, there was a $12\%$ increase in cutting force between geometry A down milling $(122.78 N)$ and geometry C up-down milling $(137.49 N)$, and a $5.4\%$ increase between geometry A up milling $(130.41 N)$. This can be attributed to the geometric challenges associated with up-down milling.

When geometry A was compared with geometry D which up-down milling and cleaned the channel walls in each cycle, it was seen that the geometry D cutting force value was the same as the geometry A down and up milling cutting force averages. The difference between geometry D $(127,98 N)$ and geometry up and down milling averages $(126.60 N)$ was $1.1\%$.
When geometry B and geometry D was compared, it was seen that clearing the channel walls in every cycle reduced the cutting forces in up-down milling applications. This was seen as an advantage of cleaning the channel walls in every cycle in up-down milling applications. Geometry D up-down milling $(127.98 N)$ and B down milling $(138.64 N)$ with $8.3\%$ increase and D up-down milling with B up milling $(146 N)$ with $14.1\%$ increase.
When the geometry D up-down milling $(127.98 N)$ was compared with the geometry C up-down milling $(137.49 N)$, it was seen that the cleaning of the channel walls in each cycle in the up-down milling applications reduced the cutting force. The cleaning of the channel walls in each cycle in up-down milling applications reduced the cutting force by $6.9\%$. The lowest force was seen in the geometry A down milling $(122.78 N)$ application and the largest force geometry B in the up milling $(146.06 N)$ application. There was a $19\%$ increase between geometry A down milling and geometry B up milling.

Ozel and Altan \cite{makale_13} studied the cutting force and temperature estimation model using the finite element method (FEM) in high speed milling. The temperature and stress values concentrated at the depth of cut determined in the cutting radius measurement, especially in the cutting radius region, showed the advantage of the depth of cut value determined from helix length of tool applied in this study. In this study, the contact surface area between the tool and the workpiece was approximately 10 times larger compared to conventional methods. This led to reduced cutting force values per unit area and also helped minimize tool wear. Additionally, the increased heat dissipation resulting from the larger contact surface area reduces tool wear compared to conventional methods. Jin and Altintas \cite{makale_14} used FEM to generate a ultimate force estimation model for micro-milling applications. They estimated $45N/mm$ feed force and $70 N/mm$ tangential force at 50 $\mu$$m$ uncut chip thickness with the slip-line model developed by them. Experimental results were obtained with a cutting speed of $25 m/min$ and a tool edge radius of 20 $\mu$$m$ at a diameter of $0.2 mm$. Cutting strategies had effect on cutting force as far as cutting parameters.  

In this study, it could be seen that the cutting force values obtained by the method developed when considering the depth of cut value $(1 mm)$ and cutting parameters shown in Table \ref{cuttingParameterValues} are at the optimal level. (Figure \ref{fig_8_cutting_force})



\vspace*{-5mm}
\subsubsection{ Result of Coordinate Measuring Machine Measurement  }
\label{resultOfCMM}


In CMM measurements, 0.01 mm was used as up and low tolerance. When the channel measurements were evaluated, no deviation was observed in down milling with A geometry, but the 1st, 2nd and 3rd channel widths were observed respectively to be 0.028 mm, 0.026 mm and 0.025 mm larger in the up milling application. Similar error geometry B down milling showed that the 1st, 2nd and 3rd channel widths were 0.022 mm, 0.022 mm and 0.019 mm, respectively. When the geometry C up-down milling application was examined, only 0.013 mm was detected as parallelism error between the vertical walls of the first canal. When the geometry D up-down milling application was examined, it was seen that the 2nd and 3rd channel widths are 0.017 mm and 0.019 mm, respectively.
When CMM measurements were evaluated according to geometry and machining strategy, the most appropriate result was geometry A down milling. Monroy-Vazguez et al. \cite{makale_15} applied micro-channel milling on three different materials and analysed dimensional error, channel profile shape deviation from rectangular, surface quality and burr formation depending on cutting speed, depth of cut, channel depth, feedrate and coolant application parameters. They emphasized that for all materials, the formation of burrs and the dimensional accuracy could be improved with low depth of cut per pass. They also expressed shape disturbances due to run out, tool wear and BUE. They emphasized the cutting conditions (run-out, ploughing effect, minimum chip thickness and tool wear) and especially the calibrated depth of cut value to improve the dimensional and surface quality.
In this study, three channels were machined to acceptable geometric and dimensional tolerances without the occurrence of burr and BUE at the depth of cut up to the tool helical height. This was seen as a success of the processing strategy.


