A Mathematical Model for Calculating Deviations of the Shape, Size and Geometric Relationship of Flat Surfaces

There is a variety of objectives for measuring deviations of flatness, size and mutual arrangement of flat surfaces, namely: processing accuracy control, machinery condition monitoring, treatment process control in terms of shape deviation, comparative analysis of machine rigidity. If for a processing accuracy control it is sufficient to obtain the flatness deviation, as the maximum adjoining surface deviation, the choice of the adjoining surface as a zero reference datum deviation leads to considerable difficulties in creating devices and in particular devices for measuring size and shape variations. The flat surface is characterized by mutual arrangement of its points and can be represented by equation in the selected coordinate system. The objective of this work is to provide analytical construction of the vector field F, which describes the real surface with an appropriate approximation upon modelling the face milling of the flat surfaces of body parts in conditions of anisotropic rigidity of technological system. To determine the numerical value of shape and size deviation characteristics the average surfaces can serve a basis for the zero reference values of vectors. A mean value theorem allows to obtain measurement information about deviations in shape, size and arrangement of processed flat surfaces in terms of metrology, as well as about the process parameters such as depth of cut, feed, cutting speed, anisotropic rigidity of technological system that characterize the specific processing conditions. The machining center MS 12-250 was used to carry out a number of experiments with processing the surfaces of the prism-shaped body parts (300x300x250) and the subsequent measurements of flatness on the IS-49 optical line to prove the correlation between expected and observed values of the vectors of flatness deviations