## 3 Results
### Parameter TV--Dependence on CNC Parameter Settings  
The \(TV\) parameter was found to depend on four of the investigated interpolator parameters: contour tolerance, limit frequency, axis-specific jerk, and axis-specific jerk at corners. Two types of dependence of the \(TV\) parameter were distinguished on the basis of the experiments performed. For high contour tolerances and/or high values of limit frequency, the \(TV\) coefficient was found to depend only on the corner jerk limit and the dependence could be adequately described by a quadratic model (these situations correspond to 80% of the studied cases). In contrast, when both low contour tolerance and low limit frequency were selected, the \(TV\) coefficient was found to depend approximately quadratically on both the axis-specific jerk and the corner jerk limit. In either of the two cases, the choice of limit frequency and contour error values affected the range of corner jerk limit values that had a measurable effect on the \(TV\) coefficient. In other words, the lower the limit frequency and contour tolerance, the lower the corner jerk limit threshold, after which an additional increase in the corner jerk limit did not influence the \(TV\) parameter. The values of these corner jerk thresholds depending on contour tolerance and limit frequency are presented in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Corner Jerk (m/s\({}^{3}\)) Threshold Values with Respect to Contour Tolerance Limit (mm) and** &  
For each combination of contour error and frequency limit, the corresponding \(TV\) values from each individual data source (Fan and Valley toolpaths) were min-max-normalized for the purposes of comparison. Quadratic regression models were then fitted to the Fan toolpath interpolator data and verified on the Valley toolpath data. The results show that the regression models explain a large percentage of the predicted variance (R-Sq. (adj.) \(\geq\) 0.97) and the models fitted on the Fan toolpath interpolator data generalize well (\(RMSE\leq\) 0.068) to Valley data. Figure 9 presents a comparison of the models obtained for a contour accuracy of 20 \(\upmu\)m and varying values of limit frequency. For detailed information on the regression models corresponding to high contour tolerance/high limit frequency, see Appendix A, Table A2 (contour tolerance 10 \(\upmu\)m), Table A3 (contour tolerance 20 \(\upmu\)m), and Table A4 (contour tolerance 100 \(\upmu\)m). The case of low contour tolerance limit and low frequency threshold (combinations denoted by * in Table 2) was slightly different. In these cases, the \(TV\) coefficient depended not only on the corner jerk limit, but also on the axis jerk limit. The dependence was quadratic and increasing with respect to both parameters. In other words, both the increase in the corner jerk limit and the increase in the axial jerk limit led to an increase in the \(TV\) parameter. The dependence could be adequately described by a model of the form of Equation (2)  
\[TV\sim a_{0}+a_{1}I_{c}+a_{2}J_{c}I_{a}+a_{3}J_{a}^{2}+a_{4}J_{c}^{2} \tag{2}\]  
where \(J_{a}\), \(J_{c}\) denote the values of the axial jerk limit and the corner jerk limit, respectively. Note that the linear term in \(J_{a}\) is omitted in (2), as it did not show itself to be statistically significant in the performed tests. As in the case mentioned above, the regression models explain a large percentage of the predicted variance (R-Sq. (adj.) \(\geq\) 0.87) and the models fitted on the test toolpath interpolator data generalize well (\(RMSE\leq\) 0.06) to Valley toolpath data. For the regression model surfaces, see Figure 10. For detailed information on the corresponding regression models, see Appendix A, Table A1. Figure 9: Dependence of the \(TV\) parameter on corner jerk values for contour tolerance of 20 \(\upmu\)m and tested limit frequencies based on the ”Fan” toolpath results. The results for individual frequencies are distinguished by color. The regression curves are displayed as solid lines.