\vspace*{-5mm}
\subsubsection{ Result of Tool Wear  }
\label{resultOfToolWear}

The entire helical length of the cutting tool was utilized in the cutting experiments due to the high-speed cutting strategy employing trochoid geometry. Consequently, the cutting edge wear and helical wear of the tool were also examined. A manual apparatus was designed to analyze the tool wear values using SEM \cite{makale_18,makale_19}. The detection of 3D wear of micro-cutting tools has been studied by Helmli et al. and Kunpeng et al. \cite{makale_16,makale_17}


The wear images of cutting tools after six experiments are given in Figures \ref{fig_9_wear} - \ref{fig_14_wear}
 and Table \ref{cuttingParameterValues}


When the tool was examined in the geometry A down milling application, 20 $\mu$$m$*5 $\mu$$m$ tool wear was observed on one tooth when looking at the tool face point of view. No wear was observed in the helix part of the tool. The tool view can be seen in Figure \ref{fig_9_wear}. 

\begin{figure}[t]
	\centering	
	\subfigure{
	\includegraphics[width=0.75\textwidth]{figures/fig_9_wear.jpg}
	}
	\vspace*{-3mm}
	\caption{Tool wear view used in experiment 1 using down milling strategy that do not clean micro-channel walls a) Front view X100 b) Isometric view X140.}
\label{fig_9_wear}       
\end{figure}

When the tool was examined in the geometry A up milling application, it was observed that there was 256 $\mu$$m$$^2$ length wear in the tool helix. The tool wear was observed at 20 $\mu$$m$*10 $\mu$$m$ on one tooth and BUE when looking at the tool face point of view. The tool view can be seen in Figure \ref{fig_10_wear}. 

\begin{figure}[H]
	\centering	
	\subfigure{
	\includegraphics[width=0.75\textwidth]{figures/fig_10_wear.jpg}
	}
	\vspace*{-3mm}
	\caption{Tool wear view used in experiment 2 using up milling strategy that do not clean micro-channel walls a) Front view X100 b) Isometric view X140.}
\label{fig_10_wear}       
\end{figure}


When the tool was examined in the geometry B down milling application, 30 $\mu$$m$*10 $\mu$$m$ tool wear was observed on one tooth and BUE when looking at the tool face point of view. No wear was observed in the helix part of the tool. The tool view can be seen in Figure \ref{fig_11_wear}.

\begin{figure}[H]
	\centering	
	\subfigure{
	\includegraphics[width=0.75\textwidth]{figures/fig_11_wear.jpg}
	}
	\vspace*{-3mm}
	\caption{Tool wear view used in experiment 3 using down milling strategy that clean micro-channel walls a) Front view X100 b) Isometric view X140.}
\label{fig_11_wear}       
\end{figure}


When the tool was examined in the geometry B up milling application, it was observed that there was wear 200 $\mu$$m$$^2$ length in the tool helix. The tool wear was observed at 90 $\mu$$m$*30$\mu$$m$ on one tooth when looking at the tool face point of view. The tool view can be seen in Figure \ref{fig_12_wear}.

\begin{figure}[H]
	\centering	
	\subfigure{
	\includegraphics[width=0.75\textwidth]{figures/fig_12_wear.jpg}
	}
	\vspace*{-3mm}
	\caption{Tool wear view used in experiment 4 using up milling strategy that clean micro-channel walls 
a) Front view X100 b) Isometric view X140.}
\label{fig_12_wear}       
\end{figure}


