scholarly journals PARTICLE MOTION ON THE SPHERICAL SEGMENT WITH VERTICALS RADIALLY INSTALLED BLADES

2021 ◽  
Vol 3 (1) ◽  
pp. 27-36
Author(s):  
T. Volina ◽  
◽  
S. Pylypaka ◽  
A. Nesvidomin ◽  
◽  
...  
Keyword(s):  
Friction Coefficient ◽  
Angular Velocity ◽  
Relative Motion ◽  
Particle Motion ◽  
Equations Of Motion ◽  
Analytical Description ◽  
Vertical Axis ◽  
Disk Surface ◽  
Spherical Segment ◽  
Technological Parameters

The relative motion of a particle on the inner surface of a horizontal spherical disk along a vertical blade mounted in the radial direction is considered in the article. The disk rotates around a vertical axis with a given angular velocity. A system of differential equations of motion of a particle is compiled and solved by numerical methods. The kinematic characteristics of the motion are found, the regularities of the relative motion of the particle on the surface of the cylinder are clarified. Graphs characterizing the motion of a particle at certain given parameters are constructed, namely: graph of angle change, which sets the position of the particle on the surface of the sphere in the direction of the meridian, graphs of absolute and relative velocities, graphs of change of forces of the reaction of the spherical disk and blade. Numerical integration of the obtained differential equation showed that in half a second the particle rises to the height of the hemisphere, and then begins to fall. In this case, the descent alternates with the rise to a complete stop of the particle at a certain height, i.e. the particle “sticks” and then rotates with the hemisphere. The angle of “sticking” can be found analytically. In addition, numerical calculation methods have shown that at zero value of the friction coefficient of the particle on the disk surface, i.e. at its absolutely smooth surface, and at the non-zero value of the friction coefficient of the blade surface, and at an unlimited increase of the disk angular velocity the particle “sticks” at the height of the center of the sphere. If both surfaces are absolutely smooth, then the damping oscillations of the angle that determines the position of the particle on the surface of the sphere in the direction of the meridian, occur indefinitely. The working surface of the disk of the centrifugal apparatus, which is made in the form of a spherical segment, provides the beginning of the flight of the particle at the time of ascent from the disk at a given angle to the horizontal plane, increasing the scattering area of the technological material. The analytical description of the particle motion obtained in the article makes it possible to investigate its acceleration along with the blades of the disk and to find the relative and absolute velocities at the moment of particle ascent from the disk. The found analytical dependencies allow determining the influence of constructive and technological parameters on the process of particle acceleration.

scholarly journals MOVEMENT OF THE PARTICLE ON THE INTERNAL SURFACE OF THE SPHERICAL SEGMENT ROTATING ABOUT A VERTICAL AXIS

2020 ◽  
pp. 79-88
Author(s):  
Sergiy Pylypaka ◽  
Victor Nesvidomin ◽  
Tatiana Volina ◽  
Larysa Sirykh ◽  
Liudmyla Ivashyna
Keyword(s):  
Numerical Methods ◽  
Experimental Research ◽  
Relative Motion ◽  
Particle Motion ◽  
Internal Surface ◽  
Vertical Axis ◽  
Relative Displacement ◽  
Spherical Segment ◽  
Velocity Changes ◽  
Theoretical Results

The particle relative motion on a spherical segment rotating about a vertical axis was considered in the article. The differential equations of the relative displacement of a particle were completed and solved by numerical methods. The relative and absolute trajectories of particle motion and graphs of relative and absolute velocity changes were constructed. The regularity of particle motion as it is lifted over the surface was found out. The conducted experimental research has confirmed the received theoretical results.

