## 4 Discussion  
This study investigated the effects of CNC parameter settings (contour tolerance, limit frequency, and axial and corner jerk limits) on the quality and accuracy of the interpolator output in corner neighborhoods. The results obtained on the basis of a full factorial test performed on a simplified testing toolpath consisting of linear blocks were used to build regression models, which were then verified on a general piecewise linear toolpath. The results of this study show that excessively high corner jerk limits can lead to a significant overshoot of the programmed path tolerance (by as much as 85% in some cases) in corner neighborhoods. This study, therefore, presents the maximum values of corner jerk limits for which the programmed path tolerance is maintained, independent of the magnitude of the angle between two adjacent linear blocks. The values of these jerk limits depend on the chosen tolerance limit and the value of the limit frequency of the interpolator. In addition to the toolpath accuracy, the variation in the deviation from the ideal surface along the toolpath has a significant effect on the quality of the final workpiece. This study presents a method to quantify this oscillation of the deviation in the toolpath from the ideal surface and, thus, evaluate the geometric quality of the interpolator output in corner neighborhoods. The results of the tests performed show that the quality of the interpolator output around corners is primarily dependent on the choice of the tolerance limit and the interpolator limit frequency, and secondarily on the choice of the corner and axial jerk limits. Therefore, for successful quality control, it is first necessary to specify the desired tolerance and limit frequency of the interpolator and then control the resulting quality of the interpolator output by the choice of the jerk limits. In practice, this requirement is not limiting, as the parameters of the tolerance limit and the limit frequency result from the overall accuracy requirements (tolerance limit) or the dynamic characteristics of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Maximal Contour Error: Maximal Values of Corner Jerk (m/s3) for Which Contour Tolerances** & \multicolumn{3}{c}{**Are Satisfied**} \\ \hline
**Contour Tolerance (mm)** \(\backslash\)**Limit** & **0.01** & **0.02** & **0.1** \\
**Frequency (Hz)** & & & \\ \hline
**10** & 0.8 & 2.4 & 7.3 \\
**15** & 3.6 & 4.5 & 19.3 \\
**20** & 5.9 & 9.8 & 43.8 \\
**25** & 9.5 & 17.4 & 86.7 \\
**30** & 14.9 & 28.3 & 138.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dependence of maximal contour error on corner jerk values. The presented corner jerk values (m/s3) represent maximal values for which the contour tolerance was not exceeded for any of the tested angle sizes. The values were obtained by interpolation/extrapolation of the respective regression models formulated on the basis of “Fan” toolpath data and rounded to one decimal place. the machine (in the case of the limit frequency) and are, thus, known in advance for the application. The results obtained show that, once these parameters are fixed, the choice of the corner and axial jerk limits can effectively reduce the rate of deviation oscillation in corner neighborhoods. Previous studies investigating the topic of interpolator parameter optimization differ from the present study in several important ways. In addition to the influence of the interpolator itself, previous studies simultaneously include the influence of feed drive control and machine dynamics [28; 29; 30; 31]. These models are certainly more comprehensive, but at the same time, their results are only valid for a specific machine tool, and to apply them to a machine with different mechanical and kinematic properties, the demanding optimization process must be repeated. In contrast, the results of the presented study are directly applicable to any machine tool equipped with the same interpolator module, as the consistent behavior of the interpolator is guaranteed by the manufacturer.