Vibration Control of Resonant Vibratory Feeders With Electromagnetic Excitation

The vibratory feeders with electromagnetic excitation called electromagnetic vibratory feeders (EMVF) are commonly used for performing gravimetric flow of granular and particulate materials in processing industry. This drives offer easy and simple control the mass flow of conveying materials. In comparison with other drives (pneumatics, inertial, centrifugal, etc...), these have a more simple construction and they are compact, robust and reliable in operation. The absence of wearing mechanical part, such as gears, cams belts, bearings, eccentrics, etc., makes EMVF, most economical equipment. Standard power electronic output stages intended for control of theEMVF using SCR devices (thyristors and triacs). This implies phase angle control (PAC) and constant frequency of vibration. In this way control circuit must be synchronized to the mains supply frequency 50(60) Hz. PAC can only accomplish tuning amplitude of vibration, but not vibratory frequency. Application of transistor (IGBT or MOSFET) switch mode power converters enables accomplishing the amplitude and (or) frequency control of EMVF. Their use implies the excitation of an EMVF independent of the mains supply frequency. In addition, the frequency control ensures operation in the region of mechanical resonance. This operation is highly efficient, because large output displacement is provided by small input power. An optimal and efficient operation requires tracking of resonant frequency. This paper presents possible solution of the amplitudefrequency control of EMVF and corresponding simulation and experimental results.


INTRODUCTION
The vibration energy has proved, for many years its operational reliability in various technological processes: discharging bulk materials from bins, conveying them over limited distances, charging and dosing them continuously, compacting, loosening, screening, grading them (including dedusting and dewatering)...etc.From the macroscopic point of view, the process of vibratory processing is based on microthrows of particles of the material.Therefore the material obtains character of a "viscous fluid" and thus becomes suitable for conveying or further processing [1][2][3][4][5].Vibratory feeders with electromagnetic excitation (drive) are used extensively in controlling the discharge of bulk solids from bins and stockpiles.Electromagnetic drives offer step-less, accurate and repeatable setting of the oscillation amplitude, a long life (absence of wearing mechanical part, such as gears, cams belts, bearings, eccentrics i.e. they have no rotating parts), and they reach the desired amplitude immediately upon switching on, and they come to a rest after being turned off in very short time (several milliseconds).
The design of the vibratory feeder with electromagnetic excitation i.e. electromagnetic vibratory feeder (EMVF) is based on a system of two masses coupled by means of an elastic component consisting of flexible leaf composite springs (commonly Fiberglass™).The quantity of leaf springs fitted up determines the resonant operation of the equipment.A driving electrical current excites the magnetic core, attracting the moving armature, which is attached to the load carrying element (LCE) of EMVF i.e. vibratory trough.The energy accumulated in the leaf springs is used to return the system to its position of equilibrium.By realizing free vibrations of variable amplitude and frequency, over a wide range application of the twomass oscillatory system , suitable power converter and the corresponding controller, continuous conveyance and dosing of granular materials have been provided for various operating conditions.In this way, the whole system power converter-power controller-vibratory actuator-vibratory feeder i.e. regulated vibratory conveying drive, has behavior of the controllable mechanical oscillator [6][7][8][9].
By applying sophisticated vibration control based on adjusting the amplitude of oscillation and tracking/tuning the resonant frequency, it is possible to accomplish the operation the entire mechanical system in the resonance range.Operation of EMVF in the mechanical resonant range becomes favorable, because the final values of the oscillation amplitude can be obtained for relatively small energy of excitation.Operation in this region is the most energy efficient, since then, the entire vibratory drive has minimal power consumption [10].
Standard power output stages intended for vibration control of EMVF, using SCR devices (thyristors and triacs), imply the use of phase angle control.Since the supply network frequency is constant (50Hz/60Hz), the adjusting of phase angle can only accomplished control of the amplitude oscillations, but not and their frequency [6][7], [9].Application of switch mode IGBT power converters enables accomplishing the amplitude and/or frequency control of EMVF [11][12][13].Their use makes the excitation of EMVF independent of the supply network frequency.In addition, the control of frequency ensures operation of vibratory feeder in the region of mechanical resonance.

THE CONSTRUCTION OF RESONANT ELECTROMAGNETIC VIBRATORY FEEDER
There is a wide range of design and variety constructions of EMVF currently available that are in some way flexible.The basic construction and mechatronic design of flexible vibratory feeding systems are available in literature [14][15][16].This paper is interested in the construction of linear resonant EMVF.

Figure 1. Typical construction of resonant EMVF
A typical arrangement of resonant EMVF is presented in Figure 1.Its main components are: load carry element (LCE) -1, electromagnetic vibratory actuator (EVA) as source of excitation force F and flexible elements -2.Flexible elements are made of composite leaf (Fiberglass) springs.These elements are rigidly connected with the LCE on the one side, while, on the other side, they are fitted to the base-3 of the device and sloped down under certain angle.The base of vibratory conveyor is resting on rubber pads-4 to the foundation.EVA consists of a magnetic core-5, covered by continuous windings coil-6.As the ferromagnetic material has a very high permeability, all energy of the magnetic field is stored in air gap of the actuator.Created magnetic field which produce the electromagnetic force F acts on armature-7 attached to the LCE.This element carries the vibratory trough-8 along with conveying material.The vibratory displacement between base-3 and LCE -1 is detected by a non contact inductive sensor -9.The material which is dosed is brought to the LCE from a storage hopper -10.Adjustment of the material inflow is accomplished by a movable shutter -11 which is placed at the bottom of the hopper.

THE DYNAMIC MODEL OF RESONANT ELECTROMAGNETIC VIBRATORY FEEDER
To define the control strategy of the vibratory conveyor, it is required to analyze the electromagnetic and mechanical parts of the system.Detailed dynamic model of EMVF is presented in [6][7], [16] and [16][17].In general vector form, this model can be represented as: Vector   If one considers movement around the equilibrium position 0 p p  , (2) becomes: The electromagnetic part is represented by the vibratory actuator EVA as the generator of the excitation force F which is, through the electromagnetic field in the air gap between the inductor and armature, transferred to LCE.Detailed model of EVA, presented in [9], [13] and [17][18][19], in the form: Where c R represents active resistance and Quantities i and u represent the EVA current, and EVA voltage, respectively.The bronze disc with thickness  doesn't permit inductor to form a complete magnetic circuit of iron; in other words, it inhibits "gluing" of armature and inductor, which is undesirable.In the real cases is Parameter c R , represents the equivalent resistance which is dependent on the speed of LCE dt dp / and gradient of the coil inductance / L p   at the operating point 0 p p  , and is given as: Based on (3) -( 8) is formed a complete dynamic simulation model of the resonant EMVF.The simulation model is shown in Figure 3.It is clearly that the presented model is nonlinear, which is due to the nonlinear functions of EVA inductance, which is shown a functional block EVALUE3.Additional nonlinearity brings a functional block EVALUE4.Product represents counter electro motive force that is presented with ( , , )  e p p t  .This induced voltage opposes the voltage ( ) u t that is applied to the terminal ends of the EVA. is much longer than their duration.On the basis of this, it can be concluded that  in ( 7) can be neglected.Finally, the approximation of ( 7) is given by: As already mentioned, the pulse excitation is, from the energy point of view, the most suitable method of excitation of resonant EMVF.Owing to the predominantly inductive nature of EVA coil, indicated by (9), it is very simple, by applying a suitable transistor power converter and corresponding control [13], to generate triangular current pulses with changeable frequency and time duration.
For most technical systems operation in the resonance range is unfavorable because it can lead to significant stresses and fracture of mechanical construction, since in this case, for small values of excitation forces, amplitude of oscillations get very large.The limitation of the significant amplitude oscillations can be achieved by appropriate control of excitation force of EMVF.
Application of the phase controlled SCR converters in vibration control of EMVF implies a fixed frequency of vibrations, imposed by the supply network frequency.A serious problem arises when the mass of the conveying material is changed, i.e. mechanical resonance of the system has changed.In such case the whole vibratory system will not operate efficiently.It is possible to tune amplitude but not the frequency of the vibrations.Variation of the mechanical resonance due to variation of the mass of the conveyed material, or even variation of the system parameters (characteristics of the springs, damping, etc.), leads to reduction of efficiency of the EMVF.In order to accomplish an optimal and efficient operation at a new resonant frequency, it is necessary to change the frequency of EVA coil current, rather the frequency of electromagnetic excitation force of the resonant EMVF.
Application of transistor switch mode power converters [12][13], [20][21], enables accomplishing the amplitude and/or frequency control of resonant EMVF.Their use makes the excitation of EMVF independent of the supply network frequency.In addition, the control of frequency ensures EMVF operation in the region of mechanical resonance (tracking and tuning of resonant frequency).
Figure 4 shows the simple switch mode topology of power converter for driving resonant EMVF. Figure 3(a) shows the basic topology which provides current power control which generates a triangular half-wave of EVA current with variable frequency and time duration.The Figure 3  V is achieved by high frequency step-down ("buck") switching power converter which consists of: switch 1 Q , diode 1 D and 0 0 L C filter.

SIMULATION RESULTS
Based on a simulation model of the resonant EMVF in Figure 3 and the topology of power converter in Figure 5 (b) was formed the simulation circuit of the complete vibratory system.In this simulation circuit are implemented and then tested amplitude and frequency control of resonant EMVF.In simulations were set parameters that correspond to real EMVF system and real EVA.The most important parameters are given in Table 1.  .In this case excitation (driving) frequency was equal to resonant frequency i.e. .Simulation results for this case are given in Figure 7 (c).Based on the presented simulation results, it can be concluded that the current pulse excitation of EVA provides continuous sinusoidal function of vibratory displacement.
From the spectral point of view, a triangular EVA current excitation is characterized by a high harmonic content (the fundamental harmonic 0  plus higher harmonics at frequencies 0 2 , 0 3 , etc…).In view of (5), the excitation force is proportional to the square

F k i
  , and it is concluded that it will contain the same harmonic spectrum.However, irrespective of the pulse excitation of LCE, the output displacement p is a "smooth" sinusoid, as a consequence of the character of the mechanical part of the system, which, according to (3), attenuates higher harmonics for frequencies 0    , as shown in Figure 2.

PRACTICAL REALISATION
A practically realized power converter for excitation of a resonant EMVF is described in this section.Figure 8shows block diagram of the complete system of vibratory control.Power converter is really consists of three power converter: (1) front end high frequency AC/DC converter with power factor correction (PFC) control, (2) DC/DC link converter with duty-cycle control (step-down or "buck" converter) and (3) low frequency IGBT converter with triangle pulsating output current for driving EVA.
The namely "front end" AC/DC converter is in fact a controllable transistor PFC rectifier with twin "boosts" stages (two MOSFET's and two boost diode) and inductance in L on the side of power mains 230V, 50Hz.This converter with advantages over the conventional PFC (diode bridge rectifier-power switch-diodeinductance on DC side) is described in detail, in [22][23].PFC converter is in fact pre-regulator which stabilize mains AC maims voltage 230V to 400VDC.The voltage 400VDC is input voltage of DC/DC link "step-down" converter with duty-cycle control.Main components of this power stage are: MOSFET powers switch Q1, free-willing diode D1 and , so that the output voltage of this converter is . The output converter for excitation of EVA coil realized using the IGBT power switch Q2 and return diodes D2.This diode return accumulated electrical energy (energy accumulated during rising current-ON time) from inductance of EVA coil to input capacitor in C , placed to the DC output of PFC rectifier.The current controller is realized with circuit shown in Figure 5(a), in the discrete technology.The value of EVA current is measured by a Hall Effect based current sensor (LEM current sensor).Reference inputs of current controller are f V (reference frequency) and Mref I reference amplitude of EVA current.Also, the current controller includes overload and short circuit protection.
The "intervening" system of protection is applied.Under normal conditions, the load current is programmed by the current controller.In the case of a direct short circuit or overload, protection circuit takes over.The vibratory control (amplitude and /or frequency control) is based on industrial PC104 module where the algorithms for search and tracking of the resonant frequency are implemented, together with reference input signals for current controller (adjusting the amplitude and frequency of the EVA current pulses).Measurement of the output displacement of the LCE and detection of its passage through the equilibrium position ( 0 p p  ) is accomplished by a non-contact inductive displacement sensor, operating in the displacement range ±5mm and frequency range 0-1kHz.The signal of this sensor is transmitted by an electronic amplifier and normalized to the input level 0-5V (analogue input AI1 of PC104 module).Vibratory amplitude mref P is set to analogue input AI2.

EXPERIMENTAL RESULTS
The experimental results are obtained with a realized laboratory prototype of the resonant EMVF, where the amplitude-frequency control has been applied.In the experiments the measured quantities of interest were: EVA current ( ) i t , EVA voltage ) (t u and displacement of LCE ( )  p t .The influence of variations of the amplitude and time duration of the EVA current pulses on the LCE displacement at excitation frequency equal to resonant frequency 0 44.5 is shown in Figure 9.The presented experimental results in Figure 9, relate to amplitude control of resonant EMVF, are fully consistent with simulation results presented in Figure 6.

CONCLUSIONS
The most significant contribution of this research is a development of an optimal control for the electromagnetic resonant vibratory feeder and an increase of theirs energy efficiency.There has been achieved a compensation of required resonant regime and change resonant frequency.Dominating influences are: changing of conveying material mass, changing stiffness of flexible element, variation of mains voltage supply.With proposed method of vibratory control of resonant EMVF are achieved number advantages: -freedom to operate a resonant EMVF with any resonant frequency from 5 Hz to 150 Hz (frequency control) -proposed vibratory controller will continually search for the natural frequency of the EMVF(resonance) and excite it at that frequency (active tuning); in the located natural (resonant) frequency, it is possible to tune amplitude and time duration of the EVA coil current i.e. amplitude oscillations of the LCE (amplitude control ) -flexible automation with minimum change-over time because electronics replace the comprehensive and the complicated calibrations and mechanical settings -vibratory drive can operate nondependent on mains frequency (50Hz-Europe or 60Hz-North America) without changing the flexible springs and balancing masses (manual retuning process) The presented simulations and experimental results which relate to proposed amplitude and frequency control are shown that regulated resonant EMVF drive provide high energy efficiency: minimum EVA coil current, minimum EVA coil heating, minimum supply current, minimum power consumption, input power factor correction.

КОНТРОЛА РЕЗОНАНТНИХ
and it contains the relative displacement p , of the LCE with respect to the base, displacements of the base , u w in the horizontal and vertical directions respectively, and angle of inclination of the base  with respect to its centre of gravity.Matrices of masses, damping and stiffness M , C and K , respectively, are the symmetric.force acting on the LCE.Equation (1) indicates that the mechanical system has four resonant modes.It should be mentioned that for the range of interesting vibrations, all four modes are not of interest.The typical Bode diagrams and simplified presentation of EMVF are given on Figure 2 [6-7].The characteristic (1) refers to a complete model of resonant EMVF, while characteristic (2) refers to its simplified representation.The whole system is reduced to mass of moving material including masses of LCE and vibratory trough [ ] m kg , equivalent stiffness of composite springs k [N/m] and equivalent coefficient of damping b [N/m/s].

Figure 2 .
Figure 2. Typical amplitude -frequency characteristics and simplified presentation of resonant EMVFIn practical applications the largest contribution to moving the LCE has a dominant oscillatory mode, coming from high quality composite springs and related to the displacement p[17]:

0 p
 .Mechanical force F produced by the electromagnetic action of EVA coil acts on its armature which is a constituent part of LCE.If the short excitation current pulse for EVA is synchronized with the instant when the armature is passing through the equilibrium position, i.e .Now, (4) in the vicinity of the operating point can be represented as:

Figure 3 .
Figure 3. Complete simulation model of resonant EMVF The model can be linearized around the operating point 0 p p  .In this case, for small values of displacement p , EVA can be understood as a linear actuator whose inductance is (b) show the characteristic waveforms (displacement p , EVA voltage ( ) u t , EVA current ( ) i t and control voltage C V ) .The rising of EVA current is achieved by short turn-on of power switch Q.Then the voltage on the inductance of EVA coil is positive and equal 0 / 2 0 V  .After power switch Q turning-off, the voltage on the inductance of EVA coil, becomes negative (  ), and hence the decrease of the EVA current.Since the excitation force is proportional to the square of the current, it will be very close to the Dirac excitation pulses ( ) t  , as show on Figure 4(b).

Figure 4 .
Figure 4. Switch mode power converter for driving resonant EMVF, (a) basic topology circuit, (b) characteristic waveformsThe detailed presentation previously described topology, including the principle diagram of the current control is shown in Figure5.The control circuit which provides control of the amplitude, duration, and

Figure 5 .i
Figure 5. Programmed power current control of resonant EMVF; (a) basic topology circuit, (b) characteristic waveforms The control circuit of this converter is based on duty-cycle control and maintaining the voltage ratio / out in D V V  on the value 0.5, i.e. for 0 in V V  implies that 0 0 / 2 V V  .Instantaneous value of the actuator current ) (t i is measured by the corresponding current sensor.The measured signal is amplified by gain factor i K and the amplified signal is compared with the reference value Mref I .This reference value determines the amplitude of EVA current and its time duration.Setting the RS flip-flop FF is accomplished from a voltage controlled oscillator (VCO).By signal pulse from the VCO to SET input of flip-flop FF, the state of logical "1" is established at its output Q , i.e. switch 2 Q is turned-on.This establishes the current through EVA coil in the form a rising ramp since voltage 0 / 2 V , is applied across the EVA coil terminals.The rising of current continues until the instantaneous current value

Figure 6 .Figure 7
Figure 6.Amplitude control of resonant EMVF at mechanical resonant frequency 0 44.45 f Hz  amplitude/duration of EVA current 0.5A/2ms, (b) amplitude/duration of EVA current 1A/4ms Figure 7 presents results of a simulation related to the frequency control of the resonant EMVF.Observed variables that are of interest vibratory displacement and EVA current, are given in three characteristic cases.In Figure 7 (a) shows the characteristics waveforms for the case of the established resonant at the unloaded resonant EMVF (empty vibratory trough), i.e. 0 k k m m  .In this case excitation (driving) frequency was equal to resonant frequency i.e.Hz f f drv 50 01   .In Figure 7 (b) shows typical waveforms for the case of loaded vibratory trough ( kg m m m

Figure 7 .
Figure 7. Frequency control of resonant EMVF; (a) the MOSFET Q1 is realized by a "floating" drive circuit which can sustain high voltage and is immune to sharp voltage edges ( dt dv / ).Duty-cycle D is maintained to value 5 .0  D

Figure 9 (Figure 8 .
Figure 8. Block scheme practical realized system for vibratory control of resonant EMVF

Figure 9 .Figure 10
Figure 9. Amplitude control of real resonant EMVF at resonant frequency 0 44.5 f Hz  , EVA voltage ±200V (a) LCE displacement ±0.7mm,(b) LCE displacement ±1.4mm Figure 10 shows the compensation of the disturbance caused by a mass change of LCE load.In this loading process are presented the oscilloscopic records of LCE displacement and EVA current.At the time moment marked with arrow-↑, LCE was suddenly filled (with sugar material mass of g m k 300  ) at

Figure 10 .
Figure 10.Frequency control of resonant EMVF and change mass compensationThe oscilloscopic records in Figure11, corresponding time interval 1 t  , in which is driving frequency equal to mechanical resonant frequency i.e. 1 0 1 50

Figure 11 .
Figure 11.Frequency control of resonant EMVF: detailed scope of time interval 1 t  Figure 12 shows the characteristics oscilloscopic records for time interval 3 t  in which is driving frequency equal to new mechanical resonant (after loading of LCE with sugar material 300 k m g   ) i.e.
amplitude value of the EVA current has remained unchanged i.e.
time duration is remained about the same, but due to frequency control, and monitoring and adjusting the excitation frequency to the new resonance frequency, is achieved maintaining the vibratory amplitude to the value 2

Figure 12 .
Figure 12.Frequency control of resonant EMVF: detailed scope of time interval 3 t  The presented experimental results in Figures 11 and 12, relate to frequency control of resonant EMVF, are fully consistent with simulation results presented in Figures 7(a), and 7(c), respectively.