A study of motions in a rotating liquid

1951 ◽  
Vol 206 (1084) ◽  
pp. 108-130 ◽  
Keyword(s):  
Angular Velocity ◽  
Equations Of Motion ◽  
Vertical Axis ◽  
The Body ◽  
Forced Oscillations ◽  
Infinite Cylinder ◽  
Two Dimensional ◽  
Small Motion ◽  
Axis Of Rotation ◽  
Rotating Liquid

Starting with the equations of motion for a perfect, incompressible fluid referred to a coordinate system which rotates about a vertical axis with uniform angular velocity R , the physical condition of ‘small motion’ is determined which permits the equations to be linearized. The small motions resulting from forced oscillations of a rotating liquid are investigated. It is shown that there are three types of flow depending on the relative magnitudes of the impressed frequency β and the angular velocity R of the fluid. Two of the regimes are studied in detail. A similarity law is developed which gives the solution of a class of problems of oscillations for β > 2 R in terms of the solutions to similar irrotational problems. An attempt is made to explain how slow, two-dimensional motion can be produced by introducing a boundary condition which is three-dimensional (as observed in experiments performed by G. I. Taylor), by considering problems from the moment at which the disturbance is created from rest relative to the rotating system, with the only initial assumption that the fluid is rotating uniformly like a solid body. For the particular cases studied the results are in agreement with Taylor’s experiments, in that the flow is found to become steady and two-dimensional if the disturbance which causes it approaches a steady state. If the disturbance is due to a body which moves along the axis of rotation of the fluid, the steady two-dimensional behaviour may be expected everywhere except in the neighbourhood of the surface of an infinite cylinder which encloses the body and whose generators are parallel to the axis of rotation. To resolve an apparent disagreement between certain theoretical results by Grace on the one hand, and experimental evidence by Taylor and the author’s conclusions, on the other, arguments are advanced that the various results may be in agreement, provided Grace’s are given a new interpretation.

scholarly journals The dynamics of revolving fluid on a rotating earth

1921 ◽  
Vol 99 (700) ◽  
pp. 397-402 ◽  
Keyword(s):  
Angular Velocity ◽  
Horizontal Plane ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Vertical Axis ◽  
The Earth ◽  
Axis Of Symmetry ◽  
Rotation Of The Earth ◽  
Special Case ◽  
Complete Account

In a paper on the dynamics of revolving fluids, the late Lord Rayleigh considered the special case of fluid revolving about a fixed vertical axis, neglecting the rotation of the earth. The object of the present paper is to investigate the modifications of Rayleigh’s results which are brought about by the rotation of the earth, and by translation in a vertical plane of the axis of symmetry. Air is treated as an incompressible non-viscous fluid. Let the motion be referred to rectangular axes, x, y, z, rotating with the earth, the axis of z being vertical and the axes of x and y in the horizontal plane. At a point x, y, z , the components of velocity are u, v, w, the pressure is p , and density p . If gravity is the only impressed force, the equations of motion are D u /D t = —1/ p dp / dx + lv , (1) D v /D t = —1/ p dp / dy — lu , (2) D w /D t = —1/ p dp / dz + g , (3) where D/D t = d / dt + ud / dx + vd / dy + wd / dz and the equation of continuity is du / dx + dv / dy + dw / dz = 0, (4) where l — 2ω sin Φ, ω being the angular velocity of rotation of the earth, and Φ the latitude. The terms lv , — lu , in the first two equations represent components of the deviating force due to the earth’s rotation, and the inclusion of these terms takes complete account of the rotation of the earth.

scholarly journals Mathematical Model of Pressure Formation Process along the Helix Channel Length of Screw Grinder

2020 ◽  
Author(s):  
Valery Pelenko ◽  
Ilkhom Usmanov ◽  
Vyacheslav Pokholchenko ◽  
Irina Smirnova
Keyword(s):  
Energy Consumption ◽  
Mathematical Description ◽  
Analytical Description ◽  
High Energy ◽  
Channel Length ◽  
Operating Conditions ◽  
Technical Equipment ◽  
Mining Equipment ◽  
Technological Parameters ◽  
Total Energy Consumption