When the tool was examined in the geometry C up-down milling application, it was observed that there was wear 45 $\mu$$m$ length in the tool helix. The tool wear was observed at 50 $\mu$$m$*20$\mu$$m$ on one tooth and BUE when looking at the tool face point of view. The tool view can be seen in Figure \ref{fig_13_wear}.

\begin{figure}[H]
	\centering	
	\subfigure{
	\includegraphics[width=0.75\textwidth]{figures/fig_13_wear.jpg}
	}
	\vspace*{-3mm}
	\caption{Tool wear view used in experiment 5 using zig-zag milling strategy that do not clean micro-channel walls 
a) Front view X100 b) Isometric view X140.}
\label{fig_13_wear}       
\end{figure}


In Geometry D up-down milling application, when the tool was examined, two different areas of wear were observed in the helices of the tool at 120 $\mu$$m$ and 60 $\mu$$m$. The tool wear was observed at 40 $\mu$$m$*5 $\mu$$m$ on both tooth and BUE when looking at the tool face point of view. The tool view can be seen in Figure \ref{fig_14_wear}.

\begin{figure}[H]
	\centering	
	\subfigure{
	\includegraphics[width=0.75\textwidth]{figures/fig_14_wear.jpg}
	}
	\vspace*{-3mm}
	\caption{Tool wear view used in experiment 6 using zig-zag milling strategy that clean micro-channel walls 
a) Front view X100 b) Isometric view X140.}
\label{fig_14_wear}       
\end{figure}

Zhou L et al. studied tool wear in high speed milling applications. It was observed that flank wear values decreased by about 40\% when cutting speed increased. In this study, the effect of cutting strategy on tool wear was observed by keeping the cutting speed and feedrate values constant \cite{makale_18}.

When cutting wear was evaluated, the least wear was seen in up milling with Geometry A. Toh CK et al. worked on alternative tool path strategies for high speed applications of tool wear and lifetime. Experiments with axial depths of cut values of 10-20 mm, radial depth of cut of 0.5 mm, cutting speed of 314 m/min and feed per tooth of 0.067 mm were performed on AISI H13 material with 52 HRC hardness using a 10 mm diameter tool \cite{makale_19}. It was declared that tool path strategy and axial depths of cut values had an effect on tool life and wear.

In conventional micro-milling applications, when the depth of cut is applied as much as the corner radii of the tools, the cutting forces are concentrated in this small area, geometrically difficult to produce accelerate tool wear. Lai X et al. modelled micro-milling applications by examining the relationship between tool radius value and depth of cut and figured out the optimum depth of cut depending on the tool radius \cite{makale_20}. Xian Wu et al. investigated the influence of cutting edge radius and the material grain size on the cutting force\cite{makale_21}.



\subsubsection{ Surface Roughness Results  }
\label{surfaceRoughnessResults}

When the surface roughness values were examined, the channel walls and the bottom were assessed separately. Table \ref{surfaceRoughness} shows the surface roughness values obtained from the experiments. When the surface roughness of the down milling of the geometry A was examined, the average surface roughness value of the channel wall was 0.89 $\mu$$m$ and the surface roughness value of the channel bottom surface was 0.62 $\mu$$m$. When the surface roughness was examined with the geometry A up milling, 99\% increase in channel walls and 53\% increase in channel bottom were observed. This adversely affected the surface roughness of the up milling.

% Please add the following required packages to your document preamble:
% \usepackage{graphicx}
\begin{table}[]
\centering
\caption{Surface roughness value of experiments}
\label{surfaceRoughness}
\resizebox{0.75\columnwidth}{!}{%
\begin{tabular}{|l|l|l|}
\hline
\textbf{Experiments}          & \textbf{Wall} \textbf{($\mu$$m$)} & \textbf{Bottom} \textbf{($\mu$$m$)} \\ \hline
Geometry A Down Milling Ra    & 0.89        & 0.62       \\ \hline
Geometry A Up Milling Ra      & 1.77        & 0.95       \\ \hline
Geometry B Down Milling Ra    & 1.70        & 0.51       \\ \hline
Geometry B Up Milling Ra      & 1.36        & 0.64       \\ \hline
Geometry C Up-Down Milling Ra & 0.88        & 0.61       \\ \hline
Geometry D Up-Down Milling Ra & 1.44        & 0.75       \\ \hline
\end{tabular}%
}
\end{table}


