Increasing the Overlap Factor in the Elastic Model of a Modified Gear

Coupled and approximate gears are considered in this article. Methods of localization of the contact patch and the elimination of edge impact are analyzed. Based on the solution of the Hertz problem, mathematical models of gearing in the MathCAD program are constructed, with the help of which the overlap ratio of the gearing is calculated taking into account contact deformations. Circular and parabolic modifications for cylindrical spur gears are proposed. The allowed values of the modification parameters are determined. Contact stresses are equal to the allowable stresses when calculating multi-cycle fatigue. The influence of contact deformation on the load capacity of non-conjugate gears is analyzed.

The establishment of the form of bullet morphology of fractures of the flat bones

In the work were studied morphological features of bone tissue destruction, which may set the shape of the bullet. We considered problems of theoretical mechanics helped to explain the mechanism of formation of a perforated fractures of the flat bones from the effect of gunshot shells one - and doradca form. The proposed mechanisms allow to explain the difference in terms of destruction of bone tissue when exposed to fire shells one - and doradca forms, and as a consequence conduct a group identification form a firearm projectile according to the morphological characteristics of gunshot gunshot fractures of the flat bones. The objects of the study there was an entrance gunshot gunshot fractures, which were formed from bullets one and Dorado form of the archival material Department of forensic crimaldi Kiev city clinical Bureau of forensic medical examination and obtained experimentally gunshot gunshot fractures of the flat bones. To assess the fracture mechanics of the flat bones, we used the data of theoretical mechanics. Justification of destruction of flat bones from the bullets odnorodno forms we considered for the problem Businesa, and destruction of flat bones from the bullets doradca forms on the example of the Hertz problem and model of hill-Johnson. The results obtained were processed by methods of variation statistics.

On the numerical treatment of the contact problem

The problem of the contact of two elastic bodies of arbitrary shape with a kernel in the form of a logarithmic function—which is investigated from Hertz problem—is reduced to an integral equation. A numerical method is adapted to determine the pressure between the two surfaces under certain conditions.

SOME APPLICATIONS OF THE FRACTAL PARAMETRIC-HOMOGENEOUS FUNCTIONS

The purpose of this paper is to present some recent results concerning applications of so-called parametric-homogeneous (ph) functions to some problems of solid mechanics. The ph-functions have often fractal graphs and can be nowhere differentiable. An example of ph-function is the Weierstrass-Mandelbrot one. We introduce some ways of construction of the ph-function of both arbitrary degree and fractal dimension. We consider the discrete Hertz problem of contact between a punch, whose shape is described by a positive ph-function, and a deformable half-space. General expressions for changes of all functions, giving the solutions of the contact problems for a fractal punch, are derived exactly, without solving the field equations.