The improvement of the technical equipment effectiveness is currently becoming particularly important. This applies not only to large and high-energy-intensive machines, but also to household appliances, the total energy consumption of which often exceeds the energy consumption of the overall equipment. These types of devices include, in particular, grinding and cutting equipment. The mathematical description of the processes carried out on this equipment is generalized and can be extended to a wider class of machines, including waste processing and mining equipment. The technological parameters, the design of screw grinders, and the processes of movement, deformation, extrusion and cutting carried out in them are characterized by a significant number of factors affecting the energy intensity. The main ones are the geometric parameters of the screw, machine’s body, cross knife, grinding plate’s thickness, the number and diameter of holes in it, as well as the product’s physical-mechanical characteristics and operating conditions. The most important for the mathematical description are the zones and processes where the main share of the consumed power is spent. The complexity of their analytical description is due to a simplified consideration of either individual technological zones of grinders’ existing designs, or the use of unreasonable simplifications.

scholarly journals On rolling friction

2019 ◽  
Vol 485 (3) ◽  
pp. 295-299
Author(s):  
A. P. Ivanov
Keyword(s):  
Friction Coefficient ◽  
Angular Velocity ◽  
Viscous Friction ◽  
Rolling Friction ◽  
The Body ◽  
Normal Velocity ◽  
Contact Conditions ◽  
Combined Motion ◽  
Pure Rolling ◽  
Over Time

The dependence of rolling friction on velocity for various contact conditions is discussed. The principal difference between rolling and other types of relative motion (sliding and spinning) is that the points of the body in contact with the support change over time. Due to deformations, there is a small contact area and, entering into contact, the body points have a normal velocity proportional to the diameter of this area. For describing the dependence of the friction coefficient on the angular velocity in the case of “pure” rolling, a linear dependence is proposed that admits a logical explanation and experimental verification. Under the combined motion, the rolling friction retains its properties, the sliding and spinning friction acquiring the properties of viscous friction.

Desirability of Tribo-Performance of Natural Based Thermoset and Thermoplastic Composites: A Concise Review

2021 ◽  
Author(s):  
Aravind Dhandapani ◽  
Senthilkumar Krishnasamy ◽  
Thitinun Ungtrakul ◽  
Senthil Muthu Kumar Thiagamani ◽  
Rajini Nagarajan ◽  
...  
Keyword(s):  
Friction Coefficient ◽  
Wear Rate ◽  
Relative Motion ◽  
Operating Temperature ◽  
Natural Fibers ◽  
Specific Wear Rate ◽  
Thermoplastic Composites ◽  
Sliding Velocity ◽  
Concise Review ◽  
Sliding Distance

Tribology, which may be defined as an interdisciplinary subject, deals with relative motion between two or more bodies, i.e., surfaces that are interacting relatively. Thus, tribology is a science covering three vital classes, namely, 1) wear, 2) friction, and 3) lubrication. The focus of this article is to bring out the elements that are influencing the wear-resisting behavior of thermosetting and thermoplastic composites with natural-based constituents. It was also identified from the literature sources that 1) the treatments on the natural fibers acting as reinforcement and 2) the addition of fillers in resin acting as matrix could improve the wear-resisting behavior of the composites. Additionally, other conditions such as 1) sliding speed, 2) sliding velocity, 3) sliding distance, and 4) operating temperature could also influence the friction coefficient and specific wear rate of the natural-based composites.

scholarly journals The Magnetic Fields of Pulsars

1974 ◽  
Vol 64 ◽  
pp. 187-187
Author(s):  
D. M. Sedrakian
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Magnetic Fields ◽  
Relative Motion ◽  
Kinematic Viscosity ◽  
Charged Particles ◽  
Normal Fluid ◽  
Inertia Effects ◽  
Generation Mechanisms ◽  
Image Position

Two generation mechanisms of magnetic fields in pulsars are considered.If the temperature of a star is more than 108K, the star consists of a normal fluid of neutrons, protons and electrons. Because the angular velocity of pulsars is not constant dω/dt ≠0, inertia effects can occur, and generate magnetic fields through the relative motion of charged particles with different masses. The kinematic viscosity of electrons is 30 times larger than that of protons; hence electrons move with the crust, but the proton-neutron fluid will move relative to the electrons. The magnetic momentum can be calculated by the following formula where Meff = Mp + Mn(Nn/Np), R = radius of the star, σ = conductivity. For typical neutron stars we have dω/dt~ 10-8 s-2, R~106 cm, σ~1029 s-1 and we get a magnetic field of the order of 1010 G.

