Transport properties of the new vibratory conveyor at operations in the resonance zone

Witold Surówka; Piotr Czubak

doi:10.1515/eng-2021-0122

Article Open Access

Transport properties of the new vibratory conveyor at operations in the resonance zone

Witold Surówka and Piotr Czubak

Published/Copyright: December 31, 2021

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From the journal Open Engineering Volume 11 Issue 1

Abstract

The new vibratory conveyor intended for the precise material dosage was investigated in the hereby study. The transport possibilities in the circum-resonance zone were tested analytically as well as by simulation. The optimal working point of the system, allowing to lower the vibration amplitude of the eliminator on its own suspension, was found. Transport velocities in dependence on the excitation frequency were determined by simulation. The results were verified on the specially designed industrial conveyor whose parameters were determined using analytical and simulation investigations, built according to the patent application.

Keywords: vibrations; vibratory conveyor; dynamic eliminator; transport stopping; feeder; variable output

1 Introduction

The new vibratory conveyor, being the subject of the authors’ patent application, allowing accurate dosage of the feed was investigated in the hereby study. It is used for the transport and dosage of loose materials or objects of small dimensions, providing the possibility of a sudden stoppage of transport, regardless of the application of a small and relatively cheap electrovibratory drive [1,2,3].

It often occurs in the production line that there is either a necessity of the immediate feeding or a sudden stoppage of the feed material flow. In case of classic vibratory conveyors, their switching off is connected with the necessity of the system passing through successive resonance zones at start-up and coasting of the machine. During such stages, an uncontrolled transport occurs.

Feeders of small sizes are most often made on the suspension of leaf springs and they are usually driven by the expensive electromagnetic excitation [4], which provides a total and immediate control over the trough movement allowing the material dosage [5]. The solution, in which the dosing feeder is driven by the system of counter running vibrators, is also known [6]. In this solution, the dosage by decreasing the transport velocity is realized by a significant decrease in the excitation frequency causing steep angles of the material feed flow at the trough edge. The wide review of various solutions of conveyors allowing for the precise material dosage can be found in paper [7].

The authors investigated the transport possibilities of the patented conveyor in the zone being in front of the antiresonance related to an additional eliminator and in the antiresonance zone. The main problem of this type of operation constitutes a significant amplitude of the eliminator, which is placed on a highly stiff suspension, during the steady state work at a relatively high amplitude of the trough (allowing the typical transport velocity for the given machine class). High amplitudes of the stiff suspension will be causing its cracking. In this article, the authors investigated the transport possibility in the second resonance zone, which significantly decreased the eliminator amplitude in relation to the through amplitude at the material transport with a typical velocity. Such control of the system also provides a possibility of additional increase in the transport velocity, while maintaining safe amplitudes of the eliminator. On the basis of the analytical and simulation investigations performed in this work, the conveyor – of parameters allowing its operation in the second resonance zone – was constructed. Experimental tests of this conveyor fully confirmed previous analyses.

Works concerning the analysed solution cannot be found in the world scientific references, since this is the authors’ patent. However, several papers concerning conveyors, in which the trough constitutes the dynamic eliminator, can be found. These conveyors are base excited, not as in the hereby article, by the vibration excitation of elements attached to the trough. The first construction of the conveyor operating on the basis of dynamic elimination was described in the paper [8]. In the paper [9], authors analysed the conveyor behaviour around the assumed excitation frequency (being the vibroinsulating Frahm’s damper). The authors noticed that in this type of conveyors, due to the attachment of the excitation system to the mass, which – in theory – is not vibrating, the service life of this system as well as of its suspension is prolonged. The same author with the team [10] investigated the possibility of controlling the excitation frequency around the work point. In the paper [11], authors tested the material feed influence on the conveyor operating on the Frahm’s eliminator bases. The author substituted the conveyor model, in which the feed was moving in the direction of the trough movement, by the two-mass model, in which the feed was influencing in vertical direction. The advantage of such solutions of base excited conveyors is minimisation of forces transmitted to foundations; however, regardless of a relatively similar construction to the one proposed in this article, they are suitable neither for dosing nor for rapid stopping of the feed flow.

