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2THE SYSTEM OF FORMING THE CONTROL MODE OF THE ELECTRIC DRIVE DURING THE START-UP OF THE VIBRATION MACHINE
Nozhenko Viktoriia, Candidate of Technical Sciences, Senior lecturer, Kremenchuk Mykhailo Ostrohradskyi National University, Kremenchuk, Ukraine, ORCIDID: https://orcid.org/0000-0003-0126-6970
Bialobrzheskyi Olexii, Candidate of Technical Sciences, Associate Professor, Kremenchuk Mykhailo Ostrohradskyi National University, Kremenchuk, Ukraine, ORCID ID: https://orcid.org/0000-0003-1669-4580
Rodkin Dmytro, Doctor of Technical Science, Professor, Kremenchuk Mykhailo Ostrohradskyi National University, Kremenchuk, Ukraine, ORCID ID: https://orcid.org/0000-0003-2625-3869 Druzhynina Viktoriia, Doctor of Economic Science, Professor, Kremenchuk Mykhailo Ostrohradskyi National University, Kremenchuk, Ukraine, ORCID ID: https://orcid.org/0000-0001-8776-1408 Yakymets Serhii, Candidate of Technical Sciences, Associate Professor, Kremenchuk Mykhailo Ostrohradskyi National University, Kremenchuk, Ukraine, ORCID ID: https://orcid.org/0000-0002-2797-2796
DOI: https://doi.org/10.31435/rsglobal_ws/30072021/7639
ARTICLE INFO
Received: 23 May 2021 Accepted: 21 July 2021 Published: 30 July 2021
KEYWORDS
control system, induction motor, above resonance vibration machine, starting mode, resonance zone.
ABSTRACT
The above resonance vibration machines are widely used in various industries, but have a number of shortcomings associated with increasing of the oscillations amplitude when passing the resonance zone during start-up. It is noted that to reduce the oscillations amplitude and quickly pass the resonance zone, it is advisable to use a frequency-controlled electric drive with the formation of additional control effects. Features of frequency start of the electric drive of the vibration machines are noted. The structure of the electric drive control system during passing the resonance zone in the process of starting the above resonance vibration machine in the form of a block-scheme is proposed. The algorithm of operation of the control system is given.
Citation: Nozhenko Viktoriia, Bialobrzheskyi Olexii, Rodkin Dmytro, Druzhynina Viktoriia, Yakymets Serhii. (2021) The System of Forming the Control Mode of the Electric Drive During the Start-Up of the Vibration Machine. World Science. 7(68). doi: 10.31435/rsglobal_ws/30072021/7639
Copyright: © 2021 Nozhenko Viktoriia, Bialobrzheskyi Olexii, Rodkin Dmytro, Druzhynina Viktoriia, Yakymets Serhii. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Introduction. The above resonance vibration machines (VM) are widely used in construction, mining, engineering, metallurgy and other industries, where the stability of the equipment functioning is required when changing the load during operations such as transportation of bulk cargo, compression of concrete mixtures, crushing of rocks, abrasives, etc. [1, 2]. Such VM are usually equipped with unbalance vibration exciters, are large and powerful. As you know, the main problem of this type VM is to pass the resonance zone during the start-up, because most of VM shortcomings are related to this [2-6]. To partially solve this problem, in practice, it is used the unregulated induction motor drive with 2-5 times high capacity of drive motors. This solution allows you quickly overcome the resonance zone, but leads to low energy performance compared to the electromagnetic drive of vibration device [7]. In this regard, a number of ways have been developed to reduce the amplitude of oscillations of VM actuating device during passing the resonance zone both by upgrading the mechanical part of VM and with the help of electric drive systems. However, the analysis of existing
methods, which is given in [8], allowed to identify shortcomings that prevent their widespread use, namely insufficient reliability, high cost, sensitivity to errors in determining the parameters of the oscillating system, the possibility of using only to VM start with self-synchronizing, unconnected among themselves unbalance vibrating exciters, lack of control exit to the resonance mode. In the writings [8, 9], to reduce the amplitude of oscillations of VM actuating device during passing the resonance zone, it is offered the use of a frequency-controlled electric drive. This solution allows turning off the possible "jamming" of the drive motors rotors and reduces the dynamic loads on VM structural elements when using motors with the power required operating in the technological operating mode. Therefore, for wide application of this method to the above resonance VM of various purposes, a timely and urgent task is to build a control system for starting the electric drive of VM, taking into account the peculiarities of passing the resonance zone.
The objective of the work is to develop the structure of the electric drive control system of the above resonance vibration machine during passing of the resonance zone during start-up.
Research and results. In designing the structure of the control system of the electric drive of the above resonance VM, it is important to take into account the peculiarities of the behavior of oscillating systems during passing the resonance zone during start-up, which include [2-4, 10]:
- the maximum value of the oscillations amplitude is observed a little later than the moment of compliance of the frequency of forcing oscillations with the natural frequency of the oscillating system;
- the greater the acceleration of the drive affects the oscillating system, the smaller will be its oscillations amplitude, which corresponds to the resonance value;
- a vibration moment occurs when the actuating device of VM oscillates, which creates the additional load on the rotors of the drive motors and has a resonance character.
In [8, 9], the studies of VM start-up using frequency-controlled electric drive were carried out taking into account the above-mentioned features of VM behavior during passing the resonance zone. The analysis of these researches allowed defining the following requirements to frequency start of VM electric drive for maintenance of guaranteed passing of the resonance zone without "jamming" of drive motors rotors:
- starting of drive motors must be carried out with the law of frequency control U/f = const;
- the frequency sweep time should be chosen to ensure that the resonance zone is pass with maximum acceleration;
- when approaching the resonance zone, the supply voltage of the drive motors must be increased abruptly to exceed the dynamic torque of the motor over the vibration moment.
To implement the frequency start-up of VM electric drive, taking into account the above requirements, the structure of the above resonance VM electric drive control system in the form of a block-scheme is proposed (Fig. 1). In Fig. 1 is defined: VM - vibration machine; IM - induction motor with short-circuited rotor; QF - circuit breaker; FBR - full bridge rectifier; C - capacitor; I -inverter; SU - sensor unit, which includes current sensor and voltage sensor; L - choke; IPCU -instantaneous power calculation unit; APCU - active power calculation unit; PAU - power approximation unit; EDU - extremum detection unit; EDCU - electric drive control unit; SDU - slip detection unit; UFTM - unit of formation of a technological mode; VCU - voltage calculation unit; ICU - inverter control unit; Uabc - amplitude value of supply voltage of IM; ©op - angular idle rotation rate of IM; ©ref - set value of angular rotation rate of IM in the technological mode; uabc -instantaneous values of the stator phase voltage A, B, C of IM; iabc - instantaneous values of the stator phase current A, B, C of IM; p - instantaneous power; s - slip; P - active power; AP - approximate active power; APe - greater extremum of the approximated active power; AU - magnitude of the supply voltage, which is an abrupt increasing; U%c - set amplitude value of the supply voltage of IM;
Ui - inverter control pulse voltage. A vibration platform with unbalance vibrating exciters was chosen as VM, which is used for compression of concrete mixtures in the form of.
The algorithm for controlling the start-up of the electric drive of the above resonance VM is shown in Fig. 2. The operation of the control system begins with the entry of IM rated values and the calculation of its replacement scheme. With the help of UFTM unit (Fig. 1) the amplitude value of IM supply voltage of (Uabc), the angular idle rotation rate of IM (©op) and angular rotation rate of IM in the technological mode (©ref) are entered. And after that, the start-up of VM IM starts with the frequency control law U/f = c\ and the set value of the frequency sweep time.
Next, the important step in the process of VM start-up is timely determination of the moment when it is necessary to abruptly increase the supply voltage.
Fig. 1. Block-scheme of the control system for starting the electric drive of the above resonance vibration machine
In the writings [8, 9], it is proposed to perform the abrupt increase in the supply voltage when IM supply frequency is equal to the resonance frequency of VM. However, it is advisable to apply this solution to VM with a predetermined resonance frequency. Since in practice, usually the mass of the treated medium on VM can vary, which will affect the value of the resonance frequency of the entire oscillating system, so to effectively pass the resonance zone, the moment of abrupt increase in supply voltage must be determined regardless of VM parameters.
In the proposed control system (Fig. 1), the moment when it is necessary to abruptly increase the supply voltage is determined by the greater extremum of the active power of IM, which indicates the entrance to the resonance zone [4]. To do this, simultaneously with the start-up of IM begins the measurement of the instantaneous values of voltage (uabc) and current (jabc) of the stator phases A, B, C of IM in SU (Fig. 1). Next, in IPCU, the instantaneous power (p) is calculated according to the equation:
P = uA1A + uB1B + uC1C . (1)
Fig. 2. Algorithm for controlling the start-up of the electric drive of the above resonance vibration machine
The active power is determined in APCU.
1 T
P = - J p (t )dt, (2)
1 0
where T- period; t - time.
After calculating the active power, it is approximation (AP) in PAU (Fig. 1) with a step At and the larger extremum of the approximated active power in EDU is measured by comparing the value of the approximated active power at the point i (APi) with the value of the approximated active power in the point i+1 (APi+1) (Fig. 2). If the condition Ap <Ap+1 is met, the next step is to determine the magnitude of the amplitude of the supply voltage (AU), which is necessary to make the abrupt increase. To do this, the value of the current slip according to the formula is calculated in SDU
ro,
(3)
'0 p
where © - the current value of angular idle rotation rate of IM is determined by the instantaneous values of voltage (uabc) and current (iabc) of the stator phases A, B, C of IM according to known methods [11].
After calculating the current slip, the value of the amplitude of the supply voltage AU is determined, by which it is necessary to make the abrupt increase according to the equation:
Au — U '-U
(4)
where U' - the value of the amplitude of the supply voltage of the IM at start-up current; Um - the current value of the amplitude of the supply voltage.
The value of the supply voltage of the induction motor at start-up current is determined by the equation:
U ' — I,
+ - +( X + X )2
(5)
where In - start-up current of IM; ri - stator active resistance of IM; r'2 - reduced to the stator winding rotor resistance of IM; xi - inductive stator resistance of IM; x'2 - inductive resistance of the rotor of IM reduced to the stator winding.
The current value of the supply voltage amplitude assuming it is symmetrical is determined by the equation:
T
(6)
where ua - instantaneous value of the voltage of phase A of the stator of IM.
After determining AU there is the abrupt increase in the supply voltage of IM by the value of AU and further acceleration of the motor is carried out with the law of frequency control (U + AU) / f = C2. The next step is to compare the current value of angular rotation rate of IM (©) with its specified value (©ref). If the condition © = ©ref (Fig. 2) is met, then IM goes into operation technological mode.
The frequency start checking of the electric drive of the above resonance VM according to the proposed algorithm (Fig. 2) was carried out using mathematical modeling. As the VM considered the above resonance vibration platform with a load capacity of 9.8 tons of block structure with two-shaft unbalanced vibration exciters. The mathematical model of the vibration platform consists of two parts: electrical and mechanical. The electrical part includes a frequency converter and two IM with a short-circuited rotor. Mathematical description of the frequency converter was carried out according to equations [12]. The mathematical model of IM was built in a three-phase coordinate system according to [13].
The system of equilibrium equations for the stator and rotor circuits is described as
- iÄRÄ +
— iDRD +
UC — iCRC +
dlA ■ dt '
d w b . dt ''
d Wc dt
0 — iaRa +
0 — ibRb +
0 — iR +
d Wa dt
d Wb dt
d Wc dt
(7)
where ua, ub, uc - instantaneous voltage values of the stator phases A, B, C, respectively; îa, is, ic -currents of three phases of the stator A, B, C, respectively; ia, ib, ic - currents of three phases of the rotor a, b, c, respectively; Ra, Rb, Rc - active supports of the three phases of the rotor a, b, c, respectively; Ra, Rb, Rc - active supports of the three phases of the rotor a, b, c, respectively; ^a, ^b, yc - complete flux couplings of the three phases of the stator A, B, C, respectively; ya, yb, yc - complete flux couplings of the three phases of the rotor a, b, c, respectively.
The complete flux coupling of the stator and rotor phases is determined by the expressions:
s
2
0
U
U
<
B
f n \
V A =
2 i 2 2 l1 + -li 'a +-li COS (p) ^ + -Zj cos (2p) ^ + y 3 y 3 3
(8)
+ 2 L cos (py* ) ia + 2 L cos (py* +p) 4 + 2 L cos (pYr -p) h ;
2 f 2 j 2
VB =-Llc0s (p) iA + l1 + Tl1 iB +-Llc0s (p) iC + 3 y 3 y 3
+2 Lcos (pyr -p) ia + 2 Lcos (pyr ) ib+2 Lcos (pyr +p) ic ;
Vc = 2L1 cos (p) iA + 2l1 cos (p) iB + ^l1 + 2l1 j iC + + 2 L cos (p Y R + p) ia + 2 L cos (p Y R - p ) ib + 2 L cos (p Y R ) ic ; Va = f l2 + 2L2j ia + 2L2 cos(p) ib + 2L2 cos (2p) ic +
+2 Lcos (p yr ) iA+2 Lcos (p yr - p) iB + 2 Lcos (p yr + p) ic ;
Vb = 2 L2 cos (p) ia + (l2 + 2L2 j ib + 2 L2 cos (2p) ic +
+ 2 Lcos (p Y R + p) ^ + 2 L cos (p Y R ) iB + 2 L cos (p Y R - p ) iC ; Vc = 2 L2 cos (2p) ia + 2L2 cos (p) ib + f l2 + 2L2 j ic +
+ 2Lcos(pyr -p)iA + 2Lcos(pyr +p)iB + 2Lcos(pyr)ic>
where Li, L2 - inductance of self-induction of the stator and rotor phases, respectively; l\, I2 -
scattering inductance of the stator and rotor phases, respectively; p = — - phase shift between the
stator (rotor) windings; L^ - the maximum value of the inductance of mutual induction between the phase of the stator and rotor; yR (t) = < œ(t)dt - rotor rotation angle.
The expression for calculating the electromagnetic moment has the form:
Mem = PLp ('A (fa - fa ) + h ('pC - fa ) + C ('pA - fa )) ' (9)
where p - the number of pole pairs; î^a, î^b, i^c - magnetizing currents of the stator phases.
The mechanical part of the VM mathematical model is described by a system of differential equations, which is given in [14]:
mplx" + bxx' + cxx = m1r1 sin + W"2 cos ) - m2r2 (^2 sin + W22 cos ) ;
mpiy" + byy' + cyy = m1r1 (W cos - sin ) + m2r2 (tëcos - ^22 sin ^2 ) ; (10)
J^ = Mm -Mmh + M<, ' = 1,
where x, y - relocation of an operating device of the vibration machine along an axis X and Y (vibration relocation) respectively; x', y ' - speed of the vibration machine along an axis X and Y (vibration speed)
respectively; x", y" - acceleration of the vibration machine along an axis X and Y (vibrational acceleration) respectively; mpi - the full reduced mass of the fluctuating parts of the vibration machine with the form and a concrete compound; Cx = Cy = Co - coefficients of horizontal and vertical rigidness of support of the vibration machine respectively; bx = by = bo - coefficients of horizontal and vertical damping respectively; m1 = m2 = mo - mass of the first and second unbalances, respectively; r = r2 = ro - distance of the first and second unbalances from a spin axis respectively; 91, 92 - turning angles unbalances mass;
- brought to a motor shaft of moment of inertia of i motor respectively; Mem - electromagnetic torque of i motor respectively; Mmeh - section modulus of i motor; Mv - vibration moment of i motor respectively.
The section modulus of the motors is determined mainly by the resistance in the bearings of the exciters and is determined according to the expression:
Mmehi = 0.5 fmWd, (11)
where f tr - reduced coefficient of friction in bearings; ro - rotational speed of the unbalance; d -
diameter of bearing inner race.
The vibration moment of one motor:
Mv = miri (x "sin^ + y"cos^ + gcos, (12)
where g = 9.8 m/c2 - acceleration of gravity.
To study the proposed system using mathematical modeling adopted the following parameters of above resonance vibration machine and induction motor, which are shown in table 1.
Table 1. Technical characteristics of the vibrating platform
Parameter name Parameter value
Constructional parameter of the vibration platform
The full reduced mass of the VM 11000 kg
The mass of the unbalance 22 kg
The distance of the unbalance from a spin axis 0.1 m
Rigidness coefficient of the actuating unit supports 1.268-108 N/m
Damping coefficient 30600 Ns/m
Passport data of an induction motor with a capacity of 11 kW
Rated power 11 kW
Rated voltage 220 V
Synchronous speed 1500 rpm
Rated current 21.53 A
Stator resistance 0.462 Ohm
Rotor resistance 0.312 Ohm
Stator inductive resistance 0.831 Ohm
Inductive resistance of the rotor 1.262 Ohm
Inductive resistance of the magnetization circle 27.5 Ohm
On the basis of the given mathematical model of the above resonance vibration machine electric drive time dependences of active power of induction motor (P) during start-up and the principle of formation of supply voltage of induction motor (U) at overcoming of a resonant zone (fig. 3a), and also dynamic characteristics (fig. 3b) of induction motor without abrupt increase of supply voltage abrupt increase (©(Mi)) and with abrupt increase of supply voltage abrupt increase (©(M2)) during overcoming of a resonant zone.
160 140 120 100
5
t 80 l h CL
m 60 40 20
0
0.8 1 Time (s)
a)
................ r............... ................
(jofMz)
üj(Mi)
50
200
100 150
Moment (Nm)
b)
Fig. 3. Time dependences of active power and supply voltage and dynamic characteristics of induction motor
250
As shown in Fig. 3, the abrupt increase in supply voltage is performed when the oscillations of the active power are significantly reduced, which indicates the approach to the resonance zone.
The efficiency of the abrupt increase of the supply voltage during passing of the resonance zone in the process of starting the VM is confirmed by the results of mathematical modelling and experimental studies, which are given in [9].
Conclusions. The application of frequency-controlled electric drive to the above resonance VM allows to pass the resonance zone without "jamming" the rotors of the drive motors due to the abrupt increase in supply voltage when approaching the resonance.
The proposed structure of the control system for starting the electric drive of the above
resonance VM and the algorithm of its operation allows to determine the moment of abrupt increase of
the supply voltage without previously known parameters of the oscillating system. The proposed
control system should be applied to VM with variable load.
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