CN112604954A - Double-mass four-machine frequency-doubling self-synchronous driving vibrator and parameter determination method thereof - Google Patents

Double-mass four-machine frequency-doubling self-synchronous driving vibrator and parameter determination method thereof Download PDF

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CN112604954A
CN112604954A CN202011354237.1A CN202011354237A CN112604954A CN 112604954 A CN112604954 A CN 112604954A CN 202011354237 A CN202011354237 A CN 202011354237A CN 112604954 A CN112604954 A CN 112604954A
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vibration
mass
formula
frequency
exciters
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CN112604954B (en
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张学良
胡文超
陈为昊
张伟
张旭
王志辉
闻邦椿
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Northeastern University China
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Northeastern University China
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B07—SEPARATING SOLIDS FROM SOLIDS; SORTING
    • B07B—SEPARATING SOLIDS FROM SOLIDS BY SIEVING, SCREENING, SIFTING OR BY USING GAS CURRENTS; SEPARATING BY OTHER DRY METHODS APPLICABLE TO BULK MATERIAL, e.g. LOOSE ARTICLES FIT TO BE HANDLED LIKE BULK MATERIAL
    • B07B1/00—Sieving, screening, sifting, or sorting solid materials using networks, gratings, grids, or the like
    • B07B1/42—Drive mechanisms, regulating or controlling devices, or balancing devices, specially adapted for screens
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B07—SEPARATING SOLIDS FROM SOLIDS; SORTING
    • B07B—SEPARATING SOLIDS FROM SOLIDS BY SIEVING, SCREENING, SIFTING OR BY USING GAS CURRENTS; SEPARATING BY OTHER DRY METHODS APPLICABLE TO BULK MATERIAL, e.g. LOOSE ARTICLES FIT TO BE HANDLED LIKE BULK MATERIAL
    • B07B1/00—Sieving, screening, sifting, or sorting solid materials using networks, gratings, grids, or the like
    • B07B1/28—Moving screens not otherwise provided for, e.g. swinging, reciprocating, rocking, tilting or wobbling screens
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations

Abstract

The invention discloses a double-mass four-machine frequency-doubling self-synchronous driving vibrator and a parameter determination method thereof.A vibration system comprises four vibration exciters, an eccentric rotor and a self-synchronous driving vibration system, wherein every two vibration exciters are respectively arranged at the left side and the right side of a main vibration mass; by utilizing the vibration self-synchronization principle, a dynamic model and a motion differential equation are established to obtain the synchronization condition and the stability condition of the four vibration exciters under the conditions of double frequency and triple frequency. The screening efficiency or the dewatering efficiency of the screening equipment is improved, or the vibration compacting molding effect is improved, or the working efficiency of the vibration compacting molding operation of the equipment is improved; the method is suitable for grading viscous and wet materials; the key driving part of the system is protected, the maintenance of the key vibration source part is facilitated, the structure of the working mass is indirectly simplified, and the full utilization of the working mass is realized.

Description

Double-mass four-machine frequency-doubling self-synchronous driving vibrator and parameter determination method thereof
Technical Field
The invention belongs to the field of vibrating machinery. Relates to a double-mass four-machine frequency multiplication self-synchronization driving vibrator based on vibration isolation and a parameter determination method thereof.
Background
The vibrating equipment is a machine for screening/dehydrating/compacting/forming various mesons to be processed by utilizing vibration. The vibration machine adopting single-frequency excitation has the defects of low efficiency, incapability of meeting the high-quality requirement of engineering and the like; if the throwing index is increased to improve the function of the equipment, the service life of the whole equipment is reduced, and the performance requirement of the machine in industrial production cannot be met. Therefore, the vibration machine of the single-frequency excitation type still has many problems:
1. these methods result in complex equipment structures, large volumes, and high processing costs.
2. For the classification of sticky and wet materials, the single-frequency excitation vibration sieve vibrates during working to enable the materials to be more tightly adhered to the sieve surface, so that the materials are jammed or forced to stop; the single frequency driving also results in poor dewatering effect of the apparatus and poor dense forming effect of the precast concrete member or the precision cast member.
With the continuous improvement of the vibration theory, the frequency doubling synchronization theory is applied to design a frequency doubling synchronous machine which can not only increase the working efficiency of the machine, but also improve the working quality of the machine and simultaneously ensure the performance requirement of the machine, and is urgent. The double-mass four-machine frequency multiplication self-synchronization driving vibration screening/dehydrating/compacting/forming equipment based on vibration isolation and the parameter determination method thereof are one of effective methods for solving the problem.
