When constructing a mathematical model for the interaction of a free-rotating plane disk with soil, it is necessary to take into account that the magnitude of its kinematic parameter, equal to the ratio of its circumferential velocity to the speed of translational movement of the disk, is not a given quantity, but a definite quantity. With uniform rotation of the disk and its translational movement at a constant speed, the kinematic parameter is determined from the equilibrium equation of external forces, applied to the disk. The generalized mathematical model of disk-soil interaction, proposed earlier, was taken into account, but in view of relative complexity it was not widely used. The aim of the study is to construct a simpler, but adequate mathematical model for the interaction of a free-spinning disc with soil. The model is constructed under the assumptions of the constancy of the translational velocity of the disk, the permanence of its penetration and the possibility of replacing the pressure on the disc’s lateral surfaces with its mean value and replacing the force per unit length of the blade with its mean value. Since the distribution of the elementary forces of soil reactions is ultimately determined by the distribution of the absolute velocities of the points of the disk in contact with the soil, the resultant reactions of the soil and their total moment are functions of the kinematic parameter of the disk and its relative burial. These functions are given by integrals, that are not expressed in terms of elementary functions by a finite number of operations. However, the proximity of the kinematic parameter of the free-spinning disk to unity makes it possible, with the help of an estimate of these integrals, to obtain approximate expressions in terms of elementary functions for the resultant reactions of the soil and their total angular momentum. It is shown that the accuracy of the approximations obtained is sufficient for engineering practice.

Abstract. As working units of tillage mills, both curved (L-shaped) blade knives and straight blade knives are used. The soil reactions to these working units depend on soil properties, geometric parameters of the working parts, parameters determining the modes of their operation and the angle of rotation of the working units. When constructing a mathematical model for the interaction of working parts with soil, all these factors must be taken into account, while striving to simplify the proposed model. Accounting for the dependence of force characteristics of the working units on the angle of their rotation is not an easy task, and in most cases it is solved with the help of specially set experiments. A mathematical model is proposed for the interaction of a direct lamellar milling knife with soil, which makes it possible to determine the components of the resulting soil reactions to such a knife, the total moment of these reactions, and the power consumed for cutting the soil, depending on the knife rotation angle. This model takes into account the geometry of the working unit through the radii of the hub and cutters, the angle of installation of the milling knife and its length. The operating mode of the knife is set by the kinematic coefficient, equal to the ratio of the circumferential velocity of the knife end to the speed of the translational motion of a mill, and the maximum relative depth of the milling knife in the soil. The constructed model makes it possible to determine the dependence of the maximum values of the considered power characteristics of the knife on the indicated geometric parameters and the parameters of the knife operating mode, which makes it possible to simplify experiments to determine the power characteristics of the cutter and significantly reduce its volume. This model can be used to select the optimal knife parameters. In addition, the proposed model can be used to calculate the power characteristics of the rack of a curved blade knife, which consumes a significant amount of energy during milling.

1 Пермский национальный исследовательский политехнический университет, Пермь, Россия 2 Лаборатория фотоники Пермского научного центра Уральского отделения РАН, Пермь, Россия О ПРИМЕНЕНИИ ПОЛЯРИЗАЦИОННОЙ РЕФЛЕКТОМЕТРИИ В СОХРАНЯЮЩЕМ ПОЛЯРИЗАЦИЮ ОПТИЧЕСКОМ ВОЛОКНЕ ПРИ РАЗЛИЧНЫХ УСТАНОВИВШИХСЯ ТЕМПЕРАТУРАХРассматривается использование метода поляризационной рефлектометрии для контроля распределения наведенных поляризационных дефектов в катушке при различных установивших-ся температурах. Показан переход к количественной оценке распределенной связи поляризаци-онных мод. Представлена корреляция между значениями h-параметра, измеренного стан-дартным методом, и значением, расчитанным исходя из данных поляризационной рефлек-тометрии. Проведена оценка чувствительности метода к температуре.Ключевые слова: сохраняющие поляризацию волокна, поляризационная рефлектомет-рия, экстинкция, h-параметр. AT DIFFERENT ESTABLISHED TEMPERATURESThe paper discussed the use of polarization-optical time domain reflectometry as a method for measuring the induced polarization defects distribution in polarization-maintaining fiber coil at different established temperatures. It was shown the transition to quantify estimating the polarization defects distribution. It was provided the correlation between the values of h-parameter measured by the standard method, and the value calculated from the polarization reflectometry data. The estimation of method sensitivity to temperature was done.

By means of mathematical modelling the features of an outflow of high-velocity pulsating jets out of chambers of gas-detonation installations intended for handling materials are investigated. The boundary value problem is reduced to a solution of an inhomogeneous wave equation with allowance for pressure variation on the boundary of the pulsed source. The calculation of gas-dynamic fields of velocities and pressures is carried out, the volumetric density of potential and kinetic energies and its concentration on the surface under treatment are defined.

The solutions of many problems of agricultural engineering are expressed through special functions. In particular, such problems include the problem of determining the displacement trajectories and the falling time of the hingedly working units of agricultural machines, when the suspension axis moves horizontally at a certain speed. Such working device include: a stacker valve, falling after release from the shock, a beam of transverse rakes, that falls after the release of the roll and others. The solution of such problems is to determine the motion time of a physical pendulum to a given angular position, which is expressed in terms of elliptic integrals. And although elliptic integrals are a well-studied class of functions, in many cases an approximate solution of similar problems in elementary functions is quite sufficient both from the point of view of practical application and convenience of use. In addition, this approach makes it possible to determine the approximate law of motion of a physical pendulum in an explicit form, which makes it easier to set and solve problems of optimizing the operating modes and parameters of the above-mentioned working units. By estimating the integral, such an approximate law of motion of a mathematical pendulum was obtained. Its accuracy is sufficient for engineering practice. The obtained formula for the oscillation period of a pendulum with a large amplitude makes it possible to determine the falling time of the hinged working units of agricultural machines with high accuracy.