Model of Filling the Internal Structure of Workpiece with Curved Layers for 3D Printing

This paper presents a solution to the problem of filling the internal structure of the workpiece with curve layer in 3D printing. A generalized model of filling the internal structure of workpiece with curve layer is designed. The results are presented for solving the problem on the example of curved layers of a conical shape with filling along a helical line. The research results can be in demand in the development of algorithms and software for technological equipment. They allow to ensure the formation of the internal structure of products in curved layers during 3D printing.

THERMOHYDRAULIC DISTRIBUTION IN TWISTED MICRO HEAT EXCHANGERS MOUNTED IN ANNULAR CHANNELS

The design of twisted heat exchangers provides a possibility to compensate for temperature and mechanical stresses thus ensuring continuous and failsafe operation of the equipment. The authors use fins and multiturn pipe bundles to reduce the mass and size characteristics of the heat exchangers. Such design significantly complicates the calculating method. The main aspect of swirling flows is the presence of radial and axial pressure gradients. When vapor or gas flows swirl, the flow velocity near the walls is much higher than the average values, while at the axis the flow is significantly slower and in some cases its values can become negative. The liquid flowing near the axis has a notably lower pressure, which can cause it to boil. Considerable radial gradients of axial and rotational speed, as well as static pressure contribute to turbulent pulsations. Given that the working fluid flows along a helical line, the flow in the near-wall area is similar to the flow around curved surfaces. The study analyses how the pipe bundle geometry impacts hydraulic distribution and scrutinizes the main components of pressure loss in the twisted heat exchanger. The analysis allowed simplifying the method of hydraulic calculation of the multiturn twisted heat exchanger. Solving the outer heat transfer and hydrodynamics problem for the twisted heat exchanger allowed determining the effect of the main factors and the relationship between the parameters of the coolant and the working mass on the distribution values. The paper presents the equations for determining geometry of the pipes with different coiling diameters, as well as the equation for finding hydraulic distribution in individual pipes in the layers of the pipe bundle. The obtained results can help increase the accuracy of thermal calculation. The authors propose to use sectioning of twisted heat exchangers as a way to reduce hydraulic distribution. Bibl. 12, Fig. 1.

Ergonomic aspects of material separation process modeling on stationary screw surfaces

The motion of material particles on gravitational surfaces, ie the motion of particles on surfaces under the action of its own weight, is used in special devices for their separation by physical and mechanical properties. For this purpose stationary screw surfaces of a steady step are applied. A number of papers have now considered the relationship between the kinematic parameters of motion, the coefficient of friction and the design parameters of the separator, when its surface is a deployable helicoid. The purpose of the study is to investigate helical surfaces with different design parameters in order to improve their separation ability through mathematical and geometric modeling of the process without making surface models. The problem of finding the trajectory of a material particle on the surface under the action of its own weight is preceded by the problem of finding the trajectory on an inclined plane. If a material particle with a certain initial velocity vо and a certain angle of inclination to the horizon falls on an inclined plane, it will move along a certain curve (in the absence of friction and air resistance, the trajectory will be a parabola). A system of equations is obtained, which describes the motion of a material point on the gravitational surface in the general case. If it is created for a specific surface, nonlinear and numerical methods must be used to integrate it. Modern software products allow not only to find the trajectory of the particle, but also to show it on the surface and even make an animation that essentially replaces high-speed shooting. This approach makes it possible to study the kinematic parameters of motion on different helical surfaces without full-scale samples of these surfaces, which significantly reduces the cost of finding the right surfaces. The motion of particles along a helical conoid and a deployable helicoid is considered. Simulation of the motion of a material particle on helical surfaces and its study by modern means of numerical integration and visualization have shown that for different surfaces the nature of the motion of the particle will also be different. When moving on the surface of the helical conoid, the particle in the presence of friction first accelerates, and then stops at a considerable distance from its axis. To prevent this, you need to take a limited compartment of the conoid both in height and on its periphery. When a particle moves on the surface of a deployed helicoid, its velocity becomes constant over time, and the trajectory after that will be a helical line. Key words: particle motion, helical surfaces, helical conoid, deployable helicoid, simulation

Creation of a Visual Model of the Atomic Structure as a Possible Element of a Quantum Computer

Using only the laws of classical mechanics, a possible physical model of the structure of an atom as an element of a quantum computer—- a cube is proposed. The stable motion of an electron in an atom is substantiated, which is provided not only by the motion in the main elliptical or circular orbit but also by the additional motion of the electron around the main trajectory along the trajectory (helical line), the projection of which on the plane of the main orbit has the form of a cosine. It is shown why the trajectory of the electron is “smeared”, and the electron does not fall on the nucleus and, in general, what keeps it in the sphere of influence of the nucleus.

