OZ Axis Research Articles

Theoretical and experimental research on the mechanical tests of 3D printed samples from various materials

At this moment, a real industrial, scientific and technological revolution is being discussed worldwide, consisting in the development of Additive Manufacturing AM technologies through the use of 3D printing. The FDM (Fused Deposition Modelling) 3D printing technology consists in the deposition of fusible material layer by layer in the XOY plane, the thickness of the 3D printed layer is g = 0.12 ÷ 0.24 mm, the resolution of 3D printing is r = 0.1mm, while the print head advances vertically on the OZ axis. The purpose of the work is to determine the breaking moment through destructive mechanical bending tests of some samples made by 3D printing from the following materials: ABS+, PETG and PLA. 5 samples were made in 3 printing directions: horizontal, vertical and lateral, resulting in 15 samples for each material. The total number of samples used is 45. Knowing these values, depending on the requirements of the specifications, a certain material and a certain printing position can be used.

TWO-CHANNEL BALLISTIC TRANSFORMER GRAVIMETER

The two-channel ballistic transformer gravimeter for measuring the doubled value of the acceleration of gravity contains a gravimeter that uses a fixed glass tube made of a dielectric material, a magnetized test body in the form of a layer, a computer and an inductance winding, which is characterized by the fact that the fixed tube is made of a dielectric material, the inductance winding acts as a primary excitation winding connected to the power source, which additionally contains two identical sections of the secondary output winding, connected in series-opposite, to create two measurement channels, an electromagnet consisting of an armature made of magnetic material, an additional winding connected through a switch to an additional power source. To provide free vertical movement in two opposite directions along the OZ axis of the magnetized test body, it is proposed to use the proposed electromagnet consisting of an armature made of a soft magnetic material, an additional winding connected through a switch to an additional power source. The winding of the electromagnet is connected to the power source by a switch to create an electromagnetic flux of attraction to the test body, which, thanks to this, will rise to the uppermost position. At the next moment, the electromagnet switch is turned off, and the test body falls down under the action of the acceleration of gravity. The doubled output signal of the acceleration of gravity, which is removed from the secondary winding, is free from the effects of interference: external electromagnetic flows, inertial vertical acceleration, instrumental errors caused by changes in temperature, humidity, vibrations, pressure, the moment of dry friction forces, non-identity of the parameters of two identical sections of the secondary output winding and other factors - is submitted to the computer. The output of the computer is proportional to twice the acceleration of gravity value. Increased accuracy and reliability of measurements of the doubled value of the acceleration of gravity and increased efficiency of the search for minerals have been ensured

Application of rapid prototyping technology in pump engineering

The article presents the results of the use of rapid prototyping technology when modifying the impeller of a centrifugal pump in order to increase efficiency. As a result of the implementation of the technology, the influence of parameters such as the printing speed of the main layers, the printing speed of the current layers, the thickness of the layers on the geometric accuracy of printed products was studied. According to the results of experiments, it was revealed the effect of the feed rate on the OZ axis, an increase in speed will lead to lower surface quality, higher roughness. The distance between the layers is 0,15 mm/s, getting a roughness of Ra 6,3 microns, and in the right case we used a distance of 0,05 mm/s between the layers, getting a roughness of Ra1,6 microns. The article presents the results of the analysis of the effect of exposure time and exposure time in the UV chamber on the hardness of printed products. The article presents a method for determining and compensating the geometry of prototypes based on reverse engineering technology based on the use of an optical scanner. The tests of a centrifugal pump with a prototype of a modified wheel confirm the need for such innovations as rapid prototyping to shorten the design cycle of new products, as well as reduce the cost of their development.

Traction Calculation for Modular Energotechnological Unit Given Kinematic Mismatch of Driving Axles