When the down milling surface roughness with Geometry B was examined, a mean surface roughness of 0.51 $\mu$$m$ at the channel bottom surface and 1.7 $\mu$$m$ at the walls was observed. This value was about 17,7\% lower than the bottom surface roughness in the Geometry A down milling application. The cleaning of the channel walls in every cycle improved the surface roughness of the channel bottom in down milling applications. In up milling with Geometry B, the bottom surface roughness was measured as 0.64 $\mu$$m$ and wall 1.36 $\mu$$m$. The roughness of the bottom surface increased by about 25.5\% and wall surface 20.3\% decreased using up milling instead of down milling.
In up-down milling with Geometry C, the channel bottom surface roughness was measured to be 0.61 $\mu$$m$ and the wall surface roughness to be 0.88 $\mu$$m$. These results were similar to the results of down milling with Geometry A.
In the up-down milling processing strategy with geometry D, the channel bottom surface roughness was measured to be 0.75 $\mu$$m$ and the wall surface roughness to be 1.44 $\mu$$m$. Raju K.V.M.K. et al. generated surface roughness model using genetic algorithm and optimized cutting parameters such as spindle speed, depth of cut and feedrate without considering cutting strategies\cite{makale_22}. In the up-down milling applications, when the cleaning of the channel walls in each cycle was examined, there was a 23\% increase in the channel bottom surface roughness and 59.1\% in the walls between experiments 5 and 6. This showed that the cleaning of the channel walls in every cycle had a negative effect on the surface roughness in up-down milling applications. Various surface roughness values were obtained in the experiments by employing different machining strategies with the same cutting parameters. The cutting strategy had an impact on the surface roughness, which ranged from $0.51-0.95$$\mu$$m$ on the channel bottom surface and from $0.88-1.77$ $\mu$$m$ on the walls \cite{makale_22}.


Surface roughness measurements were conducted at a distance of $3x0.8 mm$ with 5 repetitions. The obtained surface roughness values from the experiments are presented in Table \ref{surfaceRoughness} and depicted in Figure \ref{fig_15_surfaceRoughness}. The standard deviation of roughness for the wall surface was $0.38$ $\mu$$m$, while for the bottom surface it was $0.15$ $\mu$$m$. Upon examining the channels in all the test results, it was observed that no burrs were formed.

Lekkala R. et al. \cite{makale_23} and Xian Wu et al. \cite{makale_24} studied burr formation modelling in micro-milling applications. They found that the parameters of depth of cut and tool diameter were the main factors in burr formation \cite{makale_23,makale_24}. In this study no burr was seen as a result of any experiment. This was an advantage of the machining strategy without considering depth of cut and tool diameter.

\begin{figure}[t]
	\centering	
	\subfigure{
	\includegraphics[width=0.95\textwidth]{figures/fig_15_surfaceRoughness.jpg}
	}
	\vspace*{-3mm}
	\caption{Surface roughness}
\label{fig_15_surfaceRoughness}       
\end{figure}

\section{ Results and Discussion  }
\label{resultOfCUttingForce}

In the simulation of the study, parameters such as the change in the feedrates, the machining time, the vibration and the discontinuity were observed. From these obtained data, the best geometry was selected from each group. The test results provided continuity of cutting by reducing the number of NC blocks as much as possible and reducing the variation in the feedrates by keeping element lengths equal. The presence of sharp corners and movement in geometric shapes negatively affects cutting conditions. Trochoid geometry should not have sharp corners and linear movements should be connected by arc elements tangent to these straight lines. Mian AJ et al. \cite{makale_25} also defined the main factors affecting micro-milling applications as chip thickness and cutting speed. In this study, micro-milling machining strategy, cutting parameters and NC output format were examined as a whole.
Tool path geometry should be applicable to different channel metrics, tool diameter and cutting parameters. Tool path geometry can be reconfigurable when changing channel metrics, tool diameter or cutting parameters.
The start point and the end point of the geometry cycles must be on the cutting direction line and the closest distance between them. It must be as long as the stepover to the down or up milling, and twice as long as the stepover to the up-down milling. Otherwise the connection between the cycles will not be established. All the geometries are designed accordingly.
In the cutting experiments, the down milling and up milling were applied to the geometries having one-way cutting ability. Especially when the values of tool wear and cutting forces were examined, it was seen that down milling gave us better results.