Disclosure of Invention
The invention is realized by the following technical scheme:
the dynamic model of the double-mass four-machine frequency-doubling self-synchronous driving vibrator comprises the following steps: four vibration exciters, a mass 1, a mass 2, a spring A and a spring B; wherein the mass 1 is a main vibration mass, and the mass 2 is a vibration isolation mass; the plastid 1 is connected with the plastid 2 through a spring A, and the plastid 2 is connected with the foundation through a spring B; the four vibration exciters are respectively arranged on the left side and the right side of the mass 1 in pairs, each vibration exciter is provided with an eccentric rotor, the eccentric rotors are driven by respective induction motors to respectively rotate around the centers of the rotation axes, the rotating directions of the two eccentric rotors on the same side are opposite, and the vibration system equipment is driven to work in a self-synchronizing mode.
The parameter determination method for the four vibration exciters of the vibrating machine comprises the following steps:
step 1, establishing a dynamic model and a system motion differential equation
As shown in fig. 1, a coordinate system as shown is established. Four vibration exciters respectively surrounding the rotary central shaft o1,o2,o3And o4And (4) rotating. Furthermore, it is possible to provide a liquid crystal display device,
Figure BDA0002802128300000021
are the rotational angles of the four eccentric rotors (URs), respectively. According to this model, the two masses have 1 degree of freedom each. The degree of freedom of the mass 1 is defined by x1The degree of freedom of the mass 2 is represented by x2And (4) showing.
Based on the Lagrange equation, the differential equation of the following system can be obtained:
Figure BDA0002802128300000022
wherein the content of the first and second substances,
Figure BDA0002802128300000023
in the formula (I), the compound is shown in the specification,
m1-mass 1 mass;
m2mass 2 mass;
m0ithe mass of the vibration exciter i (i is 1-4);
Joithe moment of inertia (i ═ 1-4) of the vibration exciter i;
ri-eccentricity of a vibration exciter i;
fithe damping coefficient of an i-axis of the motor (i is 1-4);
Teithe motor i outputs a torque electromagnetically (i is 1-4);
kx-spring rate in x-direction;
fx-a damping coefficient in the x-direction;
Figure BDA0002802128300000031
-d/dt and d2·/dt2
Step 2, theoretical analysis of frequency multiplication synchronization of four vibration exciters
The invention is based on a double-mass mechanical system under the vibration isolation condition, the working frequency of a vibration exciter is greater than the natural frequency of a main vibration system, and the second term and the third term on the left side of the equal sign of the formula (1) are omitted. Furthermore, consider the displacement x1And x2Are very small and the operation state of the system is nearly stable, the last four expressions of the formula (1) are replaced, and x of the formula (1) is removed1And x2And take the rotation angle
Figure BDA0002802128300000032
To the second derivative of (1) to obtain
Figure BDA0002802128300000033
The approximate expression of (c) is:
Figure BDA0002802128300000034
wherein
Figure BDA0002802128300000035
Figure BDA0002802128300000036
In the formula, the small parameter epsilon is the ratio of the mass of the eccentric rotor of the vibration exciter to the total mass of the main vibration system. Sigmai(i is 1,2,3,4) indicates the rotation direction of the eccentric rotor (clockwise is positive), and therefore:
σ1＝σ3＝-1,σ2＝σ4＝1 (3)
the rotational phase angle is expressed as follows:
Figure BDA0002802128300000041
wherein
τ＝ωt,n1＝n2＝1
In the formula,. DELTA.iIs a function that varies slowly with the generation phase of the eccentric rotor due to the movement of the system.
Substituting formula (4) into formula (3) to obtain:
Figure BDA0002802128300000042
the formula (5) is a basic expression for realizing the synchronization of the vibration exciters.
Writing equation (5) as a standard expression:
Figure BDA0002802128300000043
to formula (6)
Figure BDA0002802128300000044
Is derived again to
Figure BDA0002802128300000045
The differential equation expression of the following equation (5) is as follows:
Figure BDA0002802128300000046
Figure BDA0002802128300000051
in the second equation of the equation (7),
Figure BDA0002802128300000052
and small parameters
Figure BDA0002802128300000053
In proportion of viIs a slowly varying function. V is toiSlowly varying term Ω ofiSuperimposed with the small vibration term, the first approximate solution is refined:
Δi＝Δi,i＝1,2,3,4
Figure BDA0002802128300000054
wherein
σini+σjnjP is not equal to 0ij＝1/(σini+σjnj)，σini+σjnjWhen p is 0ij＝0
σini-σjnjQ is not equal to 0ij＝1/(σini-σjnj)，σini-σjnjQ when equal to 0ij＝0
The second approximate solution is improved in the same way:
Δi＝Δi,i＝1,2,3,4
Figure BDA0002802128300000055
substitution of formula (9) for formula (7) on the left, omegaiAnd ΔiAs a fixed value and taking an average value over 0-2 pi for τ. Considering that the vibration exciters rotate reversely at the same rotation speed, the following expression can be obtained:
Figure BDA0002802128300000056
Figure BDA0002802128300000061
wherein
σini+σjnjU when equal to 0s＝1,ψij *＝σiΔi+σjΔjOtherwise us＝0
σini-2σjnjU when equal to 0l＝1,γij *＝σiΔi-2σjΔjOtherwise ul＝0
σini-2σjnj+σrnrU when equal to 0d＝1,ηijr *＝σiΔi-2σjΔj+σrΔrOtherwise ud＝0
In the formula, according to
Figure BDA0002802128300000062
Can obtain a stable solution, and can be found in the following equation (10)
Figure BDA0002802128300000063
In terms and epsilon, there is an expression for determining the phase relationship for exciters of equal speed, first
Figure BDA0002802128300000064
Second order rotating phase with 1:2 synchronous and 1:3 synchronous speed ratioA bit relation. Therefore, the synchronous phase relationship between exciters at the same rotation speed can be determined by taking the terms of the expression (10) up to the e-th order, and the phase relationship can be substituted for the expression (10)
Figure BDA0002802128300000065
And the secondary term is used for solving the synchronous phase relation between the vibration exciters with the rotation speed ratio of 1:2 or 1: 3. In addition, considering that the structure of the system is symmetrical, there are:
a12＝a21＝1,a34＝a43,a13＝a14＝a23＝a24,α1＝α2,α3＝α4,k1＝k2,k3＝k4
when the rotating speeds are the same, the term epsilon of the formula (10) is obtained, and the following terms are included:
Figure BDA0002802128300000066
Figure BDA0002802128300000067
Figure BDA0002802128300000071
when the system is in a steady state, the expression of the parameters in equation (11) is:
Figure BDA0002802128300000072
step 3, deducing the conditions of the double frequency synchronism and stability of the four vibration exciters
(1) The same frequency, the ratio of the rotating speed is 1:1, and the conditions for realizing the fundamental frequency synchronization among the vibration exciters are as follows:
Figure BDA0002802128300000073
(2)n3＝n4when the rotation speed is 2, the stable rotation speed of the vibration exciters 3 and 4 is twice that of the vibration exciters 1 and 2, and double frequency synchronization can be realized between the vibration exciters. In formula (10) with respect to
Figure BDA0002802128300000074
Considering equation (13), the following relationship can be obtained:
Figure BDA0002802128300000075
in equation (14), the frequency doubling synchronization condition is written as the following equation in consideration of the steady state:
Figure BDA0002802128300000076
assuming a steady state phase angle Δi0And Ωi0Having a slight deviation of δiAnd xiiThus, there are:
Δi＝Δi0+δi,Ωi＝Ωi0+ξi,i＝1,2,3,4 (16)
the formula (16) is substituted into the formula (10) to obtain a system differential equation expression as follows:
Figure BDA0002802128300000081
rearrangement of formula (17) to give a value related toi(i ═ 1,2,3,4) is given by:
Figure BDA0002802128300000082
the characteristic equation of equation (18) with respect to the characteristic value λ is:
Figure BDA0002802128300000083
the following stability criterion was obtained according to the Router-Hurwitz criterion analysis:
2εα1 (1)＞0,2εα3 (1)＞0，εcos(Δ20-Δ10)＞0
Figure BDA0002802128300000084
because of ε, α1 (1)，α3 (1)，a31，k1Both are greater than 0, equation (20) can be solved:
cos(Δ20-Δ10)＞0,cos(Δ30-2Δ10)＞0,cos(Δ40-2Δ20)＞0 (21)
the stable phase relation among the exciters can be obtained by combining the formulas (13), (15) and (21):
Δ20-Δ10＝0,Δ40-Δ30＝0,Δ30-2Δ10＝0,Δ40-2Δ20＝0 (22)
(3)n3＝n4when the rotation speed is 3, the stable rotation speed of the vibration exciters 3 and 4 is three times that of the vibration exciters 1 and 2, the system realizes triple frequency synchronization, and a synchronization conditional expression (13) is changed into the following steps:
Figure BDA0002802128300000091
in view of the steady state, the inter-exciter synchronization condition with a rotation speed ratio of 1:3 can be written as follows:
Figure BDA0002802128300000092
Figure BDA0002802128300000093
in order to seek a stable phase relation, as with a double frequency synchronous analysis method, an expression of the system in a stable state is solved, and a characteristic equation of the system is introduced as follows:
Figure BDA0002802128300000094
the stability criterion under the synchronous state is obtained by applying the Router-Hurwitz criterion analysis as follows:
2εα1 (1)＞0,2εα3 (1)＞0，εcos(Δ20-Δ10)＞0
ε2a31cos(Δ30-2Δ10-Δ20)＞0，ε2a31cos(Δ40-2Δ20-Δ10)＞0 (26)
the formula (26) is solved:
cos(Δ20-Δ10)＞0,cos(Δ30-2Δ10-Δ20)＞0,cos(Δ40-2Δ20-Δ10)＞0 (27)
similarly, the stable phase relation among the exciters can be obtained by combining the formulas (13), (24) and (27):
Δ20-Δ10＝0,Δ40-Δ30＝0,Δ30-3Δ10＝0,Δ40-3Δ20＝0 (28)。
the invention has the beneficial effects that:
1) the invention adopts four-machine frequency multiplication self-synchronous driving, can realize double-frequency double-linear motion tracks of the machine body no matter 2 frequency multiplication or 3 frequency multiplication, can effectively improve the screening efficiency and the dehydration efficiency of screening equipment, meets the high-quality requirement of a vibration compaction forming component, effectively improves the vibration compaction forming effect, for example, improves the compactness of a precast concrete component, improves the working efficiency of the vibration compaction forming operation of the equipment and the like.
2) The invention can realize double-frequency double-linear track motion of the screening machine, effectively improve the treatment capacity and efficiency of the vibration equipment, and is particularly suitable for grading viscous materials, dehydrating engineering slurry and vibrating, compacting and molding concrete prefabricated components and precision casting components.
3) The invention adopts the double plastids, realizes the separation of the driving plastid and the working plastid on the premise of solving the problem of system vibration isolation, thereby not only protecting key driving components of the system and facilitating the maintenance of key vibration source components, but also indirectly simplifying the structure of the working plastid and realizing the full utilization of the working plastid.
Drawings
FIG. 1 is a dynamic model diagram of a four-engine driven two-mass system under vibration isolation conditions.
In the figure: 1, a vibration exciter 2; 2 plastid 1; 3, a vibration exciter 4; 4 plastid 2; 5, a vibration exciter 1; 6, a vibration exciter 3;
7, a spring A; 8 and a spring B.
The meaning of each parameter in the figure is as follows:
ox-absolute coordinate system
O- -center of plastid 1;
O1-the centre of rotation of exciter 1;
O2-the center of rotation of exciter 2;
O3-the center of rotation of the exciter 3;
O4-the center of rotation of the exciter 4;
Figure BDA0002802128300000111
-the rotational phase angle of exciter 1;
Figure BDA0002802128300000112
-the rotational phase angle of exciter 2;
Figure BDA0002802128300000113
-the rotational phase angle of exciter 3;
Figure BDA0002802128300000114
-the rotational phase angle of exciter 4;
Figure BDA0002802128300000115
-exciter 1 rotation angular velocity;
Figure BDA0002802128300000116
-exciter 2 rotation angular velocity;
Figure BDA0002802128300000117
-rotational angular velocity of exciter 3;
Figure BDA0002802128300000118
-exciter 4 rotation angular velocity;
m01-exciter 1 mass;
m02-exciter 2 mass;
m03-exciter 3 mass;
m04-exciter 4 mass;
r1-the eccentricity of the exciter 1;
r2-eccentricity of exciter 2
r3-eccentricity of the exciter 3
r4-exciter 4 eccentricity
m1-mass 1 of plastids;
m2plastid 2 mass;
k1x-the stiffness coefficient of spring a in the x-direction;
k2xthe stiffness coefficient of spring B in the x-direction.
FIG. 2 is a graph of stability index versus operating frequency for 1.0 η;
FIG. 3 is a graph of stability index versus operating frequency for different values of η:
(a) double frequency synchronization;
(b) and (5) triple frequency synchronization.
Fig. 4 shows the result of frequency doubling simulation under the condition of η ═ 1.0:
(a) four motor rotating speeds;
(b) eccentric rotors 1 and 2 are out of phase;
(c) eccentric rotors 2 and 3 are out of phase;
(d) eccentric rotors 3 and 4 are out of phase;
(e) displacement of masses 1 and 2 in the x-direction;
(f) steady state displacement of masses 1 and 2 in the x-direction;
(g) relative displacement of the masses 1 and 2 in the x-direction.
Fig. 5 shows the results of frequency tripled simulation under the condition of η ═ 1.0:
(a) four motor rotating speeds;
(b) eccentric rotors 1 and 2 are out of phase;
(c) eccentric rotors 2 and 3 are out of phase;
(d) eccentric rotors 3 and 4 are out of phase;
(e) displacement of masses 1 and 2 in the x-direction;
(f) steady state displacement of masses 1 and 2 in the x-direction;
(g) relative displacement of the masses 1 and 2 in the x-direction.
Detailed description of the preferred embodiments
Example 1:
assuming parameters of the vibration system: m is1＝600kg，m2＝1500kg，k1x＝2000kN/m，k2x＝100kN/m，r＝0.15m，m0＝30kg,ξ1x＝0.02,ξ2xThe natural frequency of the main vibration system is easily found from the parameters of the vibration system at 0.007:
Figure BDA0002802128300000131
and vibration isolation system natural frequency:
Figure BDA0002802128300000132
type of electric motors 1 and 2: three-phase squirrel-cage type, 50Hz, 380V, 6-pole, 0.70kW, rated rotation speed: 2500 r/min. The parameters of the motors 1 and 2 are set: rotor resistance Rr3.40 Ω, stator resistance Rs3.37 omega mutual inductance Lm168mH, rotor inductance Lr180mH, stator inductance L s180 mH. Types of motors 3 and 4: three-phase squirrel-cage type, 50Hz, 380V, 6-pole, 1.15kW, rated rotation speed: 2500 r/min. The parameters of the motors 3 and 4 are set: rotor resistance Rr3.20 Ω, stator resistance Rs3.18 omega mutual inductance Lm154mH, rotor inductance Lr160mH, stator inductance Ls＝160mH。
H is defined according to the expression formulas (20) and (26) of the doubling synchronous stability criterion2＝3ε2a31 k 12 is a double frequency stability index, H3＝ε2a31Is the triple frequency stability index. FIG. 2 shows H2、H3The relationship with the excitation frequency, H, can be seen as the excitation frequency omega increases2First decreasing rapidly and then decreasing slowly and gradually approaching 0, while H3Remain substantially unchanged. But H2And H3Is always greater than 0, H2And H3The positive and negative of (2) directly influence the stable area of the phase difference, which shows that no matter how large the frequency is, the double frequency and triple frequency synchronization only have one stable state, and the stable area only has one condition.
The mass relationship between eccentric rotors of the vibration exciter is changed to obtain the variation curve of the frequency doubling and frequency tripling synchronous stability indexes with the operating frequency under the condition of different eta values, as shown in figure 3. It can be seen that the magnitude of eta does not change H2And H3The larger η, the larger the stability index. And for a double frequency stability index H2In other words, the larger η, the more pronounced the tendency to decrease with increasing frequency; h corresponding to different eta after the frequency is increased to a certain value2The values are substantially equal, indicating that the greater the frequency, the less the mass of the eccentric rotor has an effect on the stability of the double frequency synchronisation.
Example 2:
and (3) applying a fourth-order Runge-Kutta program to the formula (1) to realize the simulation of the dynamic characteristics of the system, and respectively obtaining the simulation results of the system under the synchronous conditions of double frequency and triple frequency.
(a) Simulation of system under double frequency condition
In the simulation process, the power supply frequency of the motor is adjusted to change the rotating speed of the motor, the power supply frequency of the motors 1 and 2 is set to be 20Hz, the power supply frequency of the motors 3 and 4 is set to be 40Hz, the obtained rotating speed of the motors is shown in figure 4(a), it can be seen that the rotating speed of the motors 1 and 2 is approximately stabilized at 1000r/min, the rotating speed of the motors 3 and 4 is stabilized at about 2000r/min, therefore, the system realizes frequency doubling synchronization, and the excitation frequency is omega ≈ 104.7rad/s > omega ≈ at the moment0. The eccentric rotor mass of the given four vibration exciters is the same, namely: η is 1.0, and a pi/4 phase disturbance is added to the electric machine 3 at 20 s.
From fig. 4(b) - (d), it can be seen that the phase difference between any two exciters is stable around 0 degrees, where the transition time for the double frequency synchronization phase difference to be stable is longer, which indicates that the double frequency synchronization is more difficult to achieve than the fundamental frequency synchronization. After the disturbance, the phase difference fluctuates rapidly and then returns to a steady state, and the steady value is the same as before. The displacement response curves of the two masses in the x direction are shown in fig. 4(e), and the specific motion forms of the masses 1 and 2 in the steady state are clearly seen from the partially enlarged view of fig. 4(f), and the motion forms are found to be different and opposite.
It is evident from FIG. 4(f) that the amplitude of the mass 1 is large, about 8.0 mm; the vibration of the mass 2 is weak, and the maximum displacement is 0.5 mm. Relative displacement x of two masses1-x2It can be seen from fig. 4(g) that the motion form is similar to that of the main vibrating body 1, the maximum displacement at the steady state is about 8.5mm, the displacements of the two bodies just realize the forward superposition, and the motion form of the system is the reverse phase relative motion.
(b) Simulation of system under triple frequency condition
The power supply frequency of the motor is changed, the frequency of the motors 1 and 2 is set to be 15Hz, the frequency of the motors 3 and 4 is set to be 45Hz, and a simulation result graph of the system under the triple frequency condition can be obtained. Looking at FIG. 5(a), it can be seen that the rotation speeds of the motors 1 and 2 are stabilized at about 770r/min, the rotation speeds of the motors 3 and 4 are about 2300r/min, the operating frequency is about 80.6rad/s, and the motor 3 is given a pi/4 interference at 20 s.
As shown in fig. 5(b) to (d), it can be seen that the phase difference between any two exciters is stable at about 0 degree, and the change of the stable phase difference value is not affected after the interference is applied. Fig. 5(e) shows the displacement response curves of the masses 1 and 2, and it can be seen from the enlarged view 5(f) that the specific motion process in the steady state is that the amplitude of the mass 1 is larger than that of the mass 2, and the motion directions of the two masses are opposite, indicating that the system is performing opposite phase relative motion.
The relative motion displacement curves of the two masses are shown in fig. 5(g), and the motion forms in the steady state are similar to those of the main vibration mass 1. Compared with double frequency synchronization, the specific motion form is different, and the shock wave generation can be responded similarly, so that the displacement of the mass body can be rapidly increased, and the method is useful in engineering.

Claims (2)

1. The double-mass four-machine frequency-doubling self-synchronous driving vibrating machine is characterized in that a dynamic model of the vibrating system comprises: four vibration exciters, a mass 1, a mass 2, a spring A and a spring B; wherein the mass 1 is a main vibration mass, and the mass 2 is a vibration isolation mass; the plastid 1 is connected with the plastid 2 through a spring A, and the plastid 2 is connected with the foundation through a spring B; the four vibration exciters are respectively arranged on the left side and the right side of the mass 1 in pairs, each vibration exciter is provided with an eccentric rotor, the eccentric rotors are driven by respective induction motors to respectively rotate around the centers of the rotation axes, the rotating directions of the two eccentric rotors on the same side are opposite, and the vibration system equipment is driven to work in a self-synchronizing mode.
2. The method for determining the parameters of the double-mass quadrupler frequency multiplication self-synchronous driving vibrator of claim 1, which is characterized by comprising the following steps of:
step 1, establishing a dynamic model and a system motion differential equation;
establishing a coordinate system: four vibration exciters respectively surrounding the rotary central shaft o1,o2,o3And o4Rotating;
Figure FDA0002802128290000015
rotation angles of four eccentric rotors, respectively; the two masses have 1 degree of freedom respectively; the degree of freedom of the mass 1 is defined by x1The degree of freedom of the mass 2 is represented by x2Represents;
according to the Lagrange equation, obtaining a motion differential equation of the vibration system:
Figure FDA0002802128290000011
wherein the content of the first and second substances,
Figure FDA0002802128290000012
step 2, frequency multiplication synchronous analysis of four vibration exciters
The second term and the third term on the left side of the equal sign of the formula (1) are omitted; substituting the last four expressions of formula (1), removing x of formula (1)1And x2And take the rotation angle
Figure FDA0002802128290000013
To the second derivative of (1) to obtain
Figure FDA0002802128290000014
The approximate expression of (c) is:
Figure FDA0002802128290000021
wherein
Figure FDA0002802128290000022
Figure FDA0002802128290000023
In the formula, the small parameter epsilon is the ratio of the mass of the eccentric rotor of the vibration exciter to the total mass of the main vibration system; sigmai(i 1,2,3,4) represents the rotation direction of the eccentric rotor, and the clockwise direction is positive, and the following are included:
σ1＝σ3＝-1,σ2＝σ4＝1 (3)
the rotational phase angle is expressed as follows:
Figure FDA0002802128290000024
wherein
τ＝ωt,n1＝n2＝1
In the formula,. DELTA.iIs a function that varies slowly with the generation phase of the eccentric rotor due to the movement of the system;
substituting formula (4) into formula (3) to obtain:
Figure FDA0002802128290000031
the formula (5) is a basic expression for realizing synchronization of the vibration exciters;
writing equation (5) as a standard expression:
Figure FDA0002802128290000032
to formula (6)
Figure FDA0002802128290000033
Is derived again to
Figure FDA0002802128290000034
The differential equation expression of the following equation (5) is as follows:
Figure FDA0002802128290000035
Figure FDA0002802128290000036
in the second equation of the equation (7),
Figure FDA0002802128290000037
and small parameters
Figure FDA0002802128290000038
In proportion of viIs a slowly varying function; v is toiSlowly varying term Ω ofiSuperimposed with the small vibration term, the first approximate solution is refined:
Δi＝Δi,i＝1,2,3,4
Figure FDA0002802128290000039
wherein
σini+σjnjP is not equal to 0ij＝1/(σini+σjnj)，σini+σjnjWhen p is 0ij＝0
σini-σjnjQ is not equal to 0ij＝1/(σini-σjnj)，σini-σjnjQ when equal to 0ij＝0
The second approximate solution is improved in the same way:
Δi＝Δi,i＝1,2,3,4
Figure FDA0002802128290000041
substitution of formula (9) for formula (7) on the left, omegaiAnd ΔiTaking an average value of tau being 0-2 pi as a fixed value; considering that the exciters with the same rotation speed rotate reversely, the following expression is given:
Figure FDA0002802128290000042
Figure FDA0002802128290000043
wherein
σini+σjnjU when equal to 0s＝1,ψij *＝σiΔi+σjΔjOtherwise us＝0
σini-2σjnjU when equal to 0l＝1,γij *＝σiΔi-2σjΔjOtherwise ul＝0
σini-2σjnj+σrnrU when equal to 0d＝1,ηijr *＝σiΔi-2σjΔj+σrΔrOtherwise ud＝0
In the formula, according to
Figure FDA0002802128290000044
To find a stable solution, the structure of the system is symmetric, as follows:
a12＝a21＝1,a34＝a43,a13＝a14＝a23＝a24,α1＝α2,α3＝α4,k1＝k2,k3＝k4
when the rotating speeds are the same, the term epsilon of the formula (10) is obtained, and the following terms are included:
Figure FDA0002802128290000045
Figure FDA0002802128290000046
Figure FDA0002802128290000047
Figure FDA0002802128290000051
Figure FDA0002802128290000052
when the system is in a steady state, the expression of the parameters in equation (11) is:
Figure FDA0002802128290000053
step 3, deducing the synchronization and stability conditions of the four vibration exciters
(1) The same frequency, the ratio of the rotating speed is 1:1, and the conditions for realizing the fundamental frequency synchronization among the vibration exciters are as follows:
Figure FDA0002802128290000054
(2)n3＝n4stabilisation of exciters 3 and 4 when 2The rotating speed is twice of that of the vibration exciters 1 and 2, and double-frequency synchronization is realized between the vibration exciters; in formula (10) with respect to
Figure FDA0002802128290000055
Considering equation (13), the following relationship is obtained:
Figure FDA0002802128290000056
in equation (14), the frequency doubling synchronization condition is given by:
Figure FDA0002802128290000057
Figure FDA0002802128290000058
assuming a steady state phase angle Δi0And Ωi0Having a slight deviation of δiAnd xiiThus, there are:
Δi＝Δi0+δi,Ωi＝Ωi0+ξi,i＝1,2,3,4 (16)
the formula (16) is substituted into the formula (10) to obtain a system differential equation expression as follows:
Figure FDA0002802128290000061
rearrangement of formula (17) to give a value related toi(i ═ 1,2,3,4) is given by:
Figure FDA0002802128290000062
the characteristic equation of equation (18) with respect to the characteristic value λ is:
Figure FDA0002802128290000063
the following stability criterion was obtained according to the Router-Hurwitz criterion:
Figure FDA0002802128290000064
because of ε, α1 (1)，α3 (1)，a31，k1When both are greater than 0, the formula (20) is solved:
cos(Δ20-Δ10)＞0,cos(Δ30-2Δ10)＞0,cos(Δ40-2Δ20)＞0 (21)
the stable phase relation among the exciters is obtained by combining the formulas (13), (15) and (21):
Δ20-Δ10＝0,Δ40-Δ30＝0,Δ30-2Δ10＝0,Δ40-2Δ20＝0 (22)
(3)n3＝n4when the rotation speed is 3, the stable rotation speed of the vibration exciters 3 and 4 is three times that of the vibration exciters 1 and 2, the system realizes triple frequency synchronization, and a synchronization conditional expression (13) is changed into the following steps:
Figure FDA0002802128290000071
the synchronous conditions among the vibration exciters with the rotation speed ratio of 1:3 are as follows:
Figure FDA0002802128290000072
Figure FDA0002802128290000073
in order to seek a stable phase relation, as with a double frequency synchronous analysis method, an expression of the system in a stable state is solved, and a characteristic equation of the system is introduced as follows:
Figure FDA0002802128290000074
the stability criterion under the synchronous state is obtained by applying the Router-Hurwitz criterion analysis as follows:
Figure FDA0002802128290000075
the formula (26) is solved:
cos(Δ20-Δ10)＞0,cos(Δ30-2Δ10-Δ20)＞0,cos(Δ40-2Δ20-Δ10)＞0 (27)
similarly, the stable phase relation among the exciters is obtained by combining the formulas (13), (24) and (27):
Δ20-Δ10＝0,Δ40-Δ30＝0,Δ30-3Δ10＝0,Δ40-3Δ20＝0 (28)。
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1623684A (en) * 2004-12-20 2005-06-08 天津大学 Double super stable energy saving screen
CN201702104U (en) * 2010-06-30 2011-01-12 钟祥市新宇机电制造有限公司 Novel mining vibrating screen
US20150283581A1 (en) * 2012-10-26 2015-10-08 M-I L.L.C. Shaker with automatic motion
CN107252780A (en) * 2017-06-12 2017-10-17 东北大学 A kind of three machines driving double mass subresonance motor synchronizing probability equal thick screen and parameter determination method
CN207254743U (en) * 2017-09-12 2018-04-20 鞍山重型矿山机器股份有限公司 Vibrator flat placed type motor synchronizing classifying screen
CN109622368A (en) * 2018-12-17 2019-04-16 东北大学 A kind of subresonance energy saving type vibration screening/conveyer having effective vibration isolation function
CN109649965A (en) * 2018-12-17 2019-04-19 东北大学 A kind of parameter determination method of four machine of subresonance double mass driving vibrosieve conveyer

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1623684A (en) * 2004-12-20 2005-06-08 天津大学 Double super stable energy saving screen
CN201702104U (en) * 2010-06-30 2011-01-12 钟祥市新宇机电制造有限公司 Novel mining vibrating screen
US20150283581A1 (en) * 2012-10-26 2015-10-08 M-I L.L.C. Shaker with automatic motion
CN107252780A (en) * 2017-06-12 2017-10-17 东北大学 A kind of three machines driving double mass subresonance motor synchronizing probability equal thick screen and parameter determination method
CN207254743U (en) * 2017-09-12 2018-04-20 鞍山重型矿山机器股份有限公司 Vibrator flat placed type motor synchronizing classifying screen
CN109622368A (en) * 2018-12-17 2019-04-16 东北大学 A kind of subresonance energy saving type vibration screening/conveyer having effective vibration isolation function
CN109649965A (en) * 2018-12-17 2019-04-19 东北大学 A kind of parameter determination method of four machine of subresonance double mass driving vibrosieve conveyer

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