The power of the engine of energy-saturated tractors often proves not to be fully used. One of the solutions to this problem might be the use of the unit technological part as an active coupling weight. To implement it, an energotechnological modular unit was created.Research purpose The purpose of the study is to determine the traction efficiency of a block-modular energotechnological unit given a kinematic discrepancy between the tractor wheels.Materials and methods The system of equilibrium equations for the transport-technological module being free-attached to the energy module is presented as the sum of forces projections on the axis. The tangent thrust force and the rolling resistance force of each axle of the energy vehicle were expressed through the corresponding normal soil reactions. When calculating multiaxle running systems, it was taken into account that the rolling resistance coefficient depends on the number of wheel passes along one trace and the degree of soil deformation by previous passes. Normal reactions of the soil to the energy module supports have been determined by considering the modular energotechnological unit as a whole, equating to zero the sum of the forces projection on the OZ axis and the sum of the moments at the point of contact between the energy module’s front wheels and the soil.Results and discussion The influence of the kinematic mismatch between the third axle and the second one on the undercarriage efficiency was investigated. Analyzing the dependence of the running system efficiency on the kinematic mismatch of the first and third axles at the traction of 30 kilonewtons, the extremes of all the dependencies at the kinematic mismatch between the third bridge and the second one different unit were detected.Conclusions It has been revealed that the change in the efficiency of the chassis system of the modular energotechnological unit depends on the kinematic mismatch between the third axle and the second one at a predetermined kinematic mismatch between the first axle and the second axle, which is a structural feature for 4K4 wheeled tractors. The excess in the values of running system efficiency equals 1.04-1.06 if the constructive kinematic mismatch between the third bridge and the second one is within 1.06-1.08.

MODELISATION AND NUMERICAL SIMULATION OF SALT GRADIENT SOLAR POND: THE ALTERNATING DIRECTION IMPLICIT METHOD

Solar energy as free and abundant energy is considered among the renewable energy that can replace disappearing fossil fuels. Many solar power systems can be used to capture this energy, but the majority does not have the ability to store this energy in different weather and time conditions. Therefore, salinity gradient solar ponds used in the present work can overcome this issue by simultaneously capturing and storing solar energy. A solar pond is being built at Annaba. In this present work we consider two identical solar ponds subjected to the same solar radiations during a period of 28 days, and exposed to the same climatic conditions, initial and at the limits. in the first pond, nanoparticles of conductive metal, namely copper, are injected with a concentration of $0.09\%$, while the second pond does not contain any nanoparticles. a comparative study was carried out on the temperature profile in the two solar ponds mentioned above to see the influence of nanoparticles on the thermal performance of the solar pond. The mathematical model adopted in this work is based on the equation of heat conduction in two dimensions with an external source of energy to the system. The method of finite differences with ADI scheme was used to determine the temperature distribution in two different directions according to the horizontal axis ox and to the vertical axis OZ representing the depth. An average temperature and insolation values for the last ten years were obtained using the data provided by Annaba saline station. Finally, a comprehensive study was carried out in order to highlight the convergence, consistency and stability properties of the discrete model representing the solar pond.

Formation of an Acoustic Field in a Waveguide by a Spherical Sound Source

This paper presents the initial output and calculated ratios for a full acoustic pressure field in a waveguide with soft boundaries. In addition, the paper describes the basic steps for obtaining the data of the initial and calculated ratios, as well as approaches and methods for analyzing the field in the waveguide for the case where the sound source is not point, but spherical. Based on the obtained relationships, a computer model was developed and analyzed and further studies were developed.This work contains the formulation and partial solution of the problem of forming a complete acoustic field in a waveguide with soft boundaries. Estimates were given to approximate the direct field in a certain approximation. The calculated ratios for the approximation of the reflected field along the OZ direction are also given. The above relations can be used in further studies, in particular to extend the reflection field calculations to the entire first quadrant, since the problem is symmetric. This can be done using the so-called imaginary source method.To analyze the reflected field, a direct spherical field was represented by a set of plane normal waves. Since only normal waves are used for approximation, the approximated field describes a spherical one with a certain approximation. The expression to describe the reflected field was obtained from the classical expression for the approximation of a spherical wave by a set of planes. A reflection coefficient was found to describe the approximated reflected field. It can be considered a design in this case. It is useful for describing the reflected field along the OZ axis. The obtained coefficient can be used in further studies, in particular, to extend the reflection field calculations to the entire first quadrant, since the problem is symmetric. This can be done using the so-called imaginary source method.A mathematical computer model was developed in MATLAB to analyze the results. The calculations were performed for different waveguide depths and operating frequencies. In the model, the waveguide fills the water and the air serves as the boundary, so the boundaries of the waveguide are acoustically soft.The paper deals with a flat problem within the first quadrant.In general, this paper presents the formulation and solution of the problem of forming acoustically soft surfaces. In this case, the calculated ratios for the approximation of the direct field in a given approximation (taking into account only homogeneous waves) are given. And also the calculated ratios for the approximation of the reflected field along the OZ direction.The results are basic and can be applied to formulate and solve the problems of sounding shallow seas in the framework of elastic and hydroelectric productions.The paper also provides general expressions for the search of a reflected field based on Fresnel zones.