Due to the trochoid geometry, scallop heights formed in the channel walls in two different ways, one at each trochoid cycle and one after the completion of all the trochoid cycles. Especially when evaluated by the surface quality, as a second process, the application of cleaning the channel walls produced better surface quality.


Owing to the trochoid geometry, scallop heights were formed on the channel walls in two distinct manners: one at each trochoid cycle and another after the completion of all trochoid cycles. Particularly when considering surface quality, the additional process of cleaning the channel walls resulted in improved surface quality ( Table \ref{surfaceRoughness} Geometry C and Geometry D).


Cutting force values were measured and analysed with dynamometer. The smallest cutting force values were observed with geometry A with the down milling.
When CMM measurement results were evaluated, it was seen that there were no large error differences between 3 channels in the same experimental part. This stability in the cutting process proved the success of the applied strategy.
When tool wear values were examined, less cutting wear was observed in down milling than in up milling. In these cutting strategies which all used the tool helix, it was observed that there was no wear in the tool helix region especially in the down milling experiments.
No geometric burr formation, geometric and dimensional defects, were observed due to the developed machining strategy. Geometry A with down milling was selected by examining the tool traces and surface roughness of the channel surface. The difference between channel bottom and wall surface roughness values was seen in this geometry.
Chip structures are the most important feature in the determination of the quality of the cutting process. Quality chip formation make cutting progress easy. Particularly in micro-milling, the chip structure micro-scale may adversely affect cutting. It is desirable to fracture the chip in the process of separating from the workpiece in order to move it away from the cutting zone easily. This process also removes the heat that occurs during milling. With the new machining method developed, the chip volume was increased and it was easily broken away and easily separated from the work.


\subsection{ Comparison of Classic Method with High Speed Processing }
\label{highSpeedProcessing}

High speed machining method was compared with the conventional method in relation to tool path length, machining time, tool wear and surface quality. 
Advantages of high speed machining in micro-milling compared to conventional machining;

\begin{itemize}
\item [-] The use of the cutting parameter depth of cut value up to the tool helical length allows the cutting force to spread over a larger surface of the tool. In this case also, the entire helix of the tool can be used. This reduces tool wear, leads to higher cutting forces and reduces tool costs.
\item [-] In the cutting zone the friction surface between the cutting tool and the workpiece increases and the friction times are reduced.
\item [-] The heat generated during cutting is easily separated from the cutting area together with the chip.
\item [-] Due to the helical angle of the cutting tool, the chip is easily broken off from the workpiece.
\item [-] The length of the tool path in high speed machining is much shorter than the conventional machining method.
\item [-] High speed machining method processing minimizes vibration particularly important with parts with thin walls.
\end{itemize}


\subsection{ The Experimental Results Obtained for Developed Tool path Strategies}
\label{developedToolpathStrategies}


As seen in Table \ref{resultsOfExperiments}, the largest cutting force value of $146N$ was found in the geometry B up milling application. The worst surface roughness was found in this study at $0.95$ $\mu$$m$ on the bottom and $1.77$ $\mu$$m$ on the walls. The maximum tool wear was observed in the B up milling application at the tool face view $90$ $\mu$$m$*30 $\mu$$m$ and $200$ $\mu$$m$ in the helix of the tool. Due to geometric difficulties, the lowest effective feedrate value was seen in geometry C up down milling with $142.3 mm/min$. When the tool path length and effective feedrate were evaluated together, the maximum machining time was found to be $51.54 sec$ with geometry B, up and down milling.

