Experimental verification of new features of bearing operation under combined loading conditions

Bearing units of lifting machines, products of construction, road, aviation, space and other branches of technology are very important structural elements, since the failure of even one bearing can cause the failure of the entire product. The results of experimental verification of the theoretical model of bearing operation under combined loading conditions are presented. The behavior under load of bearing units in the most general case can be represented by a sequence of five design schemes, expressed in the form of five statically indeterminate beams. The purpose of the experiments was to test this model under real loading conditions. The experiments were based on the analysis of the geometric shape of the curved elastic line, which the shaft of the bearing assembly acquires under load. The experimental results confirmed the validity of the model and showed that the previously generally accepted model of a two-support beam is not implemented. The conclusion is confirmed that in responsible lifting machines, as well as in responsible products of construction, road, aviation, space and other branches of technology, it is impractical to calculate bearings according to the traditional method, since an erroneous value of bearing durability can be obtained, overestimated from 28.37 to 26.663.9 times.

Buckling under the action of loading by aerodynamic and inertial forces during ground track tests of aviation equipment

The article analyses the choice of a rational layout of the test object with a propulsion system (PS). One of the design examples of calculating the longitudinal stability and strength of the structure is given. The purpose of the article is to solve the problem of bending the elastic line of a cantilever tubular rod with a hinged termination during tests of a propulsion system for various aircrafts. On the example, the estimates of the approximate test object, accelerated on the track to a speed of 1200 m/s, are carried out. The aerodynamic loading of the structure of the mobile track installation is considered using the methods of mathematical modelling and the development of an algorithm for the numerical solution of the problem of bending the elastic line of a cantilever tubular rod. The deflection from the forces of external and internal loads of the outer shell of a movable track installation is considered, provided that the diameter of the outer contour is equal to the minimum and it is constant along the entire length.

Approximation of Physical Spline with Large Deflections

Physical spline is a resilient element whose cross-sectional dimensions are very small compared to its axis’s length and radius of curvature. Such a resilient element, passing through given points, acquires a "nature-like" form, having a minimum energy of internal stresses, and, as a consequence, a minimum of average curvature. For example, a flexible metal ruler, previously used to construct smooth curves passing through given coplanar points, can be considered as a physical spline. The theoretical search for the equation of physical spline’s axis is a complex mathematical problem with no elementary solution. However, the form of a physical spline passing through given points can be obtained experimentally without much difficulty. In this paper polynomial and parametric methods for approximation of experimentally produced physical spline with large deflections are considered. As known, in the case of small deflections it is possible to obtain a good approximation to a real elastic line by a set of cubic polynomials ("cubic spline"). But as deflections increase, the polynomial model begins to differ markedly from the experimental physical spline, that limits the application of polynomial approximation. High precision approximation of an elastic line with large deflections is achieved by using a parameterized description based on Ferguson or Bézier curves. At the same time, not only the basic points, but also the tangents to the elastic line of the real physical spline should be given as boundary conditions. In such a case it has been shown that standard cubic Bézier curves have a significant computational advantage over Ferguson ones. Examples for modelling of physical splines with free and clamped ends have been considered. For a free spline an error of parametric approximation is equal to 0.4 %. For a spline with clamped ends an error of less than 1.5 % has been obtained. The calculations have been performed with SMath Studio computer graphics system.

Experimental demonstration of the novel “van-Hove integral method (vHI)” for measuring diffusive dynamics by elastic neutron scattering

Quasi-elastic neutron scattering (QENS)—based on the seminal work of Nobel Laureate Brockhouse—has been one of the major methods for studying pico-second to nano-second diffusive dynamics over the past 70 years. This is regarded as an “inelastic” method for dynamics. In contrast, we recently proposed a new neutron-scattering method for dynamics, which uses the elastic line of the scattering to access system dynamics directly in the time domain (Benedetto and Kearley in Sci Rep 9:11284, 2019). This new method has been denoted “vHI” that stands for “van Hove Integral”. The reason is that, under certain conditions, the measured elastic intensity corresponds to the running-time integral of the intermediate scattering function, $$I\left( {Q,t} \right)$$ I Q , t , up to a time that is inversely proportional to the energy band-width incident on the sample. As a result, $$I\left( {Q,t} \right)$$ I Q , t is accessed from the time derivative of the measured vHI profile. vHI has been supported by numerical and Monte-Carlo simulations, but has been difficult to validate experimentally due to the lack of a suitable instrument. Here we show that vHI works in practice, which we achieved by using a simple modification to the standard QENS backscattering spectrometer methodology. Basically, we varied the neutron-energy band-widths incident at the sample via a step-wise variation of the frequency of the monochromator Doppler-drive. This provides a measurement of the vHI profile at the detectors. The same instrument and sample were also used in standard QENS mode for comparison. The intermediate scattering functions, $$I\left( {Q,t} \right)$$ I Q , t , obtained by the two methods—vHI and QENS—are strikingly similar providing a direct experimental validation of the vHI method. Perhaps surprisingly, the counting statistics of the two methods are comparable even though the instrument used was expressly designed for QENS. This shows that the methodology modification adopted here can be used in practice to access vHI profiles at many of the backscattering spectrometers worldwide. We also show that partial integrations of the measured QENS spectrum cannot provide the vHI profile, which clarifies a common misconception. At the same time, we show a novel approach which does access $$I\left( {Q,t} \right)$$ I Q , t from QENS spectra.

Approximation of Physical Spline with Large Deflections

Physical spline is a resilient element whose cross-sectional dimensions are very small compared to its axis’s length and radius of curvature. Such a resilient element, passing through given points, acquires a "nature-like" form, having a minimum energy of internal stresses, and, as a consequence, a minimum of average curvature. For example, a flexible metal ruler, previously used to construct smooth curves passing through given coplanar points, can be considered as a physical spline. The theoretical search for the equation of physical spline’s axis is a complex mathematical problem with no elementary solution. However, the form of a physical spline passing through given points can be obtained experimentally without much difficulty. In this paper polynomial and parametric methods for approximation of experimentally produced physical spline with large deflections are considered. As known, in the case of small deflections it is possible to obtain a good approximation to a real elastic line by a set of cubic polynomials ("cubic spline"). But as deflections increase, the polynomial model begins to differ markedly from the experimental physical spline, that limits the application of polynomial approximation. High precision approximation of an elastic line with large deflections is achieved by using a parameterized description based on Ferguson or Bézier curves. At the same time, not only the basic points, but also the tangents to the elastic line of the real physical spline should be given as boundary conditions. In such a case it has been shown that standard cubic Bézier curves have a significant computational advantage over Ferguson ones. Examples for modelling of physical splines with free and clamped ends have been considered. For a free spline an error of parametric approximation is equal to 0.4 %. For a spline with clamped ends an error of less than 1.5 % has been obtained. The calculations have been performed with SMath Studio computer graphics system.

Deformation of elastic-viscous beams by explosive load in water

Представлено аналитическое решение задачи о деформировании взрывом сосредоточенного заряда конденсированного взрывчатого вещества (ВВ) балки, материал которой чувствителен к скорости деформации. Влияние внешней среды (воды) на процесс и результаты деформирования учитывается введением присоединенной массы. Коэффициент вязкости и модуль упругости в фиксированных интервалах скоростей деформирования определяются из экспериментов. Для этих параметров, характеризующих материал балки при импульсном деформировании, получена аналитическая взаимосвязь и нижняя граница значений для коэффициента вязкости. Решение задачи найдено методом разделения переменных в определяющем уравнении движения. При этом форма упругой линии балки для каждого момента времени выбрана, исходя из требования выполнения граничных условий и принципа минимума работы деформирования. An analytical solution to the problem of deformation by an explosion of a concentrated charge of a condensed explosive (HE) of a beam, the material of which is sensitive to the rate of deformation, is presented. The influence of the external environment (water) on the process and the results of deformation is taken into account by introducing the added mass.The viscosity coefficient and the modulus of elasticity in fixed intervals of strain rates are determined from experiments. For these parameters, which characterize the material of the beam under impulse deformation, an analytical relationship and a lower limit of values for the viscosity coefficient are obtained. The solution to the problem is found by the method of separation of variables in the governing equation of motion. In this case, the shape of the elastic line of the beam for each moment of time is selected based on the requirement to fulfill the boundary conditions and the principle of minimum deformation work.

NUMERICAL DIFFERENTIATION OF BEND FORMS OF THE LONG ELASTIC RODS

The technique of numerical differentiation of the bend forms of long elastic rods is presented. This technique is based on search for new bend forms of the rod by solving the equations of oscillations with using the time integration method and the polynomial spline-functions that are being described the current bend form. In it, the spline-functions are found by current bend form approximation where each of the found functions is responsible to certain point of rod elastic line and describes the position of nearby points. Using the described approximation technique with subsequent numerical differentiation, the dependences of the derivatives on an arbitrary bend form of the rod with a length that is equal to 100 m are shown. To confirm the reliability, the results of numerical differentiation of the bend forms of the elastic rods described by given functions are presented and the numerical results obtained using the proposed method are compared with the results of analytical differentiation of the original functions. The graphs of values derivatives dependence to rod length are drawn and tables with numerical values of differentiation results are shown. It is concluded that the considered technique of numerical differentiation of rods bend forms allows to do the research of dynamics of rod systems. It gives the exact result of differentiation, provides the continuity and smoothness of all four derivatives functions of spline that are being described the bend form with considerable length. Described technique was realized in a computer program with graphic user interface. Program allows to monitor for dynamics of the oscillatory motion of the modeled system in real-time by calculating and drawing the current band forms of the rotating rod during the oscillation.

NATURE-LIKE CURVE MODELING

A physical spline is called an elastic rod the cross- section dimensions of which are rather small as compared with the length and radius of its axis curvature. Such a rod when passing through specified points obtains in natural way a nature-like shape characterized with minimum energy of inner stresses and minimum mean curvature. A search for the equation of elastic line is a difficult mathematical problem having no elementary solution. The work purpose: the development of the experimental-rated procedure for modeling a nature-like elastic curve passing through complanar points specified in advance. The investigation methods: methods of piece-cubic interpolation based on the application of polynomial splines and compound curves specified by parametric equations. In the paper there are considered polynomial and parametric methods of the geometric modeling of the physical spline passing through the points specified in advance. The elastic line of the physical spline is obtained experimentally. The investigation results: it is shown that unlike a polynomial model a parametrized model on the basis of Fergusson curve gives high accuracy of approximation if in basic points there are specified tangents to the elastic line of the physical spline with large deflections. Novelty: there is offered a simplified method for the computation of factors of an approximating spline allowing the substitution of the 2n system of nonlinear equations (smoothness conditions) by the successive solution of n systems of two equations. Conclusions: for the modeling of nature-like curves with large deflections there is offered the application of Fergusson cubic spline passing through specified points and touching the specified straight lines in these points. The error of the modeling of the natural elastic line with free ends at n=5 does not exceed 0.4%.

Comparative analysis of calculation methods for enclosing pit structures

Choosing the calculation method for the enclosing excavation pit structures is an urgent issue, since the results of the calculations determine the selection of the geometric and mechanical parameters, as well as the estimated cost of materials and works. At present, at calculation of the enclosing structures of excavation pits, there are used classical semi-graphical solutions, semi-analytical programs and software packages based on the finite element method. Each method has its own prerequisites and assumptions, as well as advantages and disadvantages. The purpose of this article is presentation of comparative analysis results of the main methods for calculating the enclosing structures of excavation pits considering their features and boundary conditions of application. The author has performed test calculations of the excavation pit enclosing structures using the elastic line method in the SCAD and PLAXIS 2D software packages. The author has also developed and proposed a simplified method for calculating pit fences. This method can be used at the pre-project stage of construction in the form of preliminary calculation or as additional verification calculation of the stability, strength and deformability of pit enclosing structures.