Оценка шероховатости при пятикоординатном чистовом фрезеровании поверхностей сфероцилиндрической фрезой

Unlike three-axis machining, five-axis machining allows the end tool or workpiece to be oriented at any angle relative to the machine axis OZ. It can be achieved by changing the values of the tool tilt angle and lead angle relative to the surface normal in the contact zone of the tool surface and the workpiece, taking into account the direction of the table feed. The article presents experimental results of analyzing the influences of tool orientation on transverse roughness during ball end milling using 2-flute and 4-flute 8 mm diameter mills. The analysis the arithmetic mean deviation of the assessed profile at various values of tool tilt angle and lead angle showed that the position of the tool point with a zero cutting speed significantly affects the surface quality. The results of the evaluation of the tool orientation influence on the surface roughness enable the selection of optimal tool orientation angles when developing control programs for end milling of free-form surfaces on five-axis CNC milling machines.

MATHEMATIC MODEL OF AND METHOD FOR SOLVING THE DIRICHLET HEAT-EXCHANGE PROBLEM FOR ONE-SHEET ROTARY HYPERBOLOID

It is the first generalized 3D mathematical model developed for calculating temperature fields in the thin-wall one-sheet rotary hyperboloid, which rotates with constant angular velocity around the axis OZ, ; the model was created with the help of known equations of generating lines in cylindrical coordinate system with taking into account finite velocity of heat conductivity and in the form of the Dirichlet boundary problem for the hyperbolic equation of heat conduction under condition that heat-conduction properties of the body were constant, and no internal sources of the heat were available. At initial moment of time, the body temperature was constant; values of temperature on outside surfaces of the body were known and presented continuous function of coordinate.The hyperbolic heat-conductivity equation was derived from the generalized energy transfer equation for the moving element of continuous medium with taking into account finiteness of the heat conductivity velocity.In order to solve the boundary problem, the desired temperature field was represented as a complex Fourier series. The obtained boundary problems for the Fourier coefficients were found with the help of Laplace integral transformations and the new integral transformation for two-dimensional finite space. Intrinsic values and intrinsic functions for the integral transformation kernel were found by method of finite element and the Galerkin methods. Besides, the domain was divided into simplex element.As a result, the temperature field in the thin-wall one-sheet rotary hyperboloid was found in the form of convergent series in Fourier functions.

The Mathematic Model and Method for Solving the Dirichlet Heat-Exchange Problem for Empty Isotropic Rotary Body

It is the first generalized 3D mathematic model, which is created for calculating temperature fields in the empty isotropic rotary body, which is restricted by end surfaces and lateral surface of rotation and rotates with constant angular velocity around the axis OZ, with taking into account finite velocity of the heat conductivity in the form of the Dirichlet problem. In this work, an integral transformation was formulated for the 2D finite space, with the help of which a temperature field in the empty isotropic rotary body was determined in the form of convergence series by the Fourier functions.

MATHEMATICAL MODELS AND METHODS OF SOLVING SPATIAL GENERALIZED BOUNDARY VALUE PROBLEM HEAT ROTATING HOLLOW PIECEWISE HOMOGENEOUS CYLINDER

Context. The phenomenological theory of heat conduction speed of heat propagation is assumed infinitely large. However, the high intensity of the observed transient processes such as explosions, supersonic flow, high speeds of rotation of the use of this assumption leads to errors, so it is necessary to take into account that the distribution of heat takes place at a finite rate.Objective. Development of a new generalized mathematical model of the temperature distribution in the hollow piecewise uniform cylinder in the form of a boundary value problem of mathematical physics for the heat equation and the solution of the resulting boundary value problem.Method. The use of known integral Laplace transforms, Fourier series, and developed a new integral transformation for piecewise homogeneous space.Results. Found Polga transient temperature field of a circular cylinder in a cylindrical coordinate system, a piecewise homogeneous polar radius direction, which rotates at a constant angular velocity about the axis OZ, with the ultimate heat propagation speed. Thermal properties of each layer does not depend on the temperature at an ideal thermal contact between the layers, and there are no internal sources of heat.Conclusions. For the first time developed a mathematical model of the temperature distribution in the empty piecewise uniform cylinder, which rotates at a constant angular velocity about the axis OZ, taking into account the finite speed of propagation of heat in the form of mathematical physics boundary value problem for hyperbolic partial differential equations of heat conduction with boundary conditions of the first kind. Thermal properties are in each layer does not depend on the temperature at an ideal thermal contact between the layers, and there are no internal sources of heat.Created a new integral transform of a piecewise-homogeneous space, with which found the temperature field of the hollow piecewise homogeneous circular cylinder in the form of convergent orthogonal series of Bessel functions and of Fourier. The obtained analytical solution of a generalized boundary value problem of heat transfer cylinder, which rotates, given a finite amount of heat propagation velocity can be used for modeling of temperature fields, which occur in many technical systems (satellites, forming rolls, turbines, etc.).

