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Studies and Research Concerning the
Displacement of Solid Particle on an Oscillatory
Flat Surface
Article

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Applied Mechanics and Materials
· October 2014
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DOI: 10.4028/www.scientific.net/AMM.659.521
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Studies and Research Concerning the Displacement of Solid Particle on
an Oscillatory Flat Surface
MOȘNEGUTU Emilian1,a*, NEDEFF Valentin 1,b, PANAINTE – LEHĂDUȘ
Mirela 1,c, BONTAȘ Ovidiu 2,d, BARSAN Narcis 1,e, TOMOZEI Claudia 1,f and
CHIȚIMUS Dana 1,g
1„Vasile Alecsandri” University of Bacau, 157 Calea Marasesti, 600115 Bacau, Romania
2„George Bacovia” University of Bacau, 96 Pictor Aman, 600164 Bacau, Romania
[anonimizat], [anonimizat] , [anonimizat] , [anonimizat] , [anonimizat] ,
[anonimizat] , [anonimizat]
Keywords: solid particle, oscillating flat surface, time, distance, speed.
Abstract . The article shows how the operating parameters of a machine used for the separation of a
heterogeneous mixture of solid particles a ffect particle residence time on the working surface in
use, the distance followed, respectively the travel speed . Experimental determin ations were
performe d in the laboratory on a stand which work ing surface runs an alternative oscillatory
motion. In the experimental measurements there have been used real particles, respectively small
grain beans. Stand parameters which were considered we re the angle of the swing plane surface (5ș,
7ș and 10ș) and the crank speed (91, 240 and 405 rpm). As a result of t he analy sis it was found that
between the functional parameters of the working stand (the distance travelled by the par ticle
oscillating solid surface , the time in which the particle follows the distance used as a reference , the
linear velocity of the solid part icles on the travelled distance ) are closely related .
Introduction
Vegetable products from agriculture and some of the products resulting from various industrial
processes (grinding, granulating, briquette etc.) representing a heterogeneous mixture. To separate
such a mixture its use different methods, which are chosen ta king into account the nature of the
system and its properties (phase discontinuous nature, size, temperature etc .) [1,2,3 ].
The separations of solid particles by size represent the most old separation technology and we
find many studies about it.
These studies are both:
– theoretical [4,5,6,7,8,9 ] – In the article “Particle stratification and penetration of a linear
vibrating screen by the discrete element method", J. Xiao and X. Tong conducted a simulation
aiming the stratification and the passage of particles through the mesh sieve under different working
conditions [7]. LI Ai- min, LV Rui -ling and LIU Chu – sheng using the Autodesk 3DS Max
software analyzed the separation process on an oscillating sieve v arying some design parameters
(length and angle of the vibrating surface ) but also the functional ones of the separator (frequency,
amplitude and direction of vibration and tr acked the separation efficiency ) [10].
– experimental [11,12,13 ] – G. Kovacs followed in his experiments the influence of the
friction coefficient on the distance that a particle passes through the work surface and the in fluence
of the speed of the eccentric upon the distance followed by the solid particle and the speed with
which the latter follows the working surface in use [14].
The process of sorting mixtures of particles per sieves is influenced by many factors, of which
the most important are [4,15,16,17,18,19,20,21 ]:
a) screen : sieve loading ; sieve size; size of the sieve holes in the screen; kinematical regime (of
movement) o f the sieve;

Advanced Concepts in Mechanical Engineering
b) for the material which will be sorted: the granular component of the material to be sorted; the
difference between the size of the particles to be sorted; the nature of the particles to be sorted; the
moisture of the particles etc.
In the l iterature there are very few experimental measurements aimed at determining the
parameters of the actual movement of a real particle on an oscillating surface.
Based on this conclusion, the Department of Environmental Engineer ing and Mechanical
Engineering from the "Vasile Alecsandri" University of Bacau was designed and conducted a series
of experiments to this end, and in this paper we present some experimental results .
Materials and equipment
In the experimental determinatio ns there have been used real particles which form are differs from
the ideal shape; respectively small grain beans particles (particles with an elongated shape) [1].
The characteristics of the used particles are presented in Table 1.

Table 1. Characteristics of the studied particles .
Particle type Shape
approximation Characteristics
Dimensions [mm] Spheroid Ф Mass
[g] Length Width Thickness
Small grain bean L>l≈g 13.40 8.30 7.40 0.699359 0.53
Experimental determinations were performed on a laboratory bench having oscill ating flat sieves
(Fig. 1) with multiple adjustment possibilities of the inclination of the block site, of the speed crank
mechanism.
In order to highlight only the behaviour of solid particles on a flat tilting, the exp erimental
measurements used a blank screen inclined to the horizontal (Fig . 2). The area is bounded to the
distance that was intended the movement by drawing reference lines. Theoretical distance of
movement of particles of all subjects is 265 mm. In order to view the sideway moving of the
particle on the surface of the sieve there has been drawn a longitudinal grid line in the middle of the
working surface.
In the experimental determinations the working stand parameters were varied:
– the angle of the flat oscillating surface: 5 ș, 7ș and 10 ș;
– crank device speed : 91 r pm, 240 rpm and 405 rpm.

Fig. 1. Laboratory stand [1]. Fig. 2 . Blind oscillating surface with the used markers [1].

In order to follow th e space trajectory of the solid particle on the flat oscillating surface, there
have been used two video equipments , Sony DCR -SR 36, which had a recording speed of 25 frames
/second. In order to get a final tri -dimensional trajectory, the equipments were placed o n two
perpendicu lar flat surfaces , aiming to follow the motion of the particle on flat surfaces (Fig. 3):
XOY – camera video number 1 and XOZ – camera video number 2.
The working methodo logy for determining the real motions and travel speeds of the studied
particles is presented in Fig. 4.

