АНАЛІТИЧНЕ ВИЗНАЧЕННЯ КОЕФІЦІЄНТА ФОРМИ ЗУБЦЯ ПИЛОК

Abstract

The paper presents the results of the study of analytical dependencies of saw tooth shape coefficient. In the course of research we have revealed that the values of saw tooth shape coefficient, recommended in the literature, do not allow to accurate determining the coefficient of tension of the cavity and the feed speed of wood, as they have a wide range of values. To calculate the actual values of the saw tooth shape coefficient for a known pitch of the teeth, it is necessary to know the areas of cavities, because inaccuracies in determining these areas on the basis of recommended in the literature values of the tooth shape coefficient are significant. This is confirmed by determining the actual areas of the interteeth cavities from the impressions of the toothed crowns of saws. Using the methods of analytical geometry, the analytical dependences of the areas of interteeth cavities and the tooth shape coefficient of saws, the profiles of the toothed crowns of which correspond to the international standard, are obtained. Furthermore, based on the geometry of the toothed crown of the saw with NV profile with a rounded cavities and a straight back surface, the formulas of the areas of the interteeth cavities and coefficients of the saw tooth with the toothed crowns of the NU, KV, KU, PV, PU profiles were developed. The following parameters of the toothed crown are taken into account in the analytical dependences: pitch of teeth; angular parameters of teeth: the main front angle, the main angle of sharpening, the main back angle; radius of rounding of the interteeth cavity. For the toothed crown of the KV saw profile in the formulas of the area of the interteeth cavity and the coefficient of the shape of a tooth the decrease in the area of the interteeth cavity comparing to the area of the NV profile by the presence of a triangular protrusion was considered. For a saw with PV profile teeth, it is assumed that the radius of curvature of the rear surface is equal to twice the pitch of the tooth. In that case the decrease of space of the interteeth cavity of the toothed crown of the PV profile compared to the NV profile is taken into account by the presence of a circular sector. For toothed crowns of saws with NU, KU, and PU profiles, the increase in the area of interteeth cavities compared to the areas of interteeth cavities of NV, KV, PV profiles was taken into account by adding the area of the rectangle, equal to the multiplication of the cavity bottom length and the tooth height. Dependences for the saws tooth shape coefficient with toothed crowns of NV, NU, KV, KU, PV, and PU profiles are obtained as the ratio of the areas of the interdental cavities to the pitch of the teeth squared. To conclude, the obtained analytical dependences allow determining the areas of interdental cavities and shape coefficients of tooth quite accurately