2 Construction of the analysed conveyor

The new vibratory conveyor [1,2], being the subject of the patent application, is presented in Figure 1. This conveyor is built of a classic trough 1, elastically supported 2 on stiff base in the horizontal orientation. It is equipped with the system of two counter running vibrators 3, suspended on the conveyor trough at an angle β. In the steady state, these vibrators are synchronised and rotate in different directions, providing the rectilinear resulting force, passing through the mass centre of the trough system as well as through the centre of its suspension system. Drive motors of inertial vibrators are equipped with inverter 4, by means of which the control system is able to control the rotational speed of electrovibrators 3.

Figure 1

Schematic presentation of the conveyor (according to the invention).

The inertial drive contrary to the electromagnetic drive is much cheaper in terms of cost and exploitation. In practice, this type of drives are not subjected to breakdowns, and when they happen most often they are related to over-used bearings (so the repair is cheap). A negative side of this type of drives constitutes the necessity of maintaining the self-synchronisation of two electrovibrators providing the directional force. In case of operations in the antiresonance zone, at a wrong selection of the supporting points of these electrovibrators on the trough, maintaining this self-synchronisation might not be successful and machine operations might be impossible [12]. Other disadvantages, as compared to the electromagnetic drive, are long coasting time as well as longer reaction for the frequency change tasks.

The coupling method for the electrovibrators is based on a self-synchronisation, which at the proper parameters, based among others, on moving away of electrovibrators from the centre of gravity, occurs spontaneously [12]. The utilised electrovibrators are three-phasal and star connected. Each of them has 40 W – which is power efficient, since usually conveyors weighing approximately above 50 kg need electrovibrators of a power of 150–200 W for their operations. There is a scalar control of a rotational speed (Volts-per-Hertz) and one inverter controls both the motors simultaneously. There is no vector controlling of the speed of the electrovibrators because the self-synchronisation would not be possible.

Additional mass 5, on its own suspension 6, is connected to the main mass 1. The aim of this additional mass is the elimination of trough vibrations at the proper control of the excitation frequency of vibrators, in accordance with the Frahm’s eliminator principle [13], when the excitation frequency ω is equal to

(1) ω = k T m e ,

stoppage of trough vibrations causes stopping of the feed transport 7.

In the previous works of the authors [14], the possibility of a material transport was investigated for the excitation frequency lower than the antiresonance frequency of the system, while the transport stoppage was tested at the antiresonanse frequency. In this article, it was revealed that the conveyor operation is more favourable behind the antiresonance frequency, since this allows a decrease in the maximal amplitudes of the eliminator.

3 Analytical studies of the substituting system of two degrees of freedom

Based on the assumptions that the centres of gravity of the trough and eliminator are overlapping and stiffness of suspensions in x and y directions is the same and that the force originated from synchronised electrovibrators passes through the centre of gravity, the system presented in Figure 1 can be substituted by the two-mass system presented in Figure 2 [14].

Figure 2

Simplified two-mass model of the device.

Equations of the system are in the form:

(2) m k x ̈ 2 + b 2 x ̇ 2 + k 2 x 2 + b 1 ( x ̇ 2 − x ̇ 1 ) + k 1 ( x 2 − x 1 ) = P 0 sin ( ω t ) m e x ̈ 1 − b 1 ( x ̇ 2 − x ̇ 1 ) − k 1 ( x 2 − x 1 ) = 0 ,

where x ₁ – displacement of the eliminator harmonic movement along coordinate x ₁, x ₂ – displacement of the trough harmonic movement along coordinate x ₂, ω – excitation circular frequency of force P(t), m _k – mass of the conveyor trough, m _e – mass of the dynamic eliminator, k ₁ and b ₁ – total elasticity and damping of suspension in working direction x ₁, respectively, and k ₂ and b ₂ – total elasticity and damping of suspension in working direction x ₂, respectively.

Values of above, corresponding annotations, are listed in Table 1.