On Developing an Electromechanical Drive Equipped with a Ball Screw Protected from Jamming

At present, one of the most pressing issues is the problem of improving electromechanical drive reliability, specifically, eliminating the possibility of jamming in the ball screw. The paper proposes an engineering solution designed to replace expensive imported ball screws. We analysed alternative designs intended to improve electromechanical drive reliability. We proposed and patented a ball screw design featuring a separator, in which the nut acts as a piston. The structure consists of a smooth cylindrical body and a slotted separator, its slots positioned along a helical line with a step equal to the thread lead. The body and the separator are coaxial and rigidly fixed together at the separator end faces so that the rolling elements remain in contact with the screw thread surfaces, the internal smooth cylindrical surface of the nut body and the surfaces of the separator slots. The ball screw design proposed, which features a nut with no internal threading, significantly simplifies the structure and its manufacturing technology. We built a model of an electromechanical drive equipped with a recirculating ball screw in order to determine static and dynamic properties of an electromechanical drive containing a ball screw featuring a separator. We compared the strength of the ball screw designs considered. As the ball screw featuring a separator is simpler and more reliable, the results of our analysis and the properties of an electromechanical drive equipped with the design proposed show that it is a promising solution to the import substitution problem concerning recirculating ball screws

Moving and fixed axoids of frenet thrihedral of directing curve on example of cylindrical line

If the solid body makes a spatial motion, then at any point in time this motion can be decomposed into rotational at angular velocity and translational at linear velocity. The direction of the axis of rotation and the magnitude of the angular velocity, that is the vector of rotational motion at a given time does not change regardless of the point of the solid body (pole), relative to which the decomposition of velocities. For linear velocity translational motion is the opposite: the magnitude and direction of the vector depend on the choice of the pole. In a solid body, you can find a point, that is, a pole with respect to which both vectors of rotational and translational motions have the same direction. The common line given by these two vectors is called the instantaneous axis of rotation and sliding, or the kinematic screw. It is characterized by the direction and parameter - the ratio of linear and angular velocity. If the linear velocity is zero and the angular velocity is not, then at this point in time the body performs only rotational motion. If it is the other way around, then the body moves in translational manner without rotating motion. The accompanying trihedral moves along the directing curve, it makes a spatial motion, that is, at any given time it is possible to find the position of the axis of the kinematic screw. Its location in the trihedral, as in a solid body, is well defined and depends entirely on the differential characteristics of the curve at the point of location of the trihedral – its curvature and torsion. Since, in the general case, the curvature and torsion change as the trihedral moves along the curve, then the position of the axis of the kinematic screw will also change. Multitude of these positions form a linear surface - an axoid. At the same time distinguish the fixed axoid relative to the fixed coordinate system, and the moving - which is formed in the system of the trihedral and moves with it. The shape of the moving and fixed axoids depends on the curve. The curve itself can be reproduced by rolling a moving axoid over a fixed one, while sliding along a common touch line at a linear velocity, which is also determined by the curvature and torsion of the curve at a particular point. For flat curves, there is no sliding, that is, the movable axoid is rolling over a stationary one without sliding. There is a set of curves for which the angular velocity of the rotation of the trihedral is constant. These include the helical line too. The article deals with axoids of cylindrical lines and some of them are constructed.

