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The results of mathematical simulation have been carried out for the pattern of working medium motion providing the technological process of finishing-grinding treatment in an oscillating reservoir. With use of physics laws, it is ascertained and grounded that the flow of granules at the plane wall of reservoir is travelling oppositely to the source of vibrations, whereas the granules are drifting on the cycloidtrochoid trajectories from the wall of reservoir, where the looped displacement is maximal, to the center of reservoir in which the shift of granules is reduced to minimum because of damping and dissipation effect. The received theoretical regulations have a fundamental nature and can be used at the account of technological parameters of designed vibration machines.

When using new, very expensive superhard tool materials (diamond or CBN) for precision and ultraprecision machining of parts made, very often, from expensive materials, exact knowledge of the tool wear process (considering, of-course, its stochastic character) is absolutely necessary. It means, that we need new tool-life equations for these new tools. In the present paper, a new tool life relation is proposed based on machining experiments. It reflects the two-extremum form of tool life curves and is valid for a wide range of cutting conditions.

A finite element model is proposed to simulate the precision and ultraprecision grinding of steel and to describe the temperature fields developed during the process. The grinding is modelled using the commercial implicit finite element code MARC. In order to obtain the input data required for the model and to examine the heat damage induced to the workpiece, a series of experiments was performed with the same grinding conditions, but using different aluminium oxide grinding wheels of different bonding on the same work material. Comparison between numerical results obtained from the proposed model and experimental predictions, as well as numerical and analytical calculations reported in the literature, revealed a good agreement between theory and practice, indicating therefore that the model may be suitable for industrial applications.

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In this paper, the results of an investigation done with face milling are presented. The changes in cutting force and surface roughness were studied through changing the values of depth of cut and the feed per tooth. Meanwhile the permanent value of the undeformed chip cross section, which was determined (fz and ap), remained permanent. Increasing fz and keeping the same value of Ac chip cross section, the ratio ap/fz changed in five grades from 0.5 to 8. It is shown, that if the feed is increased in the examined range so that the chip cross section is constant, then the value of the cutting force decreases, which decrease can be observed in all three force components. Accordingly, the mechanical power required for cutting is reduced. The results of the surface roughness investigations showed that initially a significant increase can be observed in the roughness with the gradual increase of the feed (up to ap/fz = 2.5), followed by a moderate increase afterwards.