IMPACT OF LOOSE MATERIALS ON TRACK HOPPER WALLS

Objectives . During the design of different types of devices it is important to obtain reliable information concerning both the pressure distribution along the device's walls and the pressure at the level of the eduction gear. Differential equations for the equilibrium and stationary states of the loose medium accounting for the forces of dry friction between its particles are provided in the article. Methods. Both the vertical pressure component z P and its gradient along axis OZ are assumed to depend on the respective radius. Consequently, different forces will act vertically on the neighbouring elementary rings. This leads to the neighbouring outer ring being shifted downwards relative to the one under consideration; conversely the neighbouring inner ring, relative to the latter, will be shifted upwards. Therefore, the forces of dry friction acting on the inner and outer lateral surfaces of the elementary ring under consideration will be directed in opposite directions. The resultant force will be determined by the gradient of the pressure component along the coordinate P . The assumption that the components of the pressure acting on the loose material depend on the coordinates leads to the need to take this force into account. Results. The resulting differential equations are integrated by successive approximation in the boundary conditions corresponding to an extended track hopper; the derived analytical expressions for the pressure components of loose material in the hopper are illustrated with the help of graphs for the actual parameters of the hoppers; the distribution of loose material pressure along the walls of track hoppers is analysed on the basis of loose material concepts as an easily deformed anisotropic medium, which differs in its properties from a liquid and does not obey Pascal's law. Conclusion. The walls of the hopper take on all the load. To save the wall's material, its thickness can be considered not as a constant, but rather as a variable, providing maximum strength at a level of 2/3rds of the height at which vibrators are to be positioned to ensure a continuous flow of loose material from the hopper.

Implementation of Kohn's theorem for the ellipsoidal quantum dot in the presence of external magnetic field

An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls in the presence of external magnetic field is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the gas in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system. The parabolic confinement potential depends on the geometry of the ellipsoid, which allows, together with the magnetic field to control resonance frequencies of transitions by changing the geometric dimensions of the QD.

Estimating the efficiency of the simultaneous algebraic reconstruction technique (SART), Bayesian inference reconstruction (BIR), and traditional shift-and-add (SAA) tomosynthesis using medical phantoms

New parallel iteration algorithms that provide real-time reconstruction of the 3D breast images restored from an incomplete set of noisy mammograms are studied. The simultaneous algebraic reconstruction technique (SART) and Bayesian inference reconstruction (BIR) are considered as advantageous iteration methods that are most suitable for improving the quality of the reconstructed 3D images. The graphics processing unit (GPU) is used to accelerate the reconstruction. The minimization of total variation (TV) is used as a priori support for the regularization of the iteration process and decrease of the noise level in the reconstructed images. Preliminary results for medical physical phantoms show that all the methods are sufficient for the layer-by-layer reconstruction of medical model objects and separation of layers whose images are overlapped on a mammogram that corresponds to vertical transmission (direction along the OZ axis). The traditional shift-and-add (SAA) tomosynthesis is established to be less efficient than SART and BIR in terms of the anatomical-noise reduction and blurring of reconstructed 3D images between conjugate layers. Despite the fact that the estimated contrast-noise ratio, given internal structures with low contrast, is higher for SAA as compared to SART and BIR, its efficiency is very low given the highly structured background. In our opinion, optimal results can be achieved using BIR.

On the possibility of implementation of Kohn’s theorem in the case of ellipsoidal quantum dots

An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional, coupled. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the dot in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system.