Velocity Control of a Cylindrical Rolling Robot by Surface-Morphing

2015 ◽  
Author(s):  
Michael Puopolo ◽  
J. D. Jacob
Keyword(s):  
Mathematical Model ◽  
Angular Velocity ◽  
Velocity Profile ◽  
Average Velocity ◽  
Equations Of Motion ◽  
Angular Position ◽  
Velocity Control ◽  
Control Scheme ◽  
Rolling Robot ◽  
Angular Velocity Profile

A mathematical model is developed for a rolling robot with a cylindrically-shaped, elliptical outer surface that has the ability to alter its shape as it rolls, resulting in a torque imbalance that accelerates or decelerates the robot. A control scheme is implemented, whereby angular position and angular velocity are used as feedback to trigger and define morphing actuation. The goal of the control is to direct the robot to follow a given angular velocity profile. Equations of motion for the rolling robot are formulated and solved numerically. Results show that by automatically morphing its shape in a periodic fashion, the rolling robot is able to start from rest, achieve constant average velocity and slow itself in order to follow a desired velocity profile with significant accuracy.

On the Dynamics of a Weighted Bowling Ball

1979 ◽  
Vol 46 (4) ◽  
pp. 937-943 ◽  
Author(s):  
R. L. Huston ◽  
C. Passerello ◽  
J. M. Winget ◽  
J. Sears
Keyword(s):  
Angular Velocity ◽  
Velocity Component ◽  
Equations Of Motion ◽  
Mass Center ◽  
Governing Equations ◽  
Euler Parameters ◽  
Factors Affecting ◽  
Dependent Variables ◽  
And Performance ◽  
Component Parallel

An analysis of the dynamics and performance of a weighted, slipping/rolling bowling ball is presented. The analysis uses Euler parameters and angular velocity components as dependent variables. The governing equations of motion are integrated using standard digital/numerical procedures. Particular attention is given to factors affecting ball performance (“hook”) and the lane oil tracing on the ball. It is found that factors most affecting hook are the mass-center location, the lane conditions (friction), and the initial angular velocity component parallel to the lane.

Stability and Dynamics of Non-Linear Slider Behaviour Due to Disk Waviness in the Presence of Intermolecular and Electrostatic Forces

2005 ◽  
Author(s):  
Vineet Gupta ◽  
David B. Bogy
Keyword(s):  
Resonance Frequency ◽  
Equations Of Motion ◽  
Disk Surface ◽  
Air Bearing ◽  
Electrostatic Forces ◽  
Disk Interface ◽  
Non Linear ◽  
Bearing Stiffness ◽  
Stiffness And Damping ◽  
Nonlinear Nature

In this paper we present a theoretical investigation of the stability and the dynamics of the non-linear behavior of a slider at very low head media spacing. A single DOF head disk interface (HDI) model, with constant air bearing stiffness and damping has been used to study the effect of disk waviness on the nonlinear slider dynamics in the presence of intermolecular and electrostatic forces. A variational approach based on the principle of least action was used to derive the equations of motion of the slider. Further, a stability criteria was derived that helped to better understand the instabilities that appear in slider when the slider is flying in close proximity to the disk surface. Due to extremely nonlinear nature of the interaction between the slider and the disk, we observed some strange features of the motion of the slider. In particular the effects of the nonlinear interaction force, air bearing stiffness and damping on the instabilities of the periodic motions of the slider are discussed in detail. We found that the branch associated to the disk waviness frequencies larger than the resonance frequency is always stable and the branch associated to the disk waviness frequencies smaller than the resonance frequency exhibits two stable domains and one unstable domain. This analysis was further extended to include the nonlinear nature of air bearing stiffness and damping as well as contact at the HDI.

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