Electron Trembling as a Result of Its Stationary Motion in an Extra Space along Helical Line of the Compton Radius with the Speed of Light (“Zitterbewegung’’ in Multidimensional Space)

Because there is additional space in which the observed three-dimensional Universe expands, it is believed that elementary particles move at the speed of light in full space in a vicinity of a hyper-surface of three-dimensional sphere that is our Universe. Any interpretation of a spin and isotopic spin of electron requires at least three additional spatial dimensions. As applied to six-dimensional space, the simplest interpretation of the Heisenberg’s uncertainties relation, de Broglie waves, Klein-Gordon equation, electron proper magnetic moment, CPT-symmetry, spin, and isotopic spin is consistent with the results of the theory of relativity and quantum mechanics. Taking into account the movement of elementary particle (at the speed of light) along a helical line of Compton radius, when the axis of the helix is placed on that hyper-surface, we find a trajectory of the particle.

Calculation of temperature fields during finishing and strengthening electromechanical treatment of bodies of rotation moving along a helical line by a high-temperature source

The obtained approximate analytical dependences on the calculation of temperature fields in the processed part during finishing and strengthening electro-mechanical processing allow us to predict the properties of the surface layer and assign processing modes based on the characteristics of operation.

Spiral structure of the liquid particles trajectories near free surface of the vortex

Экспериментально и аналитически исследованы характеристики вихревого течения со свободной поверхностью, образующегося в результате вращения активаторного диска, расположенного на дне цилиндрического контейнера, заполненного водой. Получены аналитические выражения, показывающие, что траектории жидких частиц вблизи поверхности вихря представляют собой трехмерные спирали, по которым происходит течение от периферии к центу вихря. Показано, что рассчитанные и визуализированные траектории жидких частиц хорошо согласуются между собой и относятся к классу пространственных логарифмических спиралей. The work is aimed to compare results of analytical and experimental modeling of vortex fluid flow. The compound flow of liquid (water) occurs in a vertical cylindrical container without upper endwall under the action of the disk rotating at the bottom endwall. The two main components of the emerging flow are the toroidal vortex and the vortex with vertical axis. The equations are written in the cylindrical coordinate system dictated by the geometry of the problem. On the basis of the existing analytical expression, which describes the free surface form of the compound vortex in the zero approximation, an approach is developed to describe the trajectories of individual “liquid particles”. The obtained result allows to explore the velocity field structure near the free surface. The obtained expressions indicate that the velocity field near free surface becomes more pronounced in the tangent direction. This result is confirmed in the experimental studies of the compound vortex flow. The analytical forms of liquid particle trajectories near and on the free surface of the compound vortex are obtained. The general particle movement is from the container sidewall along the free surface to its center and further down the spiral-helical line. The images of the visualized particles trajectories both on the free surface (logarithmic spiral) and in the liquid depth are obtained in experiments and testify in favor of the implemented approach to the construction of analytical solution of the liquid particle motion for the vortex flow of the mentioned type. The correspondence of the calculated free surface forms obtained with the help of analytical expressions and those observed in the experiments with different parameters of the vortex flow shows that the developed approach to the problem can be based on a simplified description.

Projection by Conical Helical Lines With Constant Pitch

This paper’s purpose is investigation of non-traditional projection systems and their projecting surfaces, the choice of such congruence parameters for conical helical lines, which allow cover the whole complex of requirements to the surface, obtained by projecting of an arbitrary flat or spatial line with congruence beams, as well as the use of computer graphics in surface visualization. In the paper has been presented an example of analytical interpretation for an image of curvilinear projection by conical helical lines with constant pitch, and a congruence example for conical helical lines located on coaxial cones with a common vertex and a variable angle of generatrix inclination to an axis. Have been investigated properties and defined parameters of the congruence helical line passing through a space arbitrary point which is not belonging to an axis. An approach for construction of spiral surfaces, which frame consists of beams projecting an arbitrary line. A form generation of surfaces by analytical methods and their visualization by means of computer graphics is one of applied geometry’s urgent problems in connection with the use of such methods in automated systems for scientific research, design, and manufacture on equipment with computer numerical control. The leading research method for this problem is the general analytical theory for surfaces’ applied form generation developed by Professor I.A. Skidan and formed a unique apparatus, based on mathematical support of computing technologies for design and creation of objects with complex forms. On examples of visualization for projecting surfaces by means of computer graphics it is possible to show applicability of analytical models in computer technologies for scientific researches, design and manufacturing.