Dimensional analysis of plate heating

The polishing of plates by free abrasive on a ZPD�320A machine tool does not maintain the shape of the plate in most cases. This may be attributed to plastic deformation at the plate surface as a result of inadequate heat transfer from the cutting zone. The small plate thickness (0.2–0.4 mm) also contributes to its shape instability. On that basis, we need to assess the rate of heat transfer. As a result of dimensional analysis of plate polish� ing by free abrasive, we may simplify the correspond� ing model and assess the time constants of heat trans� fer, in terms of the Biot number [1–3]. The contact region is in the XOY plane and corre� sponds to the boundary of a halfspace. The character� istic dimensions along the OX and OY axes are denoted by b, while the characteristic dimension along the OZ axis is the plate thickness δ. Then X = b Y = b Z = δ where are dimensionless quantities. We will use the following notation: θ0 is the charac� teristic temperature; U0 is the characteristic slipping speed; τm is the characteristic tangential stress. The dimensionless time may be selected from the condi� tion t0 = b/Ub [1]. Hence, = t/t0. Here Ub is a charac� teristic parameter that will be established later.

Computational and experimental studies of size and shape related physical properties ofhydroxyapatite nanoparticles

In this work, the properties of hydroxyapatite (HAP) nanoparticles (NPs) havebeen studied both theoretically and experimentally focusing on computationalanalysis. HAP is widely used to fabricate implants, for drug delivery, etc. Thephysical properties of the nanosized HAP particles play an important rolein the interaction with cells in the human body and are of great interest.Computer simulation was employed to understand the properties of HAP clusters(Ca5(PO4)3OH) including formation energies, dipole moments and polarization (surface charges) by molecular mechanics(MM + ,OPLS) and mostly by quantum semi-empirical Hartree–Fock (PM3) methods. The size of the simulatedcluster is found to affect its dipole moment, polarization, and, finally, the electron work function—φ. Theseparameters depend on the concentration of hydrogen atoms H (or protons) at the surface. Values ofφ were experimentally estimated via photoelectron emission measurements. The magnitude ofφ was demonstrated to have a positive correlation on sizes. The NPs demonstrated acapability to be gathered within conglomerates. This property is confirmed bythe calculated data for various sizes. Their sizes have a positive correlation onφ by the native particles. The main results show that the distributionsof dipole moments have very different space orientations (along theOX,OY andOZ axes,the OZ axis is oriented along the OH column) and change with the addition of hydrogenatoms, which saturate the broken hydrogen bonds. This electrical property ofNP leads to different behaviors and motions with consequent aggregation: (1) forthe case of NPs having dipole moment oriented preferably perpendicular to theOZ axis (with more hydrogen bonds saturated by added H)—the HAP NP aggregates withhexagonal orientation and forms a wider and more spherical shape (sphere-like orbundle-like); (2) for the case of NPs having dipole moment oriented along theOZ axis (as is the case in the absence of added protons or non-saturated hydrogen bonds)—theNPs firstly rotated and oriented along this axis to form the most elongated cylindricalshape (rod-like).

Supporting system of a longitudinal-milling machine with a mobile gantry

A model of the supporting system for the 6675 longitudinal-milling machine is shown in Fig. 1. The dynamic pliability of this supporting system for a symmetric base configuration relative to the gantry and the middle position of the slide is shown in Fig. 2, in the form of the amplitude‐frequency characteristic for the dynamic pliability of the structure. The resonant oscillations of the supporting system for the initial 6675 milling machine and the trolleys of the portal-supply drive have been experimentally established: (1) under the action of an external force along the O X axis, at resonant frequencies f = 27, 52, and 82 Hz; (2) under the action of a force along the OY axis, at f = 20 and 86 Hz; 3) under the action of a force along the OZ axis, at f = 57 Hz. Examples are shown in Figs. 3, 4, and 5. The slide of the 6675 machine tool is mounted on a rocking guide piece (with two plates for each side of the slide). To increase the rigidity of the guide piece, we consider the use of six plates (three for each side of the slide). Calculation of the dynamic pliability of this design in the OX direction shows that the additional plates have no effect on the resonant amplitude of the dynamic pliability: the amplitude of the first resonant peak varies from 8.263 × 10 ‐8 to 8.251 × 10 ‐8 m/N. Hence, the introduction of additional plates is inexpedient. We now consider the influence of the slide extension on the dynamic pliability of the supporting system. (The slide path is 1 m.) All the previous calculations assume a middle position of the slide. The dynamic pliability of the supporting system with minimum and maximum extension of the slide in the OX direction is shown in Fig. 6, in terms of the amplitude‐frequency characteristic. Table 1 presents the dynamic characteristics of the supporting system for the 6675 milling machine. It is evident from Table 1 that changing the slide position alters the resonant amplitude in the amplitude‐ frequency characteristic of the dynamic pliability. The amplitude of resonant peak 1 varies by no more than 15%. Resonant peak 2 is more sensitive to the slide position: the resonant amplitude increases fourfold as the slide shifts from minimum to maximum extension. In this process, peak 2 becomes larger than peak 1. Analysis of the dynamic characteristics of the supporting system is necessary in order to determine the stability of the milling machine in operation. We will calculate the vibrational stability of the initial design of the 6675 milling machine with maximum extension of the slide, since the dynamic pliability is greatest in this case (Table 1). Table 2 presents the cutting conditions (the material of the blank and the geometry of the end mill). The critical gantry supply s is calculated for cutting depth t = 1, 2, and 3 mm. The corresponding graphs are shown in Fig. 7. It is evident from Fig. 7 that the critical supply s depends on the mill speed n and on the cutting depth t . Variation in n within the working range 200‐350 rpm is accompanied by change in s by up to 40% of its mean value; variation in t from 1 to 3 mm reduces s to less than a quarter of its initial value. However, even with maximum cutting depth t = 3 mm, the maximum critical sup

Structure and properties of quartz crystals grown from fluoride solutions: I. The morphology of basal pinacoid habit

The mechanism of growth of quartz crystals from fluoride media has been investigated. It is shown by different independent methods (selective etching, X-ray diffraction analysis, optical microscopy) that the faceted forms of autonomous growth regions (trigonal pyramids formed on nonsingular crystal faces) are unstable and degenerate during growth. This degeneracy is accompanied by torsion deformation of autonomous growth regions and, as a result, formation of a series of hollow helical channels at boundaries of autonomous growth regions, whose axes make an angle of ∼16° with the OZ axis, and their projections on the XOY plane are directed along the +X axes.

Simulating the junctions of basic machine-tool components

In developing models of machine-tool supporting systems, it is important to determine the initial data. For the basic parts, handbook data are available; it is more difficult to determine the initial data for the junctions. For the example of special samples, the simulation of junctions between the basic parts in the form of a thin layer of isotropic material was described in [1]. It was shown that, on the basis of experimental data on the junction deformation in specified contact conditions, a model of the junction may be developed, and the elastic moduli E and G of the material simulating the junction may be determined. However, the handbook and specialized data refer to the rigidity of the junction and the damping there, but not to the deformation. Therefore, we need to determine the initial data for a model of the junction (values of E and G of the material modeling the junction) from the known rigidity and damping of the junction. Given the benefits of shell finite elements, we use a shell model in solving this problem. As an example, consider a chuck‐column junction in a 654 noncantilever milling machine. On the basis of the dimensions and configuration of the junction (Fig. 1a), a geometric model may be developed, in the form of two identical boxes of cellular structure (Fig.1b). The dimensions of the model in the XOZ plane conform to those of the junction. The box height z in the model and its wall thickness s are assumed to be 1 and 0.02 mm, respectively [1]. In this model, the junction between the chuck and column is oriented so that its rear face is connected to the guide surface of the column and its front face to the guide surface of the chuck. Given that it is very difficult to determine the initial data for junction calculation from the known rigidity and damping, we will first consider an elementary volume dV of the material simulating the junction. To determine E and G , we analyze the compression (Fig. 2a) and shear (Fig. 2b) of volume dV . In the compression of volume dV , the displacement of its points along the OX , OY , and OZ axes will be denoted by dm , dn , and dw , respectively. Only the deformation dw of volume dV (height dz , cross-sectional area dS xy ) under the action of force dF z in the direction of the OZ axis is shown in Fig. 2a. The deformation in the direction of the OX and OY axes is analogous.

Computation limits of Current Distribution in thick Superconducting Bulks from Magnetic Field Measurements

We present the latest progress of our computation method for critical currents in bulk YBCO samples from magnetic field measurements with Hall probe, based on discretization of the magnetization M and resolution of the linearized inverse Biot-Savart problem by QR inversion. While computationally harder than other linear/FFT methods, it is more robust in front of measurement errors, and allows the computation of detailed current maps without assuming any symmetry in the OXY plane. In particular, we are able to detect irregularities such as multiple domains, or the perturbation induced by a welding. If the current in the bulk sample is not homogenous along the OZ axis, we obtain the average along the OZ axis of the current density. Moreover, the inhomogeneity of the current along the vertical axis can be detected by the user by measuring the magnetic field on the side of the bulk sample and comparing it with that induced by the computed OZ-averaged current. Finally, we discuss what must be done in the measurement of the magnetic field and mathematical processing of the data to avoid numerical pitfalls, and discuss the limits to the computation of 3-dimensional current maps.