scholarly journals Movement of a material particle on an inclined plane all the points of which describe circles in oscillatory motion in the same plane

2020 ◽  
Vol 97 (1) ◽  
pp. 122-131
Author(s):  
S.F. Pylypaka ◽  
◽  
M.B. Klendii ◽  
V.I. Trokhaniak ◽  
A.S. Pastushenko ◽  
...  
Keyword(s):  
Oscillatory Motion ◽  
Inclined Plane ◽  
Material Particle

Ergonomic aspects of material separation process modeling on stationary screw surfaces

2021 ◽  
pp. 86-95
Author(s):  
S. Pylypaka ◽  
◽  
A. Nesvidomin ◽  
Keyword(s):  
Geometric Modeling ◽  
High Speed ◽  
Physical And Mechanical Properties ◽  
Material Point ◽  
Design Parameters ◽  
Helical Line ◽  
Kinematic Parameters ◽  
Inclined Plane ◽  
Material Particle ◽  
Software Products

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

scholarly journals SCREW DESCENT, ANALYTICAL DESCRIPTION OF WHICH INCLUDES THE EQUATION OF PARTICLE MOVEMENT ON AN INCLINED PLANE

2021 ◽  
pp. 89-98
Author(s):  
Tatiana Volina
Keyword(s):  
Angular Velocity ◽  
Structural Parameters ◽  
Analytical Description ◽  
Constant Angular Velocity ◽  
Particle Movement ◽  
Inclined Plane ◽  
Material Particle ◽  
Angle Of Friction ◽  
The Coefficient Of Friction ◽  
The Difference

To study the modes of particle movement depending on the constructive parameters of the surface, it is important to have analytical dependencies of this movement. An analytical description of the movement of a load on the example of a material particle on the surface of a gravitational descent formed by a screw conoid and a coaxial vertical limiting cylinder was developed in the article. It makes it possible to find the constructive parameters of the descent, which will provide the required speed of the transportation. If the surface of the confining cylinder is absolutely smooth, then the movement of the particle along such a descent will be uniformly accelerated or equally slowed down depending on the value of the angle of inclination of the plane, that is, similar to movement along an inclined plane. If the angle of inclination of the plane is equal to the angle of friction, then the particle will move with a constant angular velocity of rotation, then one can find the linear velocity, which will also be constant. The value of this speed will be equal to the initial one. If the angle of inclination of the plane is equal to the angle of friction, but the coefficient of friction is not equal to zero, then the particle will be decelerated due to the action of the friction force of the particle on the surface of the cylinder. This is the difference from descent along an inclined plane, along which the particle in this case will move at a constant speed. In the general case, when the angle of ascent of the helix is ​​greater than the angle of friction, the driving force and the force of friction on the surface of the conoid and on the surface of the cylinder are balanced with each other and the angular velocity of rotation of the particle becomes constant. Consequently, it is possible to provide the required speed of transportation of the material at various ratios of the structural parameters of the surface with known coefficients of friction. To reduce the overall dimensions of the screw descent, it is necessary to reduce the radius of the limiting cylinder; however, with this limitation, the weight of loads should be taken into account.

scholarly journals PARTICLE MOTION OVER THE EDGE OF AN INCLINED PLANE THAT PERFORMS AXIAL MOVEMENT IN A VERTICAL LIMITING CYLINDER

2019 ◽  
Vol 59 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Serhii F. Pylypaka ◽  
Mykola B. Klendii ◽  
Viktor M. Nesvidomin ◽  
Viktor I. Trokhaniak
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Particle Motion ◽  
Vertical Cylinder ◽  
Vertical Direction ◽  
Analytical Description ◽  
Inclined Plane ◽  
Material Particle ◽  
Axis Of Rotation ◽  
Operating Element