When the geometry A down milling application was used, the optimum result was evaluated with maximum values, 19\% reduction in cutting force value was achieved. In addition, the surface roughness value decreased by 53\% on the bottom surface and by 99\% on the wall. Tool wear area from the tool face view was 26 times better then B up milling and there was no flank wear on helix of the tool. The effective feedrate value can be seen as $44.55 sec$

% Please add the following required packages to your document preamble:
% \usepackage{graphicx}
\begin{table*}[]
\centering
\caption{Results of experiments}
\label{resultsOfExperiments}
\resizebox{0.95\columnwidth}{!}{%
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\textbf{Developed tool paths} &
  \textbf{Cutting force {[}N{]}} &
  \textbf{\begin{tabular}[c]{@{}l@{}}Surface roughness bottom/\\ wall {[}$\mu$$m${]}\end{tabular}} &
  \textbf{\begin{tabular}[c]{@{}l@{}}Tool wear face {[}$\mu$$m$2{]}/\\ helix 1 {[}$\mu$$m${]}/\\ helix 2 {[}$\mu$$m${]}\end{tabular}} &
  \textbf{\begin{tabular}[c]{@{}l@{}}Effective   \\    feedrate \\    {[}mm/min{]}\end{tabular}} &
  \textbf{\begin{tabular}[c]{@{}l@{}}Machining   \\    time \\    {[}Sec{]}\end{tabular}} \\ \hline
A Down Milling & 122.78 & 0.62/0.89 & 20*5/0/0    & 255.7 & 44.55 \\ \hline
A Up Milling & 130.41 & 0.95/1.77 & 20*10/256/0 & 255.7 & 44.55 \\ \hline
B Down Milling & 138.64 & 0.51/1.70 & 30*10/0/0   & 281.1 & 51.54 \\ \hline
B Up Milling &146 & 0.64/1.36 & 90*30/200/0 & 281.1 & 51.54 \\ \hline
C Up-Down Milling & 137.49 & 0.61/0.88 & 50*20/45/0  & 142.3 & 37.31 \\ \hline
D Up-Down Milling & 127.98 & 0.75*/1.44 & 40*5/120/60 & 155.9 & 44.22 \\ \hline
\end{tabular}%
}
\end{table*}


The improved micro-channel milling tool path was facilitated by using macro programming method Table \ref{macro}

% Please add the following required packages to your document preamble:
% \usepackage{graphicx}
\begin{table}[H]
\centering
\caption{Macro programme}
\label{macro}
\resizebox{0.65\columnwidth}{!}{%
\begin{tabular}{|c|l|}
\hline
\multicolumn{1}{|l|}{Block No} & Code                                                     \\ \hline
N1                             & \#1=1.2 (Channel width)                                  \\ \hline
N2                             & \#2=0.8 (Tool diameter)                                  \\ \hline
N3                             & \#3=0.075 (Step over)                                    \\ \hline
N4                             & \#4=10 (Channel length)                                  \\ \hline
N5                             & \#5=1 (Channel height)                                   \\ \hline
N6                             & \#6=1 (Number of Z pass)                                 \\ \hline
N7                             & \#501=25 (Cutting speed)                                 \\ \hline
N8                             & \#502=0.005 (Feed rate)                                  \\ \hline
N9                             & \#503=2 (Number of fluet)                                \\ \hline
N10                            & \#504=22/7                                               \\ \hline
N11                            & \#505={[}\#501*1000{]}/{[}\#504*\#2{]}                   \\ \hline
N12                            & \#506=\#502*\#503*\#505                                  \\ \hline
N13                            & \#201=\#1-\#2                                            \\ \hline
N14                            & \#202=\#201-{[}\#3*2{]}                                  \\ \hline
N15                            & \#203=ARCTAN{[}\#3/\#202{]}                              \\ \hline
N16                            & \#204=SIN{[}\#203{]}*{[}\#3{]}                           \\ \hline
N17                            & \#205=COS{[}\#203{]}*{[}\#3{]}                           \\ \hline
N18                            & \#11={[}{[}\#202/2{]}+{[}\#204{]}{]}                     \\ \hline
N19                            & \#12=-{[}{[}\#2/2{]}+{[}\#3{]}{]}                        \\ \hline
N20                            & \#21={[}\#202/2{]}                                       \\ \hline
N21                            & \#22={[}\#12+\#3+\#205{]}                                \\ \hline
N22                            & \#31=-{[}\#21{]}                                         \\ \hline
N23                            & \#32={[}\#22{]}                                          \\ \hline
N24                            & \#41={[}\#11-\#202{]}                                    \\ \hline
N25                            & \#42={[}\#12{]}                                          \\ \hline
N26                            & \#51={[}\#11{]}                                          \\ \hline
N27                            & \#52={[}\#12+\#3{]}                                      \\ \hline
N28                            & G0 G17 G40 G49 G80 G90                                   \\ \hline
N29                            & T1 M6                                                    \\ \hline
N30                            & G0 G90 G54 X{[}\#11{]} Y{[}\#12{]}                       \\ \hline
N31                            & M3 S\#505                                                \\ \hline
N32                            & G43 H1 Z10                                               \\ \hline
N33                            & N1 G1 Z-{[}\#6{]} F{[}\#506{]}                           \\ \hline
N34                            & N2 G3 X{[}\#21{]} Y{[}\#22{]} I-{[}\#204{]} J{[}\#205{]} \\ \hline
N35                            & G1 X{[}\#31{]} Y{[}\#32{]}                               \\ \hline
N36                            & G3 X{[}\#41{]} Y{[}\#42{]} I0 J-{[}\#3{]}                \\ \hline
N37                            & G1 X{[}\#51{]} Y{[}\#52{]}                               \\ \hline
N38                            & \#22=\#22+\#3                                            \\ \hline
N39                            & \#32=\#32+\#3                                            \\ \hline
N40                            & \#42=\#42+\#3                                            \\ \hline
N41                            & \#52=\#52+\#3                                            \\ \hline
N42                            & IF{[}\#52 LE \#4{]} GOTO2                                \\ \hline
N43                            & \#6={[}\#6*2{]}                                          \\ \hline
N44                            & IF{[}\#6 LE \#5{]} GOTO1                                 \\ \hline
N45                            & G0 Z10                                                   \\ \hline
N46                            & M30                                                      \\ \hline
\end{tabular}%
}
\end{table}



\newpage
\section{Conclusion and future works}
\label{Sec-Conclusion}

In micro-channel milling applications, the cutting time may be too long with classical methods and this can cause tool wear and error of geometrical tolerance. This study showed that 3 channel with 1.2 mm width, 1 mm depth and 10 mm length can be obtained by using 0.8 mm diameter tool without seen any tool wear and error of geometrical tolerance.
When the test results were examined, it was seen that the most suitable machining strategy was down milling, which was applied with geometry A and the channel walls were cleaned by finish machining.
With this study the developed tool path with trochoid geometry length was 540 mm. In these conditions, a reduction of about 67.5\% was observed in the length of the tool path compared to the conventional method.
In addition to the reduction in tool path length, the wear of the tool was seen in the size of 20 $\mu$$m$*10 $\mu$$m$ when viewed from the tool face profile. This little wear value was a success of the developed method.
No difference was found in each channel geometry measurement with a tolerance of 0.01 mm. Surface roughness was found to be 0.62 $\mu$$m$ on the bottom and 0.89 $\mu$$m$ in the walls and no burr was formed in 3 channels. 

\section*{Declarations}

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Emre Gunaydin: Conceptualization, Methodology, Implementation, Validation, Writing.
Babur Ozcelik: Conceptualization, Methodology, Writing.
Emel Kuram: Conceptualization, Writing. 

\vspace{4mm}
\textbf{Ethics approval} Not applicable.
\vspace{2mm}

\vspace{2mm}
\textbf{Consent to participate} Not applicable.
\vspace{2mm}

\vspace{2mm}
\textbf{Consent for publication} Not applicable.
\vspace{2mm}

\vspace{2mm}
\textbf{Conflict of interest}  The authors declare no competing interests.
\vspace{2mm}


\newpage
\bibliography{References}


\end{document}