Applied Mechanics and Materials Vol.
In order to obtain the coordinates of the studied particles, regardless of the camera s position,
there has been used the SyntEyes software, as follows:
– the obtained values from the analysis of the movement in the plane XOY were used to
determine the trajectory of solid particle on an oscillating surface;
– the obtained values from the analysis of the movement in the plane XOZ were used to
determine the jumps which the solid particle carries in its movement on the blind screen .
In the processing of the experimental data we took into account the angle of the flat oscillating
surface and of the distance from the surface on which there were placed the two cameras, aiming at
computing the values obtained correspond to the real ones.

Fig. 3. The reference planes [1]. Fig. 4. Working algorithm [1].
Experimental results
Upon completion of the experimental measurements and data processing obtained there could be
determined , for a solid particle number , behaviour parameters on the oscillating surface, namely:
– average values of the projections on the axes O X, OY and O Z of the instant total distance
travelled by the particle;

Fig. 5. Variation of real distance depending on
the angle of inclination and revolution. Fig. 6. Variation of time according of the
angle of inclination and revolution.

Fig. 7. Linear velocity variation depending on the angle of inclination and revolution.

– the average amount of projection of the distance travelled;

Mathcad
software

Advanced Concepts in Mechanical Engineering
– the average time of the motion of the particle of the distance taken as a reference (265 mm);
– the average value of the instantaneous linear speed of movement of the particle;
the average linear velocity of the particle movement on the marked distance.
Of the many parameters derived there were chosen for presentation (Fig. 5, Fig. 6, Fig. 7 ):
– the change of the actual distance travelled by the particle studied ;
– the changes in time f or the solid particle to cover the distance of reference;
– the average particle velocity variation studied ;
– depending on the speed crank mechanism and the angle of the flat oscillating surface .
By analyzing the graphical representation of the change in the real distance travelled by the
particle small grain bean there can be drawn the following conclusions:
– between speeds of 244 and 405 rpm, regardless of the angle, there is a very little variation
between the values obtained in the amount of projection , wh ich is about 0.3 m;
– if the speed of 91 rpm to record a maximu m of 1.6 m at an angle of 5 °, which value
decreas es to 1.28 m (the angle of 7°) up to the 0.38 m (10° angle) ;
– it is established that the higher the speed the crank mechanism, the angle of inclina tion of
the work surface affects in an insignificant way the behaviour of the particle, respectively the sum
of the projection distance.
Analyzing changes in the time for the particle to traverse the distance of reference is established
that:
– for the speed of 244 rpm and 405 rpm, the average time in which the particle crosses the
reference distance is relatively less than 1.1 sec for all the angles of inclination of the working
surface which follows the path of the solid particle ;
– for the speed of 91 rpm at an angle of 5° to obtain the lowest for 19 s;
– by the increasing the amount of surface angle and of the flat oscillating surface it is observed
that there is a decrease of the time needed to cover the distance of 265 mm.
The analysis of experimental results describing the mean velocity variations can say that it has
the following dependence on the input parameters:
– depending on the change in the angle of tilt for all the three speeds used for the experimental
measurements, the average speed is directl y proportional to it;
– Depending on the speed variation crank device is found close relationship between the
variation of this parameter and the average speed value obtained there is a direct dependence.
Mathematical models
As in any process and in this case was followed to obtain the mathematical equivalent model of
process.
Departing from the values obtained on experimental path, with help of the program to generate
the linear equations and the nonlinear equation TableCurve 3D, was determin ate the equation on
variation of time necessary for particle to cross the marked distance , the real distance travelled and
linear speed of the solid particles depending by angle of inclination and of rotation of you crank
device of equipment which are used in our experiments ( Fig. 8).

2
2b d f yz a c y e yx x x       
, a)
2
2b d f yz a c y e yx x x        , b)

Applied Mechanics and Materials Vol.

2
21a b x c y d yze x f y g y          , c)
Fig. 8. Mathematical models for variations of:
a) time in function by angle of inclination and rotation of you crank device; b) the real distance
travel in function by angle of inclination and rotation of you crank device; c) linear speed in
function by angle of inclination and rotation of you crank device.
were: z represent parameter that are studied; x is angle of inclination and y is rotation.
Conclusion
The separation of solid particles after size is a complex process influenced by several factors,
which depend of the particles and characteristics of equipment used. Because of tyrants, stand used
in the experimental determi nations executed oscillations along three axes this fact generating a
motion of the solid particle on the three directions. By using two video cameras with purpose to
tracking the solid particle trajectory was be achieved, with help of SynthEyes program, o btaining a
three -dimensional trajectory . Also from experimental data could determine the variation of solid
particle velocity on the oscillating surface taking account by the angle of inclination of surface and
rotation of device which give motion to surfa ce.
From the analysis of results it is found that:
– between input and output parameters are a strong dependence ;
– it can be ascertained that with increasing inclination angle of the work surface at the same
speed, the time the solid particle is on the work surface decreases. Same thing can be said about the
distance travelled by the particle on the work surface and the value of the of solid particle velocity;
– by increasing speed, for the same angle of inclination of the working surface, the distance
travelled and the time there on the distance marked is decrease. Not the same thing can be said
about the linear speed, this varies directly with the variation of the speed .
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Advanced Concepts in Mechanical Engineering
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