## 2 Materials and Methods
### Selected Interpolator Parameters  
As mentioned previously, the settings of the interpolator parameters have a major influence on the machining result. A single part program can be handled in many ways with varying degrees of preference for machining speed, accuracy, and surface smoothness. These objectives are influenced by parameters such as the type of position filter used (MP1200), contour tolerance (MP1202), cutoff frequency of the position filter (MP1210 to MP1218), and maximum allowable feed values (MP1010 to MP1020), as well as accelerations (MP1060 to MP1070) and jerk limits (MP1085 to MP1090) either on the path or in the individual axes. The parameters mentioned above modify the global properties of feedrate planning. Multiple parameters are also available that specify local behavior, such as interpolation jerk values (MP1230 to MP1243) at corners and curvature changes, the reduction in the contouring feedrate at the beginning of the contour elements (MP1205), the tolerance for changes in contour curvature (MP1223) and parameters specifying when and what transition to insert between two contour elements, and how to behave on it in terms of jerks (MP7680, bits 7, 8, and 9). These machine parameters must be optimally set in relation to the preferences of the machining result, and especially with regard to the current condition and mechanical properties of the machine tool structure. The effects of multiple interpolator parameters on toolpath quality and precision in corner neighborhoods were investigated in this study. Specifically, these parameters were:  
1. Contour tolerance at machining feedrate (MP1202.0);
2. Limit frequency for the advanced HSC filter (MP1213);
3. Axis-specific jerk (MP1085.x);
4. Axis-specific jerk at corners for the advanced HSC filter (MP1233.x). The axis acceleration limit (MP1060.x) was initially included in the tests, but it was not found to have a significant effect on the quality, as evaluated by the \(TV\) coefficient (1), and was, therefore, excluded from the final tests. The tested values for each of the investigated interpolator parameters are given in 1. A full factorial experiment was performed based on the parameter values presented in Table 1. The size and type of the machine used in the experiments were key in selecting the ranges of these parameters with the default settings of the machine manufacturer taken as reference. To successfully capture the effect of the investigated parameters on the quality and precision of the interpolator output path, fixed settings were chosen for some interpolator parameters so that they did not bias the test result. For example, the path limitations on acceleration and jerk were removed so that only the settings of the individual axes were limiting and the errors were easier to observe. The same acceleration and jerk limits were always chosen in all axes so that the boundary conditions in the interpolation calculation were comparable. Acceleration values were fixed at the value of the weaker of the tested axes so that the mechanical components of the machine, which were designed by the manufacturer for a certain acceleration, could not be damaged. The Advanced HSC position filter was chosen for the tests as it allows for a good compromise between the machining speed and the quality of the machined surface. The Heidenhain technical manual offers the following comment on the HSC filters (standard and advanced) ([32], p. 829): \begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & **Units** & **Values** \\ \hline MP1202.0 (contour tolerance) & mm & 0.02, 0.01, 0.1 \\ MP1213 (limit frequency for the Advanced HSC filter) & Hz & 10, 15, 20, 25, 30 \\ MP1085.x & m/s\({}^{3}\) & 10, 12.5, 15, 17.5, 20, 25, 30, 45, 65 \\ (axis-specific jerk value) & m/s\({}^{3}\) & 1, 25, 5, 7.5, 10, 12.5, 15, 17.5, 20, 25, 30, 45, 65, 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Interpolator parameter values investigated in this study. \"The speed advantage of both HSC filters is especially large for circular contours.