In the general complex of questions on the destruction of rocks an important place is occupied by the development of the theory of strength and improvement of methods of their testing. As a result of this research, new ideas about the properties of rocks and the mechanism of their fracture have emerged. This article deals with the matter of the relationship between the theory of strength and the mechanism of fracture and provides methods of constructing stress diagrams and their interpretation. ...
In all real bodies, deformation processes proceed in time. Mechanical characterizations that do not take time into account are approximate and in many cases prove to be inadequate. Factors such as the rate and duration of loading, the energy stored by the system have a great influence on the value of the breaking stress. In LMI a lot of work has been done to establish the physical features of the process of rock fracture by shock loading and to find out the comparative efficiency of static and dynamic methods of fracture. As a result, it was found that the fracture energy, other things being equal, is a function of the impact energy, the velocity of the impact load application, and the mass of the striking body. As for the comparison of energy expenditure in static and impact tests, it is permissible only at a comparable degree of crushing, i.e., at some minimum impact work.
The modern development of rock mechanics has put forward the important task of studying the effect of strain rate on rock properties. The study of rock fracture processes under dynamic loading is of great importance for the improvement of mining technology. Mechanical properties under dynamic loading is important to know when designing mining machines, drilling wells at high speeds, destruction of rocks by explosion.
In the calculation of pillars, the study of stresses in the massif around loose excavations and in other similar problems is important to establish the value of the modulus of elasticity of rocks. When testing concrete, along with the determination of the modulus of elasticity under static loading on conventional testing machines, acoustic methods - pulse and resonance, allowing to determine the dynamic modulus of elasticity - are now widely developed. The pulse method consists in measuring the velocity of acoustic signal propagation. It is possible to determine the modulus of elasticity both in the sample and in the array. In the resonant method, the natural frequency of the bending vibrations of the specimen is usually measured ...
The problem of the calculation of a shell loaded along the formant was first solved in the study of the stresses arising in cylindrical shells used for slabs. As a result of neglecting the values of Mx and Mxy, a simple differential equation for Mx is obtained. Further development of this issue is related to works based on the assumption that Mx and Mxy are insignificant in the overall balance of forces and moments in a long shell under distributed load. Along with this, there were data indicating that this is not the case when linear or concentrated loads are applied to the shell. For example, when the load was transferred to the shell through a relatively large diameter pipe, the ratio of the maximum longitudinal bending stresses to the maximum circumferential bending stresses was half.
Полый цилиндр под действием равных и противоположных сил, направленных по диаметру, сплющивается. Эта деформация обычно сопровождается искривлением образующих цилиндра. Чем длиннее цилиндр, тем больше искривление образующих. При сравнительно коротких цилиндрах искривление образующих незначительно и им можно пренебречь. Такого рода деформация, при которой образующие цилиндра сохраняют прямолинейную форму, была рассмотрена при помощи энергетического метода. В настоящей работе эта задача рассматривается для сравнительно длинных цилиндров (труб, полых валов, барабанов), где искривление образующих значительно и пренебрежение этим фактором становится недопустимым.
При сопряжении цилиндрической оболочки с торцовой пластиной краевые условия отражают условия упругой заделки. Угол наклона изогнутой кривой в месте сопряжения пропорционален величине момента М ...
В статье А. М. Пенькова и А. С. Бондарчука 1 приведены результаты экспериментального исследования напряжений в стальных канатах. На основании разработанной авторами методики показано, что расхождение между опытными и теоретическими данными составляет от 22 до 29% в сторону уменьшения запаса прочности.
When considering corrugated couplings, along with the study of their elasticity, it is also important to find out the significance of various displacements arising in them under the action of bending moments applied to the coupling flanges. The most significant among these displacements is the largest deflection of the coupling. The greater the total length of the coupling and the distance between the corrugations, the greater the coupling deflection. Excessive coupling deflections are undesirable because they contribute to misalignment and have a detrimental effect on the bearings of the shafts to be coupled.
Due to inaccuracies in the alignment of the shafts to be coupled, as well as due to misalignment during operation, it is necessary to consider the possibility of significant misalignments that are detrimental to the operation of the machine. To reduce the harmful effect of these misalignments, the cylindrical part of the coupling is provided with one or more corrugations that increase the elasticity of the coupling. The higher the elasticity of the coupling, the lower the force required to deform it, and consequently, the easier it is to ensure normal operation of the machine in the presence of misalignments.
In many practical proposals there is a need to calculate the tangential stresses in hollow shafts in bending. The ratio of inner diameter to outer diameter in hollow shafts is chosen very differently depending on the purpose of the shaft. In cases where the removal of the central part of the cross-section is intended to control the quality of the material, the inner diameter of the shaft is usually small. The formulas available in the literature for determining the greatest tangential stress in hollow shafts in bending usually do not take into account the effect of the diameter ratio on the magnitude of the tangential stress.
The methodology for determining displacements in a semi-rigid coupling with a single corrugation has been described earlier. In practice, two or three corrugations are often used in order to increase elasticity. Increasing the number of corrugations changes the deformation conditions and requires separate consideration. The purpose of this paper is to investigate the effect of corrugations on the displacements of the entire coupling and its individual elements. The main value determining the elasticity of the coupling is the angle of rotation α (Fig. 1). It depends on the value of the bending moment M, the size and material of the corrugation. In the future, we take the angle a, as well as the dimensions of the coupling, as given.The stated methodology for determining displacements in couplings with two corrugations can be extended to couplings with three corrugations.
Increasing the elasticity of a coupling sleeve is usually achieved by installing one or more corrugations. A schematic representation of such a corrugation in deformed and undeformed states is shown in Fig. 1. (see article). The main value that determines the elasticity of the sleeve during bending is the rotation angle a. It depends on the magnitude of the bending moment, the dimensions and material of the corrugation. There are various theoretical and experimental methods for determining the value of a, which we will not dwell on - we will take the angle a, as well as the dimensions of the sleeve, as specified. The task is to determine the effect of the corrugation on the movements of the entire sleeve and its individual elements. These movements depend not only on the characteristics of the corrugation, but to a large extent on the position occupied by the corrugation on the sleeve and the dimensions of the sleeve itself.
The need to study stresses in gear disks arises when the wheel is subjected to axial forces during operation. In this case, we are dealing with a plane stress state, characterized by the magnitude of radial and tangential stresses at various points along the radius of the disk. Experimental study of stresses in a disk under static loading of a real sample is possible if the wheel's own weight is used as a load. As a support surface, one can use: 1) the end plane of the rim, loading the disks with the weight of the shaft and partially with the own weight of the disks; 2) the plane of the flange, loading the disks with the weight of the rim and partially with the own weight of the disks. The first position occurs when the wheel is freely supported on the rim, the second - when the wheel is suspended by the shaft.
Asymmetric bending of the ring plate is encountered when developing designs of couplings, compensators and various corrugated elements included in the overall system to increase its elasticity. The efficiency of such plates is determined not only by their dimensions (internal and external diameters, wall thickness), but also depends to a large extent on the rigidity of the elements to which they are directly adjacent and the design of the transition from the plate to the element conjugated with it. In some cases, the method of fixing the plate along the outer contour comes closest to rigid embedment, in others it can be considered equivalent to hinged support. The main value characterizing the elasticity of the plate is the angle of rotation of the inner contour to which the external bending moment is applied. This value for the scheme with hinged support, all other things being equal, is significantly greater than for the scheme with rigid embedment. However, along with this, there is an unfavorable factor associated with a significant increase in stresses in the scheme with hinged support compared to rigid embedment. The correct solution to the problem comes down to selecting the dimensions of the elastic element in such a way as to obtain the largest angle of rotation of the internal contour at stresses not exceeding the permissible ones. For this purpose, it would be necessary to take into account the degree of rigidity of the fastening and make the calculation as for the scheme with elastic fixing.