Table 1

Parameters of the simulated system

Symbol	Value	Unit	Definition
l ₁	0.177	m	Linear dimension
l ₂	0.177	m	Linear dimension
h	0	m	Linear dimension
h ₁	0.045	m	Linear dimension
h ₂	0.177	m	Linear dimension
a ₁	0.231	m	Linear dimension
a ₂	0.155	m	Linear dimension
d	0.35	m	Linear dimension
H	0.12	m	Linear dimension
e ₁	0.02	m	Radius of a vibrator unbalance
e ₂	0.02	m	Radius of a vibrator unbalance
k _e	320,002	N/m	Stiffness of suspension
k _x	71,690	N/m	Stiffness of suspension
k _y	71,690	N/m	Stiffness of suspension
b _x	90	N s/m	Coefficient of viscous damping
b _y	90	N s/m	Coefficient of viscous damping
b _e	300	N s/m	Coefficient of viscous damping
m _r	28	kg	Mass of the trough
m ₁	0.5	kg	Rotating mass I
m ₂	0.5	kg	Rotating mass II
m _e	26	kg	Mass of the eliminator
J ₁	0.001	kg m²	Central moment of inertia of the excitation I
J ₂	0.001	kg m²	Central moment of inertia of the excitation II
J _r	2.56	kg m²	Central moment of inertia of the trough
J _e	0.2	kg m²	Central moment of inertia of the eliminator
M _ut	5	N m	Breakdown torque
ω _ss	Variable	rad/s	Synchronous speed
ω _ut	Variable	rad/s	Breakdown torque speed
R	0.13	—	Restitution coefficient
µ	0.4	—	Coefficient of friction
k _s	10⁸	N/m	Hertz-Staierman stiffness
p	1	—	Hertz-Staierman constant
b _s1	0.0009	Nm s	Coefficient of viscous damping in bearing
b _s2	0.0009	Nm s	Coefficient of viscous damping in bearing

Figure 3 presents amplitude-frequency characteristics of the trough and eliminator; shown amplitudes are of work direction, and represent the strategy of operating before antiresonance. Both masses have the first common resonance at approximately 35 rad/s. Then, the trough amplitude together with ω decreases, which causes, in this case, requirement of relatively large electrovibrators. On the other side, the eliminator amplitude abruptly increases with ω and in the final work zone equals more than 15 mm. Analogous characteristics as in Figure 3 are presented in Figure 4, but for the strategy of controlling behind the antiresonance. The first common resonance occurs at approximately 38 rad/s, and next the trough amplitude slowly approaches zero (117 rad/s). Behind this point, both amplitudes increase with ω, entering the resonance slope. In such a way the identical coefficient of throw is obtained at three times smaller electrovibrators than in a previous strategy and the achieved amplitudes of the additional mass are more than three times smaller, which is beneficial for the suspension.

Figure 3

Amplitudes of the trough (red line) and the eliminator (blue line) as a function of the excitation frequency, for the strategy of operating before the antiresonance.

Figure 4

Amplitudes of the trough (red line) and the eliminator (blue line) as a function of the excitation frequency, for the strategy of operating behind the antiresonance.

After determining amplitudes of the trough and eliminator, for parameters shown in Figures 3 and 4, it was revealed that in order to obtain the proper throw coefficient at not very high amplitudes of the eliminator, the system working behind the antiresonance frequency is more beneficial. Eliminator amplitudes are 0.0095 m when the system is tuned to work before the antiresonance frequency and 0.0025 m when the system is working behind this frequency (Figure 4), for the same transport velocity resulting from the throw coefficient. In turn, the throw coefficient depends on the amplitude and the square of the excitation frequency. In addition, at the work on the slope of the second resonance, the proper throw coefficient can be achieved at a much lower drive ( four times lower than in case of work before the antiresonance), which significantly decreases costs of building and maintenance of the machine.

Controlling the strategies can be achieved by controlling the system represented by the scheme, as shown in Figure 10.

