Vol 39 Iss. 3

Let us limit ourselves to finding the equidistance T of the internal forces in the bottom section of the rope, giving the formula for determining the normal tensile stress o in this section the value of only an approximate characteristic of the corresponding stress state.

The numerical evaluation of rope tension is of great practical importance, but is far from being fully completed. In the present work an attempt is made to estimate the rope tension at the load suspension point during the period of uniform drum rotation, provided that this period was preceded by a period of uniformly accelerated drum rotation, accompanied from the very beginning of the load lifting by oscillatory motion of the system. Due to the action of internal resistance forces, these oscillations will be damped, and by the end of the period of uniformly accelerated drum rotation, all points of the vertical part of the rope and the load will receive the same acceleration, equal to the tangential” acceleration of the points of the drum surface. At the beginning of uniform rotation of the drum due to the change of the rotation mode the oscillations of the system are resumed and the forces of internal resistances are again manifested. However, they can be disregarded if we consider the motion of the system in a time interval close to the initial time.

Approximate determination of the tension of hoisting mine ropes is used in order to overcome the two main difficulties arising in justifying the calculation of ropes for strength. If with a known approximation can justify the application of Hooke's law for the tension of the rope, taken in theory as a perfectly elastic thread of constant cross-section, then to account for internal resistance in the rope, as well as in a rectilinear homogeneous rod, quite reasonable formula is not available. The source of the second difficulty lies in the complex form of one of the boundary conditions of the problem of mathematical physics about the longitudinal vibrations of an elastic thread of variable length with a load at the lower end, to which the determination of the tension of hoisting mine ropes is given. It is about the upper end of the rope, which due to the coiling on the drum and the assumed absence of sliding on the drum should have a given speed, coinciding with the speed of the points of the outer surface of the rotating drum.

The hollow cylinder is flattened under the action of equal and opposite forces directed along the diameter. This deformation is usually accompanied by curvature of the cylinder's constituents. The longer the cylinder, the greater the curvature of the formers. For relatively short cylinders, the curvature of the formers is insignificant and can be neglected. This kind of deformation, in which the cylinder's constituents retain a rectilinear shape, has been considered using the energy method. In the present work, this problem is considered for relatively long cylinders (tubes, hollow shafts, drums), where the curvature of the formers is significant and neglecting this factor becomes unacceptable.

When a cylindrical shell is mated to an end plate, the boundary conditions reflect the elastic confinement conditions. The angle of inclination of the curve at the interface is proportional to the magnitude of the moment M ...

The paper considers an infinite plate with a central opening, the shape of which is very close to a rectangle under the action of hydrostatic pressure on the faces of the opening. The problem posed has an independent value in the calculation of pressurized hydraulic tunnels and is a part of the problem of stresses from its own weight in arrays with openings (plane deformation).

Let us imagine several moving unchanging media S1, S2, ... Sn and a material point M moving relative to these media. Let us consider the motion of the point M relative to the medium S1, the medium S1 relative to the medium S2, . . . . the medium Sn-1 relative to the medium Sn . It is required to determine the motion of the point M relative to the medium Sn (n ≥ 3).

In the present paper, the motion of a system consisting of three solid bodies rotating around a fixed point and having a common geometric axis of proper rotations is considered. The chosen system gives a principal generalized scheme of the working part of the crusher of Mekhanobr Institute, which is implemented in different variants.

Actual processes in pneumatic engines of mining machines proceed at incomplete expansion of air. The main reason for releasing still workable air into the atmosphere is the need to limit the temperature drop inside the cylinder to a certain limit to prevent solidification of lubricant and ice formation.

Improving the technical and economic performance of manufactured machines and equipment can be achieved not only by creating new, more economical types of machines, but also by modernizing existing designs.

Transformation by inverse radiiThe reciprocal projections are based on the reciprocal transformation, or the so-called transformation by inverse radii, which follows from the involution of points on a line. In the involution of points on a line, there are two real or two imaginary double points that divide harmonically any pair of corresponding points. The middle point between the double points is called the center of the involution and it corresponds to the infinitely distant point of the line. The product of the distances of two corresponding points to the center of involution is a constant value.

The methods of projective geometry make it possible to use numerous geometric systems, which is widely used in the works of E. S. Fedorov. At present, even in the educational manuals on projective geometry do not mention the existence of various geometric systems, which, however, open wide opportunities for solving a number of problems of engineering and scientific practice.

When lifting a load lying on a fixed base, the rope is sometimes not only unloaded, but also has an overhang. It is practically important to determine under these conditions the greatest tension of the rope in the first moments of driving the drum into rotational motion. This issue is devoted to the works of V. V. Georgievskaya, who divides the process of lifting the load into three stages: 1) selection of the rope tension; 2) removal of the load from the fixed base; 3) lifting the load. It is assumed that in all three stages, the drum, on which the rope is wound, rotates at an equal speed, having left the state of rest. The author neglects the change in rope length and the influence of internal resistances in the rope.

The tachogram of the ascent is assumed by R. F. Ilyin to be trapezoidal. Due to the complexity of the exact solution, he used an approximate method for small lifting heights. The absolute elongation of the vertical parts A₁B₁ and A2B2 of the rope (A₁, A₂ - arbitrarily taken points of the rope, B₁, B₂ - points of suspension of weights) in the following form is set ...

In this article, it is intended to consider in detail the question of the distribution of stresses in a rock massif, which is assumed to be homogeneous elastic isotropic and subject to Hooke's law. The specific gravity of the rock is assumed to be constant. It is assumed that the rock in the section under consideration is bounded from above by a horizontal plane to which no forces are applied.

The paper by A. M. Penkov and A. S. Bondarchuk summarizes the results of an experimental study of stresses in steel ropes. On the basis of the method developed by the authors it is shown that the discrepancy between the experimental and theoretical data is from 22 to 29% in the direction of reducing the safety margin.