Differential equations of a relative material particle motion over the edge of an inclined flat ellipse that rotates around the axis of a vertical limiting cylinder have been deduced. The position of a plane relative to the axis of the rotation is set by the angle ranging from zero to ninety degrees in its value. If the angle is equal to zero, the plane is perpendicular to the axis of rotation and if the angle is equal to ninety degrees, it passes through the axis of rotation. The equations have been solved using numerical methods. Analytical solution has been found for certain angles. The aim of the research is to investigate the transportability of a technological material in a vertical direction by a cascade operating element that rotates in a cylindrical cover. The working part of the operating element is an inclined rigid plane, which is limited by an ellipse — the line of its contact with a cover. The objective of the research is to analytically describe the movement of a single particle of the technological material on two surfaces, namely, an inclined plane and a vertical cover. The research methodology is based on the methods of differential geometry and the theory of surfaces, theoretical mechanics and numerical methods of solving differential equations. The paper presents a first developed analytical description of the relative particle motion in an ellipse — a contact line of an inclined plane and a limiting vertical cylinder, in which the inclined plane rotates. The kinematic characteristics of such motion have been determined.

Movement of the particle on the surface of the conveyor belt, arbitrarily oriented in space

2021 ◽  
pp. 129-144
Author(s):  
S. Pylypaka ◽  
◽  
A. Nesvidomin ◽  
Keyword(s):  
Relative Motion ◽  
Initial Velocity ◽  
Conveyor Belt ◽  
Inclined Plane ◽  
Material Particle ◽  
Angle Of Friction ◽  
Straight Line ◽  
Curved Section ◽  
Rectilinear Section ◽  
The Web

The movement of the material on the inclined belt of the conveyor takes place during transportation or its frictional cleaning. For an inclined moving plane (slide), the angle of its inclination to the horizontal plane is decisive. The absolute motion of a particle is the sum of two motions - the portable belt and the relative particle along the belt, so it is affected by the angle between the vectors of the greatest inclination of the plane and the transfer velocity of the plane (tape). The purpose of the study is to determine the motion of a material particle on the conveyor belt for the case when the angle between the vector of the line of greatest inclination of the conveyor plane and the direction of its transfer speed is arbitrary. To do this, the conveyor belt element was depicted as a rectangle with an axis of symmetry drawn along the direction of translational movement. In the initial position, the plane was placed horizontally, so the angle of greatest inclination is absent. In the future, the plane was given an arbitrary location in space due to alternate rotation around the sides bounding its compartment or around the axes of symmetry of the compartment, which is equivalent. The relative and absolute motions of the material particle along the moving web of the conveyor are considered for the case when the line of the greatest inclination of the web plane makes an arbitrary angle with the direction of the portable motion of the web. A system of differential equations of motion is compiled and solved. The obtained results are illustrated graphically. It is established that the nature of the relative motion of a particle on an inclined plane moving rectilinearly and uniformly depends on the direction of the vector of the line of the greatest inclination and the value of the angle of inclination of this plane. If the angle of inclination is less than the angle of friction, then the lateral feed of the particle will eventually stop either on the curved section of the trajectory or on a straight line that is parallel to the line of greatest inclination. The stopping place of the particle depends on the value of the initial velocity. At an angle of inclination of the plane equal to the angle of friction, the particle during the movement along the curved section of the trajectory reduces its initial velocity by half and then moves in a straight line and evenly. If the angle of inclination of the plane is greater than the angle of friction, the particle in relative motion along the curvilinear section of the trajectory first reduces the velocity, and when approaching a rectilinear section, its velocity increases and continues to increase on a rectilinear section of the trajectory. Key words: material particle, conveyor, inclined plane, plane inclination angle, particle velocity

A Novel Approach for Thermomechanical Analysis of Stationary Rolling Tires within an ALE–Kinematic Framework

2013 ◽  
Vol 41 (3) ◽  
pp. 174-195 ◽  
Author(s):  
Anuwat Suwannachit ◽  
Udo Nackenhorst
Keyword(s):  
Constitutive Model ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Thermomechanical Analysis ◽  
Rolling Contact ◽  
Computational Technique ◽  
Heat Equations ◽  
Arbitrary Lagrangian Eulerian ◽  
Material Particle ◽  
Operator Split

ABSTRACT A new computational technique for the thermomechanical analysis of tires in stationary rolling contact is suggested. Different from the existing approaches, the proposed method uses the constitutive description of tire rubber components, such as large deformations, viscous hysteresis, dynamic stiffening, internal heating, and temperature dependency. A thermoviscoelastic constitutive model, which incorporates all the mentioned effects and their numerical aspects, is presented. An isentropic operator-split algorithm, which ensures numerical stability, was chosen for solving the coupled mechanical and energy balance equations. For the stationary rolling-contact analysis, the constitutive model presented and the operator-split algorithm are embedded into the Arbitrary Lagrangian Eulerian (ALE)–relative kinematic framework. The flow of material particles and their inelastic history within the spatially fixed mesh is described by using the recently developed numerical technique based on the Time Discontinuous Galerkin (TDG) method. For the efficient numerical solutions, a three-phase, staggered scheme is introduced. First, the nonlinear, mechanical subproblem is solved using inelastic constitutive equations. Next, deformations are transferred to the subsequent thermal phase for the solution of the heat equations concerning the internal dissipation as a source term. In the third step, the history of each material particle, i.e., each internal variable, is transported through the fixed mesh corresponding to the convective velocities. Finally, some numerical tests with an inelastic rubber wheel and a car tire model are presented.

A Study on Polymer Particle Flow in a Disk Zone of a Screw-Disk Extruder

2014 ◽  
Vol 35 (1) ◽  
pp. 121-135 ◽  
Author(s):  
Tomasz Rydzkowski ◽  
Iwona Michalska-Pożoga
Keyword(s):  
Mechanical Properties ◽  
Computer Simulations ◽  
Particle Motion ◽  
Polymer Melt ◽  
Experimental Tests ◽  
Polymer Particle ◽  
Particle Flow ◽  
Material Particle ◽  
Motion Trajectories ◽  
Stretching Effect

Abstract The paper presents the summary of research on polymer melt particle motion trajectories in a disc zone of a screw-disk extruder. We analysed two models of its structure, different in levels of taken simplifications. The analysis includes computer simulations of material particle flow and results of experimental tests to determine the properties of the resultant extrudate. Analysis of the results shows that the motion of melt in the disk zone of a screw-disk extruder is a superposition of pressure and dragged streams. The observed trajectories of polymer particles and relations of mechanical properties and elongation of the molecular chain proved the presence of a stretching effect on polymer molecular chains.

Non-Newtonian effects in axially symmetric oscillatory flows of some elastico-viscous liquids

1970 ◽  
Vol 68 (3) ◽  
pp. 731-750 ◽  
Author(s):  
J. R. Jones
Keyword(s):  
Elastic Properties ◽  
Equations Of State ◽  
Time Lag ◽  
Physical Constant ◽  
Oscillatory Motion ◽  
Axially Symmetric ◽  
Metric Tensor ◽  
Oscillatory Flows ◽  
Viscous Liquids ◽  
Deformation Stress

In (general) elastico-viscous liquids the response to stress at any instant will depend on previous rheological history, the equations of state needed to describe the rheological properties of a typical material element at any instant t being expressible in the form of a (properly invariant†) set of integro-differential equations relating its deformation, stress and temperature histories (as defined by a metric tensor (of a convected frame of reference), a stress tensor and the temperature measured in the element as functions of previous time t'( < t)) together with the time lag (t – t') and physical constant tensors associated with the element (1). Thus in any type of oscillatory motion a rheological history will necessarily be a function of the frequency of the forcing agent, the rheological history of a number of different types of elastico-viscous liquids in some simple shearing oscillatory flows being a rather simple oscillatory history (see, for example, (2–4)). It is, therefore, to be expected that a liquid with elastic properties will behave somewhat differently from any inelastic viscous liquid when subjected to any kind of oscillatory motion, and it is for this reason that oscillatory motions have been used extensively to detect and measure the elastic properties of liquids (see, for example, (2–5)).

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