4 Simulation investigations

Simulation investigations were performed with taking into consideration the material feed, due to a strong dependence of the eliminator efficiency on the damping in the system [9,15,16]. Calculations performed without taking into consideration the feed are usually burdened with high errors [17]. In order to determine the transport velocity in dependence on the system excitation frequency – in the analysed conveyor – the system presented in Figure 1 (together with the feed) was studied. Problems with the self-synchronisation can also occur in such system [18]. The analysed system [14] consists of two inertial vibrators with induction motors (described by a static characteristic) whitch excite the trough suspended on the spiral springs. The additional mass on the elastic suspension is connected to the trough containing the feed material [19,20].

Matrix equation (6), contains equations (7)–(9). These equations were formulated assuming following energies of the system shown in Figure 1.

(3) E k = 1 2 m r ( x ̇ 2 + y ̇ 2 ) + 1 2 m e ( ( x ̇ + τ ̇ ⋅ cos ( β ) ) 2 + ( y ̇ + τ ̇ ⋅ sin ( β ) ) 2 ) + 1 2 m 1 ( x ̇ + h 1 α ̇ + ϕ ̇ 1 e 1 cos ( ϕ 1 ) ) 2 + 1 2 m 1 ( y ̇ − a 1 α ̇ + ϕ ̇ 1 e 1 sin ( ϕ 1 ) ) 2 + 1 2 m 2 ( x ̇ + h 2 α ̇ + ϕ ̇ 2 e 2 cos ( ϕ 2 ) ) 2 + 1 2 m 2 ( y ̇ − a 2 α ̇ − ϕ ̇ 2 e 2 sin ( ϕ 2 ) ) 2 + 1 2 ( J r + J e ) α ̇ 2 + 1 2 J 01 ϕ ̇ 1 2 + 1 2 J 02 ϕ ̇ 2 2 ,

(4) E p = 1 2 k x ( x + h α ) 2 + 1 4 k y ( y − l 1 α ) 2 + 1 4 k y ( y + l 2 α ) 2 + 1 2 k τ τ 2 − m 1 g ⋅ e 1 ⋅ cos ( ϕ 1 ) + m 2 g ⋅ e 2 ⋅ cos ( ϕ 2 ) ,

(5) N = 1 2 b τ ( τ ̇ ) 2 + 1 2 b x ( x ̇ + h α ̇ ) 2 + b y 4 ( y ̇ + l 1 α ̇ ) 2 + b y 4 ( y ̇ + l 2 α ̇ ) 2 ,

where E _k – kinetic energy, E _p – potential energy, and N – dissipation potential.

The mathematical model of such system consists of matrix equation (6) describing the machine motion, equation (14) describing the electromagnetic moment of drive motors, equations (12) and (13) used for determining the motion of successive feed layers, as well as of dependencies, Equations (10) and (11) describing normal and tangent influences in between feed layers and between the feed and machine body, respectively [21].

(6) [ M ] ⋅ [ q ̈ ] = [ Q ] ,

(7) M = m r + m 1 + m 2 + m e 0 m 1 h 1 + m 2 h 2 m 1 h 1 + m 2 h 2 m 1 h 1 + m 2 h 2 m e cos β 0 m r + m 1 + m 2 + m e − m 1 a 1 − m 2 a 2 m 1 e 1 cos ( ϕ 1 ) − m 2 e 2 sin ( ϕ 2 ) m e sin β m 1 h 1 + m 2 h 2 − m 1 a 1 − m 2 a 2 m 2 ( h 2 2 + a 2 2 ) + m 1 ( h 1 2 + a 1 2 ) + J r + J e m 1 h 1 e 1 cos ( ϕ 1 ) − m 1 a 1 e 1 sin ( ϕ 1 ) m 2 h 2 e 2 cos ( ϕ 2 ) + m 2 a 2 e 2 sin ( ϕ 2 ) 0 ) m 1 e 1 sin ( ϕ 1 ) m 1 e 1 cos ( ϕ 1 ) m 1 h 1 e 1 sin ( ϕ 1 ) − m 1 a 1 e 1 cos ( ϕ 1 ) m 1 e 1 2 + J 01 0 0 m 2 e 2 cos ( ϕ 2 ) m 2 e 2 sin ( ϕ 2 ) m 2 h 2 e 2 cos ( ϕ 2 ) − m 2 a 2 e 2 sin ( ϕ 2 ) 0 m 2 e 2 2 + J 02 0 m e cos β m e sin β 0 0 0 m w ,

(8) q ̈ = [ x ̈ y ̈ α ̈ ϕ ̈ 1 ϕ ̈ 2 τ ̈ ] T ,

(9) Q = m 2 e 2 ϕ ̇ 2 2 sin ( ϕ 2 ) + m 1 e 1 ϕ ̇ 1 2 sin ( ϕ 1 ) − 2 k x ( x + h α ) − 2 b x ( x ̇ + h α ̇ ) − T 1 ( 01 ) − T 1 ( 02 ) − T 1 ( 03 ) − T 1 ( 04 ) − T 1 ( 05 ) m 2 e 2 ϕ ̇ 2 2 cos ( ϕ 2 ) − m 1 e 1 ϕ ̇ 1 2 cos ( ϕ 1 ) − k y ( y + l 1 α ) − k y ( y − l 2 α ) − b y ( y ̇ + l 1 α ̇ ) − b y ( y ̇ − l 2 α ̇ ) − F 1 ( 01 ) − F 1 ( 02 ) − F 1 ( 03 ) − F 1 ( 04 ) − F 1 ( 05 ) m 1 h 1 e 1 ϕ ̇ 1 2 sin ( ϕ 1 ) + m 1 a 1 e 1 ϕ ̇ 1 2 cos ( ϕ 1 ) + m 2 h 2 e 2 ϕ ̇ 2 2 sin ( ϕ 2 ) − m 2 a 2 e 2 ϕ ̇ 2 2 cos ( ϕ 2 ) − 2 k x h 2 α − 2 k x h x − 2 b x h x ̇ − 2 b x h 2 α ̇ − k y ( y + l 1 α ) l 1 + k y ( y − l 2 α ) l 2 − b y ( y ̇ + l 1 α ̇ ) l 1 + b y ( y ̇ − l 2 α ̇ ) l 2 + ( T 1 ( 01 ) + T 1 ( 02 ) + T 1 ( 03 ) + T 1 ( 04 ) + T 1 ( 05 ) ) H + 2 d F 1 ( 01 ) + d F 1 ( 02 ) − d F 1 ( 04 ) − 2 d F 1 ( 05 ) M e l 1 − b s 1 ϕ ̇ 1 2 sign ( ϕ ̇ 1 ) − m 1 g e 1 sin ( ϕ 1 ) M e l 2 − b s 2 ϕ ̇ 2 2 sign ( ϕ ̇ 2 ) + m 2 g e 2 sin ( ϕ 2 ) − k τ τ − b τ τ ̇ ,

where τ – dependent coordinate, F _j,(j−1,k) – normal component of the j-ts layer force on j − 1 in the k-ts column, T _j,(j−1,k) – tangent component of the j-ts layer force on j − 1 in the k-ts column, j – material layer index j = 0 refers to the machine body, and k – index of the material layer column.

When the successive feed layers (in the given column) j and j − 1 are not touching, the contact force in the normal F _j,(j−1,k) and tangent direction T _j,(j−1,k) in between these layers equals zero. In the opposite case, the contact force occurs in the normal direction in between feed layers j,k and j − 1,k (or in case of the first layer between this layer and the trough [21]). The model of this contact force is as follows:

(10) F j , ( j − 1 . k ) = ( η j − 1 , k − η j , k ) p ⋅ k s ⋅ 1 − 1 − R 2 2 [ 1 − sgn ( η j − 1 , k − η j , k ) ⋅ sgn ( η ̇ j − 1 , k − η ̇ j , k ) ] .

There is also the force, originated from a friction, in the tangent direction:

(11) T j , ( j − 1 , k ) = − μ F j , ( j − 1 , k ) sgn ( ξ ̇ j , k − ξ ̇ j − 1 , k ) .

Equations of motion in directions ξ and η of individual feed layers with taking into account the conveyor influence on the lower feed layers are of a form:

(12) m n j , k ξ ̈ = T j , ( j − 1 , k ) − T j + 1 , ( j , k ) ,

(13) m n j , k η ̈ = − m n j , k g + F j , ( j − 1 , k ) − F j + 1 , ( j , k ) ,

(14) M el i = 2 M ut ( ω ss − ϕ ̇ i ) ⋅ ( ω ss − ω ut ) ( ω ss − ω ut ) 2 + ( ω ss − ϕ ̇ i ) 2 ,

where M el – moment generated by drive motors, M ut – stalling torque moment of drive motors, ω _ss – synchronous frequency of drive motors, and ω _ut – stalling frequency of drive motors.

Simulations were performed for the parameters given in Table 1.

The mathematical model of the system contains all movements of the machine in a flat system (in case of the proposed excitation, the motion in the perpendicular direction will not be excited, and thus there is no need of investigating the spatial system). The system has three degrees of freedom of the main body, one for each electrovibrator and the additional one for the eliminator mass.

The motion of the feed is presented by means of 40 equations. Each feed element has a degree of freedom in the perpendicular and horizontal direction. The perpendicular contact force containing elasticity of foundation and feed (depends which is contacting which) of each element is determined by equation (10). Whereas the horizontal contact force is given by equation (11), which contains coefficient of friction (µ) in between successive layers. In this way the slide is taken into consideration. Displacements in time of the trough as well as – placed on it – feed grains on the direction perpendicular to the trough are presented in Figure 5. The trough performs harmonic oscillations with a high acceleration causing grains detachment from the trough surface enabling the flight phase (Figure 5).

Figure 5

Trough oscillations (blue line) carrying feed material.

During the contact phase both the trough and feed are moving together, while during the flight phase the trough moves back, which causes mutual displacement of the trough and feed at each cycle. In such a way the feed material is moved on the trough in the expected direction.

4.1 Results of simulation studies

Transport velocity of the conveyor for quasi-stationary states as the frequency function, for various masses of the feed, is presented in Figure 6. For quasi-stationary states, the feed transport occurs at the first resonance frequency; however, in the real conveyor, such state – at passing through the resonance – is so short that the transport does not occur. At the antiresonance frequency, there is a total lack of transport, while after passing this frequency the transport velocity increases. When the amplitudes of the trough and eliminator are increasing, the only real limitation of the velocity are the structural limitations resulting from too high amplitudes of main masses. It is seen in Figure 6 that at a significant increase in the feed mass, more than three times exceeding the trough mass, the significant decrease in the transport velocity occurs in the work place. There is a possibility of increasing the transport velocity at high masses of the feed by means of increasing the excitation frequency, taking into account the main mass amplitudes’ technical limitations.

Figure 6

Transport velocity as a function of the excitation frequency in dependence of the feed mass for quasi steady states.

Diagram in Figure 6 was obtained on the bases of 300 simulations quasi-stable states for various feed masses and various excitation frequencies. Overlapped 2D diagrams formed 3D diagrams allowing to analyse the feed weight and excitation frequency influence on the transport velocity characteristic of the authors’ conveyor. Experimental investigations allowing to achieve such precise diagram are – in practice – impossible due to multitude of these tests and dangers of drive overheating as well as destruction of suspension in the steady state during operations, e.g. in the resonance. The conformity of the model with the real tests is confirmed by Figures 7 and 12.

Figure 7

Transport velocity as a function of the excitation frequency, obtained by simulation for the working strategy behind the antiresonance and at a small mass of the feed.

Figure 7 presents the transport velocity for feed mass (3 kg) in dependence of the excitation frequency. The exponential character of the velocity increase – after passing the antiresonance frequency – is seen there. This is a very positive situation since the velocity change, at frequencies being near the ones at which the transport stops, is small which significantly simplifies the precise dosage. On the other hand, a significant velocity increase occurs along with distancing from the point of transport stoppage allowing for the maximum velocity of the transport.

In Figure 7 (simulation diagram), at the frequency of 150 rad/s, a collapse of the transport velocity occurs. It results from the fact that at this frequency the system: trough – feed transfers from the single-stroke activity (one flight of a feed grain for one move of the trough) to double – stroke operation. According to equations allowing to determine the transport velocity in dependence of the amplitude and frequency of excitation for an individual grain [22], the velocity at transferring from a single to double stroke operation decreases. This effect is not observed in the real system (Figure 12) since the feed has in this case significantly more layers than in case of the simulation, in which only four layers are utilised. Investigations for the real system [22] also do not show any rapid velocity decreases at transferring from the single-stroke mode to the double-stroke one.

5 Testing of the industrial conveyor

After performing analytical and simulation studies, the conveyor of industrial dimensions was designed and built in accordance with guidelines resulting from the studies. The conveyor presented in Figure 8 has parameters listed in Table 1, used in previous analyses.

Figure 8

Prototype conveyor of the industrial scale for operations on the resonance slope.

The side view of the conveyor, during testing its transport possibilities, is shown in the photograph 8.

Figure 9 presents the device from behind, where there is the excitation module. Inside the conveyor, the eliminator is attached to the backend wall. This eliminator is seen in technical scheme (Figure 10). Conveyor indicates very good transport properties and – what is most important – it indicates a possibility of the precise dosage. The time of the transport stopping from the maximum velocity to the full stop is not more than 1.5 s.

Figure 9

Device view from the side of the drive system.

Figure 10

Scheme of how the machine is controlled: 1 – trough, 2 – eliminator, 3 – supporting frame, 4 – electrovibrators, 5 – variable-frequency drive, 6 – frequency tuning dial, 7 – four-core electrical wire, 8 – DC voltage source 230 V/50 Hz.

The example of its working can be seen at the YouTube address: https://youtu.be/PmFnfySpJp8. Investigations of the feed velocity were performed as follows: fragment of the feed, singled out by its colour (Figure 11), was subjected to a velocity measurement. In the moment when the assumed excitation velocity was stabilised, the observed grain was passing the starting point (established on the scale) and the timer started measuring. After passing the middle 0.5 m of the trough length and stopping the timer, the average experimental transport velocity of the feed was obtained.

Figure 11

Trough carrying glass chippings.

In order to verify the conformity of the transport velocity between simulation models and the real machine, investigations were performed. For that purpose 3 kg mass was chosen to be tested againts various ferquencies, while using above-antiresonance-operating strategy. Figure 12 presents the real transport velocities determined on the real conveyor and they should be compared with the simulation results in Figure 7. A very good compatibility of the model with the real conveyor is seen in both figures, apart from the situation when the transport is transferring from a single to double stroke operation, which appears at the frequency of 150 rad/s.

Figure 12

Experimental results of the feed transport.

6 Conclusion

Analytical studies of the two-mass model allowed to select the proper parameters of the conveyor, allowing the reduction in the eliminator amplitudes when the conveyor is working behind the antiresonance zone.
Simulation investigations of the conveyor proved the possibility of the device working as a feeder dosing loose feed material.
Testing of the industrial conveyor constructed according to the patent application having parameters determined in the analytical and simulation investigations fully confirmed the ability of the conveyor to the feed transport (within a range of 0–100%).
The dependence of the transport velocity on the excitation frequency is nearly the same in both the conveyors (numerically investigated one and the industrial conveyor).
The accuracy of the numerical model will facilitate the planning and realisation of further tests of the machine.

Acknowledgements

The work is included in the framework of the AGH University of Science and Technology: Department of Mechanics and Vibroacoustics 16.16.130.942.

Conflict of interest: Authors state no conflict of interest.

References

[1] Surówka W, Czubak P. Vibratory conveyor. PL Pat Pending, P425950; 2018.Search in Google Scholar

[2] Surówka W, Czubak P. Vibratory conveyor of considerable length. PL Pat Pending, P425951; 2018.Search in Google Scholar

[3] Czubak P, Lis A. Analysis of a new vibratory conveyor allowing for a sudden stopping of the transport. Tech Gaz. 2020;27(2):520–6.10.17559/TV-20181206111514Search in Google Scholar

[4] Nettervibration: Feeders, 15.09.2021, https://www.nettervibration.com/en/plant-machinery/vibrating-feeders/series-powerpack-conveyor-systems.Search in Google Scholar

[5] Despotovic Z, Lecic M, Jovic M, Djuric A. Vibration control of resonant vibratory feeders with electromagnetic excitation. FME Trans. 2014;42(4):281–9.10.5937/fmet1404281dSearch in Google Scholar

[6] Zejer T, Olesiński M, Musioł K, Okoń T. Stopping Material Transport on Vibrating Feeder Chute, International Colloquium Dymamesi 2021 – Dynamics Of Machines And Mechanical Systems With Interactions, Cracow (Poland), March 2–3, 2021.Search in Google Scholar

[7] Surówka W, Czubak P. Numerical review of selected solutions of vibratory feeders capable of dosing feed material. Poznań: Vibrations in Physical Systems; 2020. ISSN 0860-6897.Search in Google Scholar

[8] Long G, Tsuchiya T. Vibratory conveyors. US Pat 2,951,581; 1960.Search in Google Scholar

[9] Jiao C, Liu J, Wang Q. Dynamic analysis of nonlinear anti-resonance vibration machine based on general finite element method. Adv Mater Res. 2012;443:694–9.10.4028/www.scientific.net/AMR.443-444.694Search in Google Scholar

[10] Liu J, Li Y, Liu J, Xu H. Dynamical analysis and control of driving point anti-resonant vibrating machine based on amplitude stability. Chin J Mech Eng. 2006;1:145–58.10.3901/JME.2006.01.145Search in Google Scholar

[11] Liu Q. The material of the resonant vibration impact motivates the influence of and the simulation analysis. Adv Mater Res. 2012;510:261–5.10.4028/www.scientific.net/AMR.510.261Search in Google Scholar

[12] Blekhman II. Synchronization in science and technology. New York: ASME Press; 1988.Search in Google Scholar

[13] Frahm H. Device for damping vibrations of bodies. US Pat, 989958; 1909.Search in Google Scholar

[14] Czubak P, Surówka W. Influence of the excitation frequency on operations of the vibratory conveyor allowing for a sudden stopping of the transport. Poznań: Vibrations in Physical Systems; 2020. ISSN 0860-6897.Search in Google Scholar

[15] Klemiato M, Czubak P. Event driven control of vibratory conveyors operating on the Frahm’s eliminator basis. Arch Metall Mater. 2015;60:19–25.10.1515/amm-2015-0003Search in Google Scholar

[16] Czubak P. Equalization of the transport velocity in a new two-way vibratory conveyor. Arch Civ Mech Eng. 2011;11:573–86.10.1016/S1644-9665(12)60102-2Search in Google Scholar

[17] Michalczyk J, Czubak P. Influence of collisions with a feed material on cophasal mutual synchronisation of driving vibrators of vibratory machines. J Theor Appl Mech. 2010;48(1):155–72.Search in Google Scholar

[18] Hou Y, Peng H, Fang P, Zou M, Liang L, Che H. Synchronous characteristics of two excited motors in an anti-resonance system. J Adv Mech Des Syst Manuf. 2019;13:JAMDSM0050.10.1299/jamdsm.2019jamdsm0050Search in Google Scholar

[19] Michalczyk J, Czubak P. Influence of the asymmetry of vibrators resistance to motion on the correctness of the vibration distribution on working surfaces of vibratory machines. Arch Metall Mater. 2010;55:331–42.Search in Google Scholar

[20] Bednarski Ł, Michalczyk J. Modelling of the working process of vibratory conveyors applied in the metallurgical industry. Arch Metall Mater. 2017;62(2):721–8.10.1515/amm-2017-0109Search in Google Scholar

[21] Michalczyk J. Phenomenon of force impulse restitution in collision modelling. J Theor Appl Mech. 2008;46(4):897–908.Search in Google Scholar

[22] Czubak A, Michalczyk J. Teoria transportu wibracyjnego. Wydawnictwo: Politechnika Świętokrzyska; 2001.Search in Google Scholar

Received: 2021-07-21

Revised: 2021-11-19

Accepted: 2021-11-26

Published Online: 2021-12-31

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/eng-2021-0122

Keywords for this article

vibrations; vibratory conveyor; dynamic eliminator; transport stopping; feeder; variable output

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BY 4.0