The failure behavior of buckling pin valve: Theoretical, numerical, and experimental study

At present, buckling pin in the bypass of piping as pressure relief valve has been gradually utilized in the low-concentration coal-bed methane (CBM), which bends to release pressure when the main valve fails leading to pipeline blockage. However, current researches mainly focused on the buckling behavior of hydraulic cylinder rod or rod string, and less consideration was given to the operational reliability of buckling pin valves. This paper deduced the calculation formula of the critical failure load based on Euler formula in the buckling pin under buckling load. Besides, three finite element models (FEM) based on Johnson−Cook constitutive model were compared to predict failure strength of buckling pin which were verified by experiment. In addition, the defect sensitivity analysis of the buckling pin under different initial geometric defects rate was carried out. The results showed that a) the experimental value of the critical failure load in the buckling pin was 206.04 N and the bending position was in the middle of the buckling pin; b) the analysis result adopting explicit dynamic method was in best agreement with the experimental results within deviation of 0.24%; and c) the initial geometric defect of buckling pin should be controlled within 1%. This study provides an important reference to predict the critical failure load of the buckling pin valve and achieve safe transportation of low-concentration CBM.

Calculation of Rail Impedance of Track Circuit Considering Earth Stratification

Rail impedance directly affects the transmission performance of track circuit . Considering the condition of earth stratification, for the difficult to calculate the rail impedance due to the semi-infinite integration interval and the oscillation of the integrand by using the Carson formula, The truncation method is proposed to divide the impedance formula is divided into definite integral and tail integral. The integral is approximated by the spline function, and the tail integral is calculated by using the exponential integral and Euler formula. Based on it, the rail impedance calculation formula of track circuit is obtained. The electromagnetic field model of track circuit with earth stratification is simulated by finite element method, and the correctness of the method is verified. Based on the formula, the influence of current frequency, soil depth and conductivity on rail impedance is studied. The relative error between the calculated results of rail impedance and the simulation results of finite element is within 5%. It can be seen that the formula has high accuracy and correctly reflects the law of rail impedance variation with current frequency, soil depth and resistivity. It provides a reliable reference for the theoretical calculation of rail impedance of track circuit.

Dynamic parameter identification method for robotic arms with static friction modelling

This paper presents an identification method for robotic manipulators. It demonstrates how a dynamic model can be constructed with the help of the modified Newton–Euler formula. To model the friction of the joints, static friction modelling is used, in which the friction behaviour depends only on the actual velocity of the given joint. With these techniques, the model can be converted into a linear-in-parameters form, which can make the identification process easier. Two estimators are introduced to solve the identification problem, the least-squares and the weighted least-squares estimators, and the determination of the independently identifiable parameter vector to make the regression matrix maximal column rank is presented. The Frobenius norm is used as the condition of the regression matrix to optimise the excitation trajectories, and the form of the trajectories has been selected from the finite Fourier series. The method is tested in a simulated environment to achieve a three-degrees-of-freedom manipulator.

Flexible bar compression test

The article considers experimental and theoretical research of longitudinal stability of a flexible steel bar design under axial compression. The bar is a flat thin-walled element, pivotally fixed at the ends. The experimental study was carried out on a Zwick/Roell Z100 installation using special equipment that simulates geometric boundary conditions. During the loading process, a diagram of the deformation of a real bar with initial shape imperfections was automatically constructed. The experimental critical force was determined from the deformation diagram. This force was compared with the critical forces obtained from calculations using two schemes: the Euler formula and the dynamic analysis methodology. In the second scheme, in contrast to the first one, the initial imperfection, established by the measurements of the tested structure, was taken into account. The design calculation errors for both schemes were determined.

An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

A system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval $[0,1]$ [ 0 , 1 ] . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

Researches of stability of monolithic and layered plates under compression

The results of calculations of the stability of monolithic and layered plates, obtained by analytical and numerical methods, are presented, which are compared with experimental data. The obtained results of stability calculations are within the limits of the permissible error. The results of numerical calculations of stability by the finite element method in the ANSYS program turned out to be higher than the values ​​determined by the Euler formula and lower than the results obtained by the formula for calculating the stability of plates. To study the bearing capacity of layered samples under compression, an assessment of their stability was carried out with different numbers and arrangement of layers of alloy and composite material. The optimal layouts of layers in the material for designing a composite panel have been determined. The results were used to design a composite wing panel based on sheets and profiles made of high-strength aluminum-lithium alloy and laminated aluminum-fiberglass. Stability of the composite panel under compression were 7% higher than the experimental values due to the local loss of stability of its elements, which precedes the general loss of stability and reduces the value of the critical load.

Experimental determination of the limiting flexibility of eucalyptus wood for axially compressed elements

Relevance. Wood is one of the most widely used building materials throughout history, and because of its physical-mechanical properties it mainly has been used in flexed and compressed elements. Eucalyptus was introduced to Latin America in the mid-19th century and nowadays is one of the most used woods for construction in the Andean region of Ecuador. To designing slender structural elements under axial loading engineers usually use the Euler formula, but it is applicable only if the compression stress does not exceed the proportional limit. One way to determine if the compression stress will be below the proportional limit is by comparing of the slenderness of the element with the limiting flexibility of its material which allows knowing if the buckling will occur in the elastic zone where Euler formula applies. The aim of the work - determine the magnitude of the limiting flexibility of eucalyptus, since this wood has been the subject of some investigations, however, no information about the limiting flexibility magnitude for the calculation of axially compressed elements. Methods. The laboratory tests to determine the magnitudes of the modulus of elasticity, proportional limit, admissible compression stress and limiting flexibility was carried out. Results. This experimental investigation shows that the magnitude of the limiting flexibility or so-called critical slenderness ratio for eucalyptus globulus is 59.

TRACTION FORCES CREATED BY FLEXIBLE ELEMENTS AND HOISTING-AND-TRASPORT, CONSTRUCTION, ROAD VEHICLES AND EQUIPMENT SYSTEMS BY MEANS OF FRICTION. LECTURE 4

The article consistently sets forth the material of the fourth lecture on the course “Theory of hoisting-and-transport, construction, road vehicles and equipment”, which included the following questions: transfer of traction efforts by flexible elements using the example of a thin inextensible thread, derivation of the Euler formula, flexible links and hoisting-and-transport, construction, road vehicle and equipment (HTCRVE) systems; the operation and calculation of the belt brake; the node attaching the rope to the drum and its calculation; the resistance in the cable system of the movement mechanism of the of the tower crane; the determination of the resistances in the cargo truck cable system of the movement mechanism; the transmission of traction by friction in the belt conveyors; the calculation of the drive station drive power of the belt conveyor while transmitting traction by friction.

Using matrix stability for variable telegraph partial differential equation

The variable telegraph partial differential equation depend on initial boundary value problem has been studied. The coefficient constant time-space telegraph partial differential equation is obtained from the variable telegraph partial differential equation throughout using Cauchy-Euler formula. The first and second order difference schemes were constructed for both of coefficient constant time-space and variable time-space telegraph partial differential equation. Matrix stability method is used to prove stability of difference schemes for the variable and coefficient telegraph partial differential equation. The variable telegraph partial differential equation and the constant coefficient time-space telegraph partial differential equation are compared with the exact solution. Finally, approximation solution has been found for both equations. The error analysis table presents the obtained numerical results.

Optimal control of a rectilinear motion of a rocket

In this work, we have modelled the problem of maximizing the velocity of a rocket moving with a rectilinear motion by a linear optimal control problem, where the control represents the action of the pilot on the rocket. In order to solve the obtained model, we applied both analytical and numerical methods. The analytical solution is calculated using the Pontryagin maximum principle while the approximate solution of the problem is found using the shooting method as well as two techniques of discretization: the technique using the Cauchy formula and the one using the Euler formula. In order to compare the different methods, we developed an implementation with MATLAB and presented some simulation results.