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3D surfaces based on the Archimedes' spiral are widely used in mechanical engineering, especially in the manufacturing the gear milling cutters. The machining process to create this type of surface is usually performed in specialized machines. In this study, relieving grinding process was conducted to machine the Archimedes surface of HSS P18 workpiece material using a specialized machine (1Б811) to investigate the influence of the grinding wheel graininess (G), hardness of grinding wheel (Hd), grinding wheel velocity (V), and feedrate (s) on surface quality including surface roughness (Ra) and surface hardening (ΔHRC). The experimental plan with 27 experiments (L27) was designed using the Taguchi method. Applying the analysis of variance (ANOVA), the influence of G, V, s, and Hd on Ra and ΔHRC was investigated. G, V, s, and Hd have different influences on Ra and ΔHRC in the relieving grinding process. V has the greatest influence on Ra and ΔHRC with 40.96% for Ra and 26.43% for ΔHRC. The grinding wheel hardness that has the lowest influence on Ra (0.82%), whereas the feedrate has a negligible effect on ΔHRC (7.01%). The interaction effect of the input parameters on Ra is not significant (2.91%). However, for ΔHRC, the interaction influence degree of these parameters on this criterion is quite high (33.77%). From the experimental data, Ra and ΔHRC were presented as a quadratic function of G, V, s, and Hd with high values of determination coefficient (R2 = 92.75% for Ra and R2 = 92.00% for ΔHRC). In the surveyed range of the input parameters, Ra decreases if G and V increase, and s decreases. Also in this survey range, the hardening increases if the values of the input parameters (G, V, and s) increase. This study also determined that there is no clear rule about the relationship between Ra and ΔHRC. Further studies need to be carried out to find the input optimal values ensuring the quality criteria of the relieving grinding process. [ABSTRACT FROM AUTHOR]

In this work, the method of drawing of nine celebrated Minoan Late Bronze Age wall-paintings, is studied. Four of these frescoes were unearthed at Akrotiri, Thera, while the other five were excavated in Crete; these frescoes have never been thoroughly studied before, concerning their method of drawing. The authors demonstrate that practically all actually drawn contours in these frescoes, optimally fit six geometric stencilsguides, namely, four hyperbolae and two Archimedes' (linear) spirals. It is important to note that the hyperbola and the linear spiral do not exist in nature, definitely not with the precision encountered here. We would like to stress that all wall-paintings the authors have studied so far, i.e. more than twenty-five (25), had been drawn via the use of the same stencils, a fact that renders the eventuality that this was indeed the method of drawing of these frescoes, almost certain. The considered wall-paintings cover a period of at least two centuries, located both before and after the gigantic eruption of Thera volcano. Moreover, here, possible methods of construction of the determined stencils are proposed, as well as the most probable one, according to our opinion. Methodologically, the authors determine couples of the longest contour parts, CP, appearing in the studied frescoes and of a proper sub-curve GPopt of one of the aforementioned stencils; these couples are chosen so as they fit with exceptionally low approximation errors. The latter terms are rigorously defined here, for the first time. Special care is taken, mathematically and programmatically, to ensure the maximum possible smoothness between successive optimally fit stencils' parts GPopt. Next, the authors employed these modern prerequisites, to introduce the more probable sequence of actions taken by the prehistoric artist(s) for drawing the specific frescoes. Finally, crucial queries and conjectures are set, together with a number of plausible answers. [ABSTRACT FROM AUTHOR]