# Analytical and Graphical Profiling of Thread-Milling Cutters for Forming Internal Threads
## 5 Research Methodology and Experimental Results
### The Influence of the Rake Angle and the Backing Off on the Tool Surface  
The deviations of the height of the profile h\({}_{0}\) and of the profile angle of the milling part \(\Delta\alpha_{0}\) were determined by the developed method. The influence of the rake angle \(\gamma_{0}\) and the diameter of the internal thread D on the profile angle \(\alpha_{0}\) was studied with a certain pitch of the thread P and at different ratios of the diameters of the tool and the thread d\({}_{0}\)/D. Forming of internal threads from M10 \(\times\) 1 to M24 \(\times\) 1 with an M10 \(\times\) 1 thread-milling cutter, threads from M10 \(\times\) 1.5 to M24 \(\times\) 1.5 with a M10 \(\times\) 1.5 thread-milling cutter, and threads from M10 \(\times\) 2 to M24 \(\times\) 2 with an M10 \(\times\) 2 thread-milling cutter was considered. The results were obtained from the three-dimensional models and sketches developed for each of the variants with the SolidWorks 2022 CAD system. Results are presented in Table 7. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{2}{c}{**Name of the Parameter**} & **Designation** & **Value** \\ \hline \multicolumn{2}{c}{Tool Parameters M10 \(\times\) 2} \\ \hline Outer diameter of the milling part of the thread-milling cutter & d\({}_{0}\), mm & & 7.335 \\ \hline \multicolumn{2}{c}{Tool surface profile parameters} \\ \hline Tool surface center trajectory radius & A\({}_{0}\), mm & & 6.333 \\ \hline Points from the tool surface profile & point 1 & point 3 & point 5 \\ \hline \multicolumn{2}{c}{Results obtained using the analytical method} \\ \hline Radius of the profiled circle & r\({}_{0i}\), mm & 3.6763 & 3.0257 & 2.5919 \\ \hline Distance from point 1\({}^{\prime}\) to point i along the “y” axis of the profiling circle & h\({}_{0i}\), mm & 0 & 0.6506 & 1.0844 \\ \hline Distance from point 1\({}^{\prime}\) to point i along the “z” axis of the profiling circle & z\({}_{0i}\), mm & 0 & 0.3750 & 0.6250 \\ \hline Tool profile angle & \(\alpha_{0i}\), \({}^{\circ}\) & 0 & 59.9192 & 59.9153 \\ \hline Deviation in profile angle & \(\Delta\alpha_{0i}\), \({}^{\circ}\) & 0 & 0.0808 & 0.0847 \\ \hline Radius of the profiled circle & r\({}_{0i}\), mm & 3.6745 & 3.0240 & 2.5903 \\ \hline Distance from point 1\({}^{\prime}\) to point i along the “y” axis of the profiling circle & h\({}_{0i}\), mm & 0 & 0.6505 & 1.0842 \\ \hline Distance from point 1\({}^{\prime}\) to point i along the “z” axis of the profiling circle & z\({}_{0i}\), mm & 0 & 0.3750 & 0.6250 \\ \hline Tool profile angle & \(\alpha_{0i}\), mm & 0 & 59.9251 & 59.9236 \\ \hline Deviation in profile angle & \(\Delta\alpha_{0i}\), mm & 0 & 0.0749 & 0.0764 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._Figures 23-26 present a graphical interpretation of the results obtained in Table 7. Based on the calculations made, the following conclusions can be drawn:  
* It was found that when milling internal threads with tools with a constant outer diameter d\({}_{0}\) and backing off height K\({}_{0}\), with an increase in the rake angle of the teeth \(\gamma_{0}\) of the milling part, the height of the profile h\({}_{0}\) and the deviation of the profile angle of the tool surface \(\Delta\alpha_{0}\) increase, and the width of the teeth b\({}_{0}\) remains constant;
* It was found that with an increase in the diameter of the internal thread D at a constant pitch of the thread P and a constant external diameter of the tool d\({}_{0}\), the profile height h\({}_{0}\) and the deviation of the profile angle of the tool surface \(\Delta\alpha_{0}\) decrease;
* It has been proven that in order to obtain an accurate profile of the internal thread, it is necessary to correct the profile of the tool surface by \(\Delta\alpha_{0}\) and \(\Delta\)K\({}_{0}\).