2.1.3. Validation of the Empirical Method

Machining times are divided into cutting time (Ct) and rapid travelling (Rt) movement time when the tool approaches the workpiece and moves between elements. These times are shown in Figure 3 and allow one to conclude that the cutting times obtained in the two methods are the same, which is explained by the fact that the same tools were used with the same cutting parameters and sequence of operations. The difference between the values obtained is in the rapid movement times. In the traditional method, the tool displacement time between elements and the tool approach time to the workpiece is calculated, while in the empirical method, due to lack of knowledge about the position of the elements in the workpiece, only the tool approach time is counted. This is the main reason for the difference in times obtained between these two methods. Thus, the empirical method is valid for calculating cutting times but is invalid for calculating rapid movement times. Thus, bearing in mind that they are the primary influence on the final machining time, as seen in Figure 4, only cutting times are used to develop the artificial neural networks.

**Figure 4.** Traditional method (**a**) and empirical method (**b**) machining time in percentage (Ct—cutting time; Rt—rapid travelling time).

After the validation of the empirical method, which has the advantage of being able to generate an infinite number of parts, two databases were created based on the features shown in Table 1 for the development of ANNs:

