CN116984219A

CN116984219A - Four-machine homodromous driving self-balancing vibrating machine and parameter determination method

Info

Publication number: CN116984219A
Application number: CN202310889720.7A
Authority: CN
Inventors: 张学良; 胡文超; 陈晨; 李子谦; 张家鑫; 程壮壮; 张振彪; 闻邦椿
Original assignee: 东北大学
Priority date: 2023-07-20
Filing date: 2023-07-20
Publication date: 2023-11-03

Abstract

The invention belongs to the technical field of vibration devices, and discloses a four-machine homodromous driving self-balancing vibration machine and a parameter determining method. In the vibration system, four inner bodies are connected with an outer body through springs A and are symmetrically distributed on the outer body; the exosome is connected with the foundation through a spring B; the four vibration exciters are respectively arranged at the mass centers of the four working bodies, the rotation directions of the four vibration exciters are the same, and the self-synchronous vibration driving equipment works; and determining parameters by a parameter determination method, realizing synchronous conditions and stability conditions of synchronous and stable operation, finally searching a stable region of the system for realizing a self-balancing function, defining a self-balancing stable operation interval of the system, and completing experimental verification. The invention can effectively improve the working efficiency of the vibration equipment; the vibration isolation problem of the system is solved from the self-synchronization and self-balancing angles of the system, so that an additional vibration isolation strategy is avoided, noise pollution is reduced, energy is saved, environment is protected, system stability is improved, and service life is prolonged.

Description

Four-machine homodromous driving self-balancing vibrating machine and parameter determination method

Technical Field

The invention relates to the technical field of vibration devices, in particular to a four-machine homodromous driving self-balancing vibration machine and a parameter determining method.

Background

The self-synchronizing vibration equipment is one of important material treatment equipment in industrial production, and achieves the functions of vibrating crushing, conveying, feeding, screening, dewatering, ball milling, grinding, polishing, drying, cooling, forming, compacting, aging, separating, tamping, stirring, shakeout and the like of materials. For example, vibration screening equipment is equipment for classifying materials by utilizing vibration, and is mainly applicable to screening and classifying materials such as coal, ore, metal, chemical industry and the like; in industries such as cement, building materials and nonferrous metal ore dressing, crushed raw ore and other surface roughened products are required to be crushed or polished, and a vibration ball mill can achieve the functions, so that the vibration ball mill is used as a high-fine grinding treatment machine with high utilization rate in industrial production, and has a very large product application market. The conventional above-described vibration apparatus causes the following problems:

1. when the traditional vibration equipment meets the self vibration function requirement, the problems of overlarge noise, overlarge transmitted base load and the like are generated, and the defects can cause the vibration of buildings in the peripheral range of a factory with the equipment as the center, influence the peripheral environment and finally influence the health and normal life of human beings.

2. When the traditional vibration equipment runs, parts of the traditional vibration equipment are damaged in an accelerating way due to vibration, so that the equipment is unstable in running and reduced in function, and the processing and maintenance cost of the equipment is increased.

3. The traditional vibration equipment is mostly single-machine and double-machine driven single-body or double-body, and has low working efficiency, low productivity, low energy consumption, poor technological effect and the like.

Along with the continuous and intensive research on the vibration exciter synchronization theory, an advanced vibration synchronization technology is applied, and a vibration machine which can meet the requirements on functions and performances of equipment and realize the self-balancing function of the equipment is designed, so that the vibration machine has the advantages of high productivity, energy conservation, vibration suppression, noise reduction, environmental protection requirement satisfaction and the like. The patent creatively proposes a new self-balancing theory of a self-synchronizing system for the first time, which is one of effective ways for realizing the functional advantages of the vibration equipment.

Disclosure of Invention

The invention belongs to self-synchronous driving and self-balancing vibration conveying/feeding/sieving/dewatering/ball milling/grinding/polishing/drying/cooling/separating/stirring/shakeout equipment and the like. The invention aims to overcome the problems in the prior art, and is realized by the following technical scheme:

the technical scheme of the invention is as follows: a four-machine co-drive self-balancing vibratory machine, the four-machine co-drive self-balancing vibratory machine comprising: four vibration exciters, five plastids, a spring A and a spring B; the four inner plastids are connected with the outer plastid through a spring A, and the inner plastids are symmetrically distributed on the outer plastid in a rectangular shape; the exosome is connected with the foundation through a spring B; the four vibration exciters are respectively arranged at the mass centers of the four inner plastids; the vibration exciter comprises eccentric rotors and induction motors, wherein the eccentric rotors are driven by the respective induction motors and respectively rotate around the rotation axis center o of the respective vibration exciter ₁ ，o ₂ ，o ₃ ，o ₄ Rotating; the four vibration exciters are identical in rotation direction, and are driven in the same direction and self-synchronization mode, so that circular track movement and self-balancing of the inner mass are achieved.

The excitation isThe excitation frequency of the device is not more than the main natural frequency omega ₀ . When the excitation frequency of the vibration exciter is designed at the main natural frequency omega of the system ₀ and ω₄ When the system is in the sub-resonance region, the self-vibration suppression function can be realized, the output of the system is improved by realizing the circular motion track of four working bodies, the working region is selected in the first sub-resonance region, the exciting force required by the system for exciting the same amplitude in the working region is 1/5-1/3 of that required by the system under the ultra-far resonance condition, and the power of a driving motor required by the vibration system is reduced.

The parameter determining method of the four-machine homodromous driving self-balancing vibrating machine comprises the following steps:

step 1, establishing a dynamic model and a system motion differential equation;

establishing a coordinate system: the four vibration exciters respectively rotate around the central axis o ₁ ,o ₂ ,o ₃ and o₄ Rotating;the rotation angles of the four eccentric rotors respectively; line o between the inner and outer plastid centroids _i The angles between the-O and the positive direction of the x axis are respectively beta ₁ ，β ₂ ，β ₃ and β₄ A representation; the four vibration exciters are respectively arranged at the mass centers of the working bodies, so that the swing angles of the four working bodies are ignored, and only the swing response psi of the vibration isolation body is considered. The degree of freedom of the five-mass vibration system driven by the whole four machines in the same direction is as follows: the response of five plastids in the x-direction and the y-direction, respectively, i.e. x _i ，y _i I=1, 2,3,4,5, wherein the mass 5 is an exosome, and the wobble response ψ of the exosome, and the rotational phase angles of the four exciters +.>n＝1,2,3,4；

According to Lagrange equation, the motion differential equation of the four-machine homodromous driving five-mass vibration system is obtained as follows:

in the formula ,l₀ The distance between the rotation center of each vibration exciter and the mass center O of the four-machine same-direction driving five-mass vibration system is set; r is the eccentric radius of the four vibration exciters; m is m _0n N=1, 2,3,4, the eccentric rotor mass of the exciter n; m is m _i I=1, 2,3,4, being the mass of the endoplasmid i; m is M _i I=1, 2,3,4 for the mass sum of the inner mass i and the eccentric rotor mounted thereon; m is m ₅ Is the mass of the exosomes; j (J) _0n Moment of inertia of induction motor for exciter n, n=1, 2,3,4, j _0n ＝m _0n r ² ；J _m5 The rotational inertia of the outer body; j (J) _ψ The moment of inertia of the five-mass vibration system is driven in the same direction for the whole four machines; t (T) _en An electromagnetic torque of an induction motor of the exciter n, n=1, 2,3,4; f (f) _w Is a spring k _w Damping coefficients in x and y directions, w=1, 2,3,4,5; k (k) _w Is a spring k _w Stiffness coefficients in x and y directions, w=1, 2,3,4,5; wherein k is _w W=1, 2,3,4 is the spring a, k ₅ Is a spring B; the stiffness and damping coefficients of the springs A and B in the x and y directions are respectively equal; f (f) _ψ Damping coefficients of the five-mass vibration system driven by four machines in the same direction in the psi direction; k (k) _ψ The rigidity coefficient of the five-mass vibration system is driven in the same direction for four machines in the psi direction; f (f) _dn The motor shaft damping coefficient of the induction motor of the vibration exciter n is n=1, 2,3 and 4;

wherein ,

M ₁ ＝m ₁ +m ₀₁ ，M ₂ ＝m ₂ +m ₀₂ ，M ₃ ＝m ₃ +m ₀₃ ，M ₄ ＝m ₄ +m ₀₄ ，M ₅ ＝m ₅ ，

l _x1 -the horizontal distance from the connection point of the spring A connected to the left side of the inner mass and the inner mass to the center of the inner mass;

l _x2 -the horizontal distance from the connection point of the spring A connected to the left side of the inner mass and the outer mass to the center of the inner mass;

l _x3 -the horizontal distance from the connection point of the spring B connected to the right side of the outer body and the outer body to the center of the outer body;

l _y1 -the vertical distance from the connection point of the spring A connected to the right side of the inner mass to the center of the inner mass;

l _y2 -the vertical distance from the connection point of the spring A connected to the left side of the inner mass and the inner mass to the center of the inner mass;

l _y3 -the vertical distance from the connection point of the spring A connected below the inner mass to the center of the inner mass;

l _y4 -the vertical distance from the connection point of the spring A connected below the inner mass and the outer mass to the center of the inner mass;

l _y5 -the vertical distance from the connection point of the spring B connected below the outer body and the outer body to the center of the outer body;

step 2, determining the response of a four-machine homodromous driving five-mass vibration system;

step 3, determining the synchronism condition of the four vibration exciters;

and step 4, determining stability conditions of the four-machine homodromous driving five-mass system.

The method comprises the steps of determining that the response of the four-machine homodromous driving five-mass vibration system is steady-state response, wherein the step of obtaining the phase, the instantaneous angular speed and the instantaneous angular acceleration of an eccentric rotor is the steady-state response of each degree of freedom of the four-machine homodromous driving five-mass vibration system;

in the stable operation process of the four-machine homodromous driving five-mass vibration system, the average phase of the four eccentric rotors is set asInstantaneous average angular velocity of +.>The method comprises the steps of carrying out a first treatment on the surface of the The phase difference between adjacent eccentric rotors is set to 2 alpha in turn ₁ ，2α ₂ ，2α ₃ Then there is

Phase of four eccentric rotors and />The expression of (2) is

in the formula ,θ_n N=1, 2,3,4, being the difference between the phase of the eccentric rotor and the average phase in the exciter n;

when the system stably operates, the exciting forces applied to the system by the four exciters are periodically changed, so that the vibration of the system is also periodic. The least common multiple of four exciting force change periods is taken as T ₀ Let T be ₀ Inner omega _m0 (t) average value of omega _m The method comprises the steps of carrying out a first treatment on the surface of the Setting epsilon ₀ and ε_h Representation ofFor omega _m The instantaneous fluctuation coefficient of (1, 2, 3) h=h, then there is

Substituting the expression (3) into the expression (4) to obtain the instantaneous angular velocity and the instantaneous angular acceleration of the four eccentric rotors,

the steady-state response of each degree of freedom of the four-machine homodromous driving five-mass vibration system is obtained as follows;

In the stable operation process of the four-machine homodromous driving five-mass vibration system, angular acceleration changes of four vibration exciters are not considered, and meanwhile, in order to ensure structural symmetry of the four-machine homodromous driving five-mass vibration system, mass m is arranged _i i=1, 2,3,4 mass and eccentric rotor mass of four exciters are respectively kept consistent, and design parameters of four groups of springs A are consistent, namely

Based on transfer function method, obtaining steady-state response of four-machine homodromous driving five-mass vibration system as

wherein ,

z _ψ ＝ω _m /ω _nψ ，

r _l ＝l ₀ /l _e ，/>M＝4M ₀ +M ₅ +4m ₀ ，

γ ₇ ＝γ ₁₃ ＝γ ₁₉ ＝γ ₁ ，γ ₁₀ ＝γ ₁₅ ＝γ ₂₀ ＝γ ₅

γ ₃ ＝γ ₄ ＝γ ₆ ＝γ ₈ ＝γ ₉ ＝γ ₁₁ ＝γ ₁₂ ＝γ ₁₄ ＝γ ₁₆ ＝γ ₁₇ ＝γ ₁₈ ＝γ ₂

m-the total mass of the entire vibration system; l (L) _e -equivalent radius of rotation of the whole vibration system about its centroid; r is (r) _m -mass ratio of standard eccentric rotor to whole vibration system; omega _nψ -natural frequency of the vibration system in the direction ψ; zeta type toy _nψ Damping ratio of the whole vibration system in the psi direction; gamma ray _i -is the hysteresis angle between the plastid response and the exciter, i=1, 2,..21;

the method comprises the steps of determining the synchronism condition of the four vibration exciters, namely calculating to obtain the natural frequency of a four-machine co-drive five-mass vibration system in the x direction and the y direction; calculating aiming at the main natural frequency, and finally obtaining the synchronicity criterion of the four-machine homodromous driving five-mass system;

neglecting the influence of system damping, obtaining a stiffness matrix K, a mass matrix M and a characteristic equation of the four-machine co-drive five-mass vibration system in the x direction and the y direction by the formula (1) as follows:

When delta (omega) ² ) When the vibration system is=0, the natural frequency of the four-machine co-drive five-mass vibration system in the x direction and the y direction is calculated to be

The principal natural frequency is determined as follows, natural frequency ω ₅ The value is very small, the system captures the synchronous stability of the system in the starting stage before the steady-state operation is realized, so the synchronous stability of the system is not practically significant, and the natural frequency omega is not considered ₅ Then only drive the main natural frequency omega of the five-mass vibration system in the same direction for four machines ₀ and ω₄ Unfolding the study;

differential calculation is performed on the equation in the formula (7) to obtainAndsubstituting them into the last equation of equation (1) and considering equation (5), when the four-machine co-drive five-mass vibration system is in stable operation, omitting v ₁ ，ν ₂ ，ν ₃ ，ν ₄ Is then added to the higher order terms of (2) and the resulting equation is then given on both sides +.>The upper integral is used to obtain the single-period average differential equation of four eccentric rotors as

wherein ,

in the formula ,T_e0n For four induction machines at a frequency omega _m Electromagnetic torque, k, output during steady-state operation _e0n At a frequency omega for four motors _m Stiffness coefficient at steady state operation;

in the integration process, the phase difference 2α ₁ 、2α ₂ and 2α₃ Respectively by integrating the median values thereof and />Instead of;

selecting four motors with the same model, wherein the parameters are the same, namely J ₀₁ ＝J ₀₂ ＝J ₀₃ ＝J ₀₄ ＝m ₀ r ² ，f _d1 ＝f _d2 ＝f _d3 ＝f _d4 ＝f _d0 The method comprises the steps of carrying out a first treatment on the surface of the The formula (10) is written in the form,

wherein ,

A＝[a _nq ] _4×4 ，u＝[u ₁ u ₂ u ₃ u ₄ ] ^T

the formula (11) is a dimensionless coupling equation of the eccentric rotors of the four motors; wherein,for the period of operation T ₀ Instantaneous average angular velocity of the internal four exciter induction motors with respect to +.>N=1, 2,3,4; the matrix A and the matrix B are a dimensionless inertial coupling matrix and a dimensionless rigidity coupling matrix of four eccentric rotors respectively, and u _n The dimensionless load torque of the eccentric rotor of the four vibration exciters is represented, and n=1, 2,3 and 4;

in the operation period T ₀ Dimensionless average disturbance parameter of instantaneous average angular velocity of inner four eccentric rotors0 for ensuring synchronous operation of four eccentric rotors, where u=0 in formula (11) is obtained, the expression is organized as

In the formula (12), the amino acid sequence of the compound,is the kinetic energy of a standard vibration exciter, < >>When the eccentric rotors of the four vibration exciters realize synchronous operation, the effective load moment of the four motors is represented, and n=1, 2,3 and 4; in formula (12)> and />Differential of each other

wherein ,

in formula (13), (T) _e0n -f _dn ω _m )-(T _e0q -f _dq ω _m ) The difference of effective electromagnetic output torque of the exciter n motor and the exciter q motor is shown when the synchronous operation is realized;the difference of effective load torque of the exciter n motor and the exciter q motor when synchronous operation is realized;

Is provided with1.ltoreq.n < q.ltoreq.4 is about +.> and />Is obtained by sorting the bounded functions of formula (13)

The formula (14) is dimensionless, the right term of the equal sign is the difference of dimensionless load moment among four motors, and the left term of the equal sign is the difference of dimensionless effective electromagnetic output torque of any two motors; the right term of equation (14) relates to and />To obtain the constraint equation of (2)

in the formula ,τ_cnqmax Is thatIs the maximum value of (2);

the synchronization criterion of the four-machine co-drive five-mass system is obtained according to formulas (14) and (15), namely

Formula (16) is described as: the absolute value of the difference between the dimensionless effective electromagnetic output torques of any two motors is less than or equal to the maximum value of the difference between the dimensionless load torques of the two motors.

The stability condition of the four-machine same-direction driving five-plastid system is determined specifically as follows;

synchronously solving the phase difference between eccentric rotors of (12) and />First-order linearization is performed without considering the damping coefficient f of the motor shaft _dn N=1, 2,3,4, while taking into account formula (5)

wherein ,

in the formula ,is a function in parentheses-> and />A value at;

the finishing type (17) is carried out to obtain,

h=1, 2,3, and the phase difference disturbance parameter generalized system is obtained by rewriting the formula (18) into the following form

Wherein C= [ C ] _nh ] _3×3 Each parameter is

/>

The characteristic equation of the phase difference disturbance system is obtained according to det (C-lambda I) =0 and is as follows

λ ³ +d ₁ λ ² +d ₂ λ+d ₃ ＝0 (20)

According to the Routh-Hurwitz criterion, the parameters in the characteristic equation (20) satisfy the following conditions, and the equation (20) relates toIs stable to the zero-point of the (c) and,

d ₁ ＞0,d ₃ ＞0,d ₁ d ₂ ＞d ₃ (21)

wherein ,

d ₁ ＝-c ₁₁ -c ₂₂ -c ₃₃ ，d ₂ ＝-c ₁₂ c ₂₁ -c ₂₃ c ₃₂ -c ₁₃ c ₃₁ +c ₁₁ c ₂₂ +c ₂₂ c ₃₃ +c ₃₃ c ₁₁

d ₃ ＝-c ₁₁ c ₂₂ c ₃₃ -c ₁₂ c ₂₃ c ₃₁ -c ₁₃ c ₂₁ c ₃₂ +c ₁₁ c ₂₃ c ₃₂ +c ₂₂ c ₁₃ c ₃₁ +c ₃₃ c ₁₂ c ₂₁

satisfy the following requirementsI.e. < ->h=0, 1,2,3, from formula (5)>At the moment, the four-machine co-drive five-plastid system meets the Routh-Hurwitz criterion, so that the four-machine co-drive five-plastid system is stable, and the formula (21) is a condition that the system realizes synchronous and stable operation; obtaining the system stability capability coefficient H from (21) ₁ ，H ₂ and H₃ The following are listed below

H ₁ ＝d ₁ ＞0,H ₂ ＝d ₃ ＞0,H ₃ ＝d ₁ d ₂ -d ₃ ＞0 (22)。

The structural parameters and the motor parameters of the system are required to meet the synchronous conditions and the stable conditions, so that the corresponding characteristic curves under different parameters can be obtained, and further, the parameter matching of the self-vibration suppression function of the system can be reasonably determined. After each group of parameters meets two theoretical conditions, a phase frequency curve can be obtained, and a resonance area for realizing the function of the equipment can be determined through the curve. And further adjusting the excitation frequency to enable the excitation frequency to work in a resonance area for realizing the function of the equipment.

The invention has the beneficial effects that: according to the invention, four working bodies and one vibration isolation body are selected, the four working bodies are symmetrically arranged on the vibration isolation body, four machines are adopted for synchronous drive, and the vibration isolation problem of the system is effectively solved while the yield of the system is improved. The four circular motion tracks of the working mass are realized, and the processing efficiency and the working quality of the equipment can be effectively improved, such as the processing capacity and the efficiency of a screen machine and the vibration crushing and grinding effect of a vibration mill. The working area is selected in a first sub-resonance area, and the exciting force required by the system for exciting the same amplitude in the working area is 1/5-1/3 of that required by the system under the ultra-far resonance condition, so that the power of a driving motor required by the vibration system is reduced. Meanwhile, the system can realize a self-balancing function in the area, so that the amplitude of the vibration isolation body is effectively reduced, the energy consumption is reduced, and the energy conservation is realized.

Drawings

Fig. 1 is a diagram of a kinetic model of a four-machine co-drive five-mass vibration system.

In the figure: 1. a vibration isolation body; 2. a second working mass; 3. a second vibration exciter; 4. a first vibration exciter; 5. a first working mass; 6. a fourth vibration exciter; 7. a fourth working mass; 8. a spring B;9. a third vibration exciter; 10. a third working mass; 11. and a spring A.

Oxy- -an absolute coordinate system; o- -the center of the entire system; o (O) ₁ -a first exciter rotation center; o (O) ₂ -a second exciter rotation center; o (O) ₃ -a third exciter rotation center; o (O) ₄ -a fourth exciter rotation center;-a first exciter rotational phase angle; />-the second exciter rotational phase angle; />-a third exciter rotational phase angle; />-a fourth exciter rotational phase angle; m is m ₀₁ -the mass of the first exciter; m is m ₀₂ -the mass of the second exciter; m is m ₀₃ -the mass of the third exciter; m is m ₀₄ -fourth exciter mass; m is m ₁ -a first working mass; m is m ₂ -a second working mass; m is m ₃ -a third working mass; m is m ₄ -fourth mass of the working mass; m is m ₅ -mass of vibration isolation mass; r- -the eccentricity of the exciter; k (k) ₁ Spring A stiffness coefficient, k ₁ ＝k ₂ ＝k ₃ ＝k ₄ ；k ₅ -the stiffness coefficient of the spring B; beta ₁ Line o between working mass 1 and mass center of vibration isolation mass ₁ -O at an angle to the positive x-axis; beta ₂ Line o between working mass 2 and mass center of vibration isolation mass ₂ -O at an angle to the positive x-axis; beta ₃ Line o between working mass 3 and mass centre of vibration isolation mass ₃ -O at an angle to the positive x-axis; beta ₄ Line o between working mass 4 and mass center of vibration isolation mass ₄ -O at an angle to the positive x-axis; l (L) ₀ -center of rotation of each exciter and center of mass of systemDistance of O; l (L) _x1 -the horizontal distance from the connecting point of the spring A connected with the left side of the working body and the working body to the center of the working body; l (L) _x2 -the horizontal distance from the connecting point of the spring A and the vibration isolation body connected with the left side of the working body to the center of the working body; l (L) _x3 -the horizontal distance from the connection point of the spring B connected to the right side of the vibration isolation body and the vibration isolation body to the center of the vibration isolation body; l (L) _y1 -the vertical distance from the connection point of the spring A connected to the right side of the working body and the working body to the center of the working body; l (L) _y2 -the vertical distance from the connecting point of the spring A connected with the left side of the working body and the working body to the center of the working body; l (L) _y3 -the vertical distance from the connecting point of the spring A connected below the working mass and the working mass to the center of the working mass; l (L) _y4 -the vertical distance from the connecting point of the spring A and the vibration isolation body connected below the working body to the center of the working body; l (L) _y5 The vertical distance from the connecting point of the spring B and the vibration isolation body connected below the vibration isolation body to the center of the vibration isolation body; psi-the angle at which the vibration isolator oscillates about the central axis.

Fig. 2 is a system stability factor graph.

FIG. 3 (a) is a graph of the relationship of stable phase differences among four vibration exciters in a system steady state;

fig. 3 (b) is a graph showing the phase difference relationship between the system steady-state vibration exciter and the mass.

Fig. 4 is a system steady state response graph.

FIG. 5 (a) shows the results of a simulation of displacement of each mass in the x-direction in the resonance region I;

FIG. 5 (b) shows the results of a simulation of displacement of each mass in the y-direction in the resonance region I;

fig. 5 (c) shows the results of a displacement simulation of each mass of the resonance region I in the ψ -direction;

FIG. 5 (d) is a simulation result of the plastid motion trajectory of the resonance region I;

fig. 5 (e) is the rotational speeds of the four motors in the resonance region I;

fig. 5 (f) shows the phase difference between the exciters in the resonance region I.

FIG. 6 (a) is a graph showing the results of a simulation of displacement of each mass in the x-direction in the resonance region III;

FIG. 6 (b) is a graph showing the results of a simulation of displacement of each mass in the y-direction in the resonance region III;

FIG. 6 (c) shows the results of a simulation of displacement of the masses in the direction of ψ for resonance region III;

FIG. 6 (d) is a simulation result of each plastid motion trajectory in the resonance region III;

fig. 6 (e) is the rotational speeds of the four motors in resonance region III;

Fig. 6 (f) shows the phase difference between the exciters in the resonance region III.

FIG. 7 (a) shows the result of an experiment in which each of the masses was displaced in the x-direction at a power supply frequency of 17.4 Hz;

FIG. 7 (b) shows the result of a test of displacement of each mass in the y direction at a power frequency of 17.4 Hz;

FIG. 7 (c) shows the result of a test of displacement of each plasmid in the direction psi at a power frequency of 17.4 Hz;

FIG. 7 (d) is a graph showing the result of an enlarged view of the motion trace of each plasmid when the power supply frequency is 17.4 Hz;

fig. 7 (e) shows test results of the rotational speeds of the four motors at a power supply frequency of 17.4 Hz;

FIG. 7 (f) shows the results of a test for the phase difference between the vibration exciters at a power supply frequency of 17.4 Hz.

FIG. 8 (a) shows the result of an experiment in which each mass was displaced in the x-direction at a power supply frequency of 18.4 Hz;

FIG. 8 (b) shows the result of a test of displacement of each mass in the y direction at a power frequency of 18.4 Hz;

FIG. 8 (c) shows the result of a test of displacement of each plasmid in the direction psi at a power frequency of 18.4 Hz;

FIG. 8 (d) is a graph showing the result of an enlarged view of the motion trace of each plasmid at a power supply frequency of 18.4 Hz;

fig. 8 (e) shows the test results of the rotational speeds of the four motors at a power supply frequency of 18.4 Hz;

FIG. 8 (f) shows the result of a test of the phase difference between the vibration exciters at a power supply frequency of 18.4 Hz.

FIG. 9 (a) is a graph showing the result of an experiment in which each of the masses was displaced in the x-direction at a power supply frequency of 20.0 Hz;

FIG. 9 (b) shows the result of a test of displacement of each mass in the y direction at a power supply frequency of 20.0 Hz;

FIG. 9 (c) is a graph showing the result of a test in which each plasmid is displaced in the direction ψ when the power supply frequency is 20.0 Hz;

FIG. 9 (d) is a graph showing the result of an enlarged view of the motion trace of each plasmid at a power supply frequency of 20.0 Hz;

fig. 9 (e) shows test results of the rotational speeds of the four motors at a power supply frequency of 20.0 Hz;

fig. 9 (f) shows the test result of the phase difference between the vibration exciters at the power supply frequency of 20.0 Hz.

Detailed Description

In a dynamics model of the four-machine homodromous self-synchronous driving five-mass vibrating machine, an inner mass is a working mass, and an outer mass is a vibration isolation mass 1; the first vibration exciter 4, the second vibration exciter 3, the third vibration exciter 9 and the fourth vibration exciter 6 are respectively arranged on the first working body 5, the second working body 2, the third working body 10 and the fourth working body 7, the four working bodies are respectively connected with the vibration isolation body through a main vibration spring A11, and the working bodies are symmetrically distributed on the vibration isolation body; the vibration isolation body is connected with the foundation through a vibration isolation spring B8; the four vibration exciters are respectively arranged at the mass centers of the four working bodies, each vibration exciter is internally provided with an eccentric rotor, the eccentric rotors are driven by respective induction motors to rotate around the centers of the rotation axes respectively, the rotation directions of the four vibration exciters are the same, and the four vibration exciters are driven in the same direction and self-synchronous manner, so that the self-balancing function of the equipment and the circular track movement function of the four working bodies are realized.

Example 1: numerical qualitative analysis of four-machine homodromous driving five-mass mechanical system

Assume parameters of the vibration system: m is m _0i ＝10kg(i＝1,2,3,4)，m ₁ ＝m ₂ ＝m ₃ ＝m ₄ ＝m ₀ ＝1000kg，m ₅ ＝10000kg，J _m5 ＝1430kg·m ² ，k ₁ ＝k ₂ ＝k ₃ ＝k ₄ ＝k ₀ ＝18000kN/m，k ₅ ＝200kN/m，k _ψ ＝2000kN·m/rad，r＝0.15m，β ₁ ＝π/4，β ₂ ＝3π/4，β ₃ ＝-3π/4，β ₄ = -pi/4. The main natural frequency is easily obtained according to the parameters of the vibration system: omega ₀ ＝133.5rad/s，ω ₄ =158.2 rad/s. Electric powerType of motivation: three-phase squirrel cage, 50Hz,380V,6-pole,0.75kW, rated rotation speed: 980r/min. Setting motor parameters: rotor resistance R _r =3.40Ω, stator resistance R _s =3.35Ω, mutual inductance L _m Rotor inductance l=164 mH _r =170 mH, stator inductance L _s ＝170mH。

According to the ratio z of the operating frequency to the natural frequency ₀ and z₄ Dividing the entire frequency domain into three resonance regions, where z ₀ ＝ω _m /ω ₀ ，z ₄ ＝ω _m /ω ₄ . The three resonance regions are respectively: (1) zone I: omega ₀ and ω₄ Is the sub-resonance region of (z) ₀ < 1 and z ₄ < 1; (2) zone II: omega ₀ And ω ₄ Is the sub-resonance region of (z) ₀ > 1 and z ₄ < 1; (3) zone III: omega ₀ and ω₄ Is z ₀ > 1 and z ₄ ＞1。

(a) Stabilization capability of the system

According to H _i The expression of (i=1, 2, 3) can give the system stability ability coefficient map shown in fig. 2. As can be seen from fig. 2, the system has a stability factor greater than 0 over all three resonance regions, satisfying equation (22), indicating that the system can achieve synchronous stable operation over the entire frequency domain. H _i With omega _m Increasing by an increase up to ω _m Increasing to omega ₀ Nearby H _i Sharply increase and then decrease when ω _m Increasing to omega ₄ Nearby H _i Again sharply increase and then decrease, after which H _i Continue with omega _m And increases with increasing numbers of (c). H _i The value in region I is smallest, at resonance point omega ₀ and ω₄ Near reaching the maximum value, H _i The larger the value of (c) indicates a stronger system stability.

(b) Phase relation during steady state operation of system

Obtaining steady-state phase differences among four vibration exciters according to the formula (16) and the formula (22)Running alongFrequency omega _m The curve of the change is shown in fig. 3 (a). Within the resonance regions I and III, < >>The value of (2) is + -180 DEG, in engineering and />The operation states of the four corresponding exciters are the same, so that in the two regions the system is in a single equilibrium point state, i.e. +.>. In this case, plastid m _i The motion track of (i=1, 2,3, 4) is circular, and the mass m ₅ Subject plastid m _i The vibration forces transmitted by (i=1, 2,3, 4) cancel each other out, and the vibration isolation body m is theoretically ₅ Maintain stationary state, plastid m ₅ The dynamic load transferred to the foundation is zero, and the system has stronger self-balancing capability. Within the resonance region II, < >>The corresponding motion mode of the system is the circular motion of four working bodies. At this time, the exciter passes through the mass m _i (i=1, 2,3, 4) to plastid m ₅ The vibration forces of (2) are superimposed on each other, and the vibration isolation body also exhibits circular motion. In the area I, the vibration isolation effect of the system is good, the self-balancing capability is high, the stabilizing capability is strong, and the running frequency of the motor is low, so that the energy consumption of the system can be reduced, and the system is an ideal working area for meeting engineering practice demands.

FIG. 3 (b) is a plastid response x _i (i＝1,2,3,4,5)，y _i (i=1, 2,3,4, 5) and ψ and the hysteresis angle γ of the excitation force _i (i=1, 2,., 21) with operating frequency ω _m Graph of the curve of the change, gamma _i The expression of (2) is shown in the formula (7). As can be seen from FIG. 3 (b), within the resonance region I, γ ₁ Stabilized around 0 DEG, when the operating frequency omega _m Run to resonance point omega ₀ In the vicinity, gamma ₁ Gradually rise to omega _m Enter zone II, gamma ₁ Stabilized at about 180 DEG, omega ₄ Nearby, gamma ₁ Suddenly drops to about 2 pi/3 and then reverts to 180 deg., and remains in this state all the way through zone III. Gamma ray ₂ ,γ ₃ ,γ ₄ Stable at about 180 DEG and omega in zone I ₀ The vicinity drops suddenly until it stabilizes around 0 ° in zone II, and then at ω ₄ The vicinity continues to rise and stabilize at about 180 deg., and in zone III remains stable at 180 deg.. Likewise, gamma ₅ and γ₂₁ At omega _m ＜ω ₄ At approximately 180 DEG up to an operating frequency omega _m Run to resonance point omega ₄ In the vicinity, gamma ₅ Gradually decreasing to 0 deg. and maintaining this value all the way through zone III, while gamma ₂₁ Does not change near the resonance point and is stable at 180 ° over the entire frequency domain. Gamma ray _i (i=1, 2,.,. 5) a significant resonance effect occurs near the resonance point, and in engineering applications, the excitation frequency of the device is usually set far from the natural frequency ω ₀ and ω₄ Where it is located.

(c) Steady state response of system

Substituting the system parameters into formula (7) to obtain the system amplitude in the x and y directions, wherein the system amplitude in the x and y directions is the same, namely lambda, as can be seen from formula (7) _xi ＝λ _yi ＝λ _i (i=1, 2,3,4, 5). FIG. 4 is a graph of system amplitude versus operating frequency, lambda _i Corresponding to the magnitudes of the five masses, respectively. As can be seen, the four working masses have the same amplitude, in the region I (ω _m ＜ω ₀ ) In, lambda _i (i=1, 2,3, 4) with ω _m The increase is in an ascending trend, at omega ₀ Suddenly rising to the maximum value; zone II (omega) ₀ ＜ω _m ＜ω ₄ ) In, four working bodies have larger amplitude up to omega _m ＝ω ₄ The time begins to fall; zone III (omega) _m ＞ω ₄ ) In, with omega _m Gradually increase lambda _i (i=1, 2,3, 4) gradually decreases but the amplitude is greater than 0. Amplitude lambda of vibration isolation body ₅ Always 0 in zones I and III, the system has good self-balancing ability, which is similar to that of FIG. 3 (a) Between the vibration exciter in the area I and the area IIIIs identical with the condition of->When plastid m _i (i=1, 2,3, 4) to plastid m ₅ The vibratory forces of (2) cancel each other out, plastid m ₅ The stress is 0, and the corresponding amplitude is 0. The excitation frequency is close to the natural frequency omega ₀ and ω₄ When in resonance effect, lambda ₅ Rapidly rises to a maximum corresponding to the amplitude of zone II.

Example 2: simulation analysis of four-machine homodromous driving five-mass mechanical system

Simulation results of different resonance regions are given by the range-Kutta method for further analysis and verification of the results of numerical qualitative analysis. In engineering practice, the resonance areas I and III can realize effective vibration of equipment and effective vibration isolation, so that simulation analysis is only carried out on the areas I and III. Vibration system parameters and motor parameters are given above. In order to obtain the motion state of the system in different areas, the spring rate k is generally changed ₀ To adjust omega ₀ and ω₄ Is a value of (2).

(a) Simulation results for region I

The system parameters and motor parameters were identical to those of example 1. The set of parameters corresponds to the natural frequency of the system as and />. As can be seen in fig. 5 (e), the system is in a new synchronized state, as the rotational speed of the four motors drops to about 819r/min (corresponding to an operating frequency of 85.8 rad/s) at the same time due to the generation of coupling torque between the exciters after the system is energized for about 25 seconds. When the system operates for 150s, the second vibration exciter 3 is applied with Pi/2, after a short fluctuation, the rotational speed of the system returns to the rotational speed before disturbance, which indicates that the synchronous state of the system is stable. The frequency ratio between the operating frequency and the natural frequency corresponding to the set of kinetic parameters is +.> and />The corresponding operating frequency of the system in numerical characteristic analysis is omega through equivalent frequency ratio calculation _m ＝z ₀ ω ₀ ≈z ₄ ω ₄ Approximately 85.4rad/s, corresponding to l in FIG. 3 (a) ₁ Is located in the resonance region I.

In FIG. 5 (f), the phase difference between the four exciters is 2α when the system is in a new synchronous state after about 25 seconds of operation ₁ ＝2α ₂ ＝2α ₃ ＝2α ₄ The vibration forces of any two adjacent vibration exciters acting on the outer body are the same in size and opposite in direction, and the four vibration forces cancel each other out to show that the stress of the outer body is 0. After the system is interfered, the phase difference among the four vibration exciters is quickly restored to a steady state value before interference after short fluctuation, which shows that the system has strong anti-interference capability and is consistent with the analysis in the figure 3 (a).

Fig. 5 (a) and (b) depict the response of five plastids in the x and y directions, respectively. From the figure, it can be seen that the amplitudes of the four working masses in the x and y directions are almost the same, about 8.5mm each, and the amplitude of the vibration isolation mass is 0. After the disturbance is applied at 150s, the response of the system can be restored to the steady value before the disturbance. In fig. 5 (c), the system has a pivot angle of about 0 °, indicating that the vibration isolator has very little response in the x, y and ψ directions, and is substantially stationary.

Fig. 5 (d) is a diagram of the motion trajectories of five masses, and it can be seen that four working masses exhibit circular motion and that the vibration isolation mass is nearly stationary. If the working area of the vibration system is selected in the resonance area I, four screening boxes or grinding drums which realize circular motion can perform good screening and grinding treatment on the filling materials, and meanwhile, the load transmitted to a foundation by the system through the vibration isolation body can be greatly reduced, and the ideal condition is 0. The above results indicate that the system has good vibration strength and self-balancing capability in the resonance region I.

(b) Simulation results for region III

Adjusting spring rate k ₀ =6000 kN/m, the other parameters being unchanged, the set of parameters being calculated As can be seen from FIG. 6 (e), the corresponding rotational speed is 981r/min and the operating frequency is +.>The corresponding frequency ratios are +.>Obtaining corresponding omega of the system in characteristic analysis through equivalent frequency ratio calculation _m ＝z ₀ ω ₀ ≈z ₄ ω ₄ 177rad/s, with l of region III in FIG. 3 (a) ₂ Has the same dynamic characteristics. Fig. 6 (e) shows that the motor is operated to be in a synchronous state and kept stable about 60s after being electrified, pi/2 interference is applied to the vibration exciter 2 when the motor is electrified for 150s, and the stable states of the system are consistent before and after the interference is applied, so that the anti-interference capability of the system is strong.

In fig. 6 (f), the phase difference between the four vibration exciters is stabilized at 180 ° due to the action of the coupling moment and the load moment between the motors, and the vibration isolation body is stressed at 0, and the dynamic load transferred to the foundation is 0, so that the vibration isolation effect is good. In addition, fig. 6 (a) - (d) show that the amplitudes of the four working bodies in the x and y directions are the same, and are about 0.8mm, meanwhile, the motion track of the four working bodies is approximately circular, the vibration isolation bodies respond to 0 in the psi direction and keep static, and the system in the resonance region III can realize good vibration isolation and noise reduction effects. But the equipment in the I area can operate at a frequency lower than that in the III area to enable the sub-working mass to realize larger amplitude, reduce energy consumption and improve power.

Example 3: test analysis of four-machine homodromous driving five-mass mechanical system

In order to further verify the correctness of theory and numerical analysis, a test bed is built according to the model, and test research is carried out. The four selected motor parameters are as follows: 380V,50Hz,0.22kW, excitation force of 0-2.5kN and rated rotating speed of 2720r/min. The parameters of the vibration synchronous test system are as follows: m is m ₁ ＝m ₂ ＝m ₃ ＝m ₄ ＝m ₀ ＝17.71kg,m ₅ ＝128.70kg,m _0i ＝1.23kg，J _m5 ＝2.34kg·m ² ,k ₁ ＝k ₂ ＝k ₃ ＝k ₄ ＝k ₀ ＝256.90kN/m,k ₅ 139.38kN/m, r=0.025 m. The main natural frequency is easily obtained according to the parameters of the vibration system: omega ₀ ＝120.44rad/s,ω ₄ = 151.28rad/s. The four working bodies are symmetrically arranged on the vibration isolation body, and the four motors are respectively arranged at the mass centers of the four working bodies, and the rotation directions of the four motors are the same. In the test, the power supply frequency of the motor is regulated by the frequency converter to obtain different motor rotating speeds, and the exciting force of the vibration exciter can be regulated by regulating the included angle of the eccentric block, so that the larger the included angle is, the larger the eccentric force is. The rotation speed and the phase of the motor are measured by utilizing the pulse trigger point of the Hall sensor, the displacement of the plastid can be indirectly measured by the acceleration sensor, and the obtained acceleration curve is subjected to secondary integration to obtain a displacement curve. And importing data acquired by the intelligent signal analyzer into Matlab software for programming processing, and finally imaging through OriginPro 8.5, so that a rotating speed, a phase difference, a displacement response graph and the like can be obtained. And respectively carrying out synchronous test on four-machine same-direction driving five-mass vibration test tables with the power supply frequencies of 17.4Hz, 18.4Hz and 20.0 Hz.

(a) Test result of excitation frequency of 17.4Hz

Before the test, the power supply frequency of each motor is adjusted to 17.4Hz through the frequency conversion cabinet, and then power is supplied to four vibration motors simultaneously, and the test result is shown in figure 7. The vibration system vibrates the test bed severely in a period of time after being electrified, because the operation frequency of the four vibration exciters can pass through the low-order natural frequency of the system in the process of improving, resonance can be generated, and the resonance response is gradually reduced under the damping effect. The operation frequency of the motors is continuously improved, the coupling moment between the motors enables the four vibration exciters to realize synchronous operation, and the vibration system finally achieves a synchronous stable state.

As shown in FIG. 7 (e), when the system is operating in a stable and synchronous mode, the motor speed is stabilized around 955r/min (99.96 rad/s), at which time z ₀ ≈0.83，z ₄ And approximately 0.66, corresponding to the resonance region I (first sub-resonance region) of the system. FIG. 7 (f) shows the results of a test of the phase difference between the respective exciters, in which the phase difference between the four exciters after the initial stage of intense vibration is 2α at steady state ₁ ≈178.9°～186.4°，2α ₂ ≈174.2°～182.7°，2α ₃ ≈170.6°～180.4°。

Fig. 7 (a) (b) (c) shows the response of five masses in the x and y directions and the swing angle of the vibration isolation mass in the ψ direction, respectively. The response of the system in stable synchronous operation can be seen in the figure as follows: in the x direction, the maximum value of single amplitude of the four working bodies is about 0.90mm, and the vibration isolation body is about 0.05mm; in the y direction, the maximum value of single amplitude of the four working bodies is about 0.85mm, and the vibration isolation body is about 0.07mm; in the psi direction, the swing angle of the vibration isolation body is 0.3 degrees at most. From the enlarged graph, the vibration waveforms of the respective masses are periodically changed, and the first and third working masses, the second and fourth working masses are respectively close to the same-phase change, and the first and fourth working masses, the second and third working masses are respectively close to the opposite-phase change, so that the phase difference between the first and third working masses and the phase difference between the vibration exciters are approximately consistent. In this case, the exciting forces transmitted to the working body by the exciter cancel each other in the x and y directions, so that the force transmitted to the vibration isolation body by the working body is approximately 0, and the foundation is almost free from load. Fig. 7 (d) is an enlarged view of the motion trace of the mass, and it can be seen that the four internal masses in the test are approximately circular in motion and the vibration isolation mass is approximately stationary.

(b) Test result of excitation frequency of 18.4Hz

The power supply frequency of each motor was adjusted to 18.4Hz, and the results of the related test are shown in FIG. 8. Similar to the test result under the power supply frequency of 17.4Hz, after the vibration system is subjected to strong vibration for a period of time after being electrified, the system gradually reaches a stable synchronous operation state along with the increase of the operation frequency and the operation time by the generation of the coupling moment between the motors.

FIG. 8 (e) shows that the motor speed is approximately 1015r/min (106.29 rad/s) when the system is operating in steady and synchronous mode, z ₀ ≈0.88，z ₄ And approximately 0.70, corresponding to the resonance region I (first sub-resonance region) of the system. FIG. 8 (f) shows the results of the phase difference test between the exciters, the system corresponding to a value of 2α at steady state ₁ ≈177.6°～188.3°，2α ₂ ≈170.8°～180.5°，2α ₃ ≈170.0°～180.0°。

Fig. 8 (a) (b) (c) can see that the system steady state response is: in the x direction, the amplitudes of the four working masses are approximately equal and are about 1.18mm, and the vibration isolation mass amplitude is about 0.08mm; in the y direction, the amplitude of the four working bodies is about 1.14mm, and the vibration isolation body is about 0.11mm; in the direction psi, the maximum response of the vibration isolator is 0.3 deg.. As can be seen from the enlarged view, the first and third working masses, the second and fourth working masses are approximately in phase change in both x and y directions, and the response hysteresis angles of the first and fourth working masses, the second and third working masses are different from each other by about 180 ° in the x and y directions. In this steady state, the vibration isolator is excited by about 0, and the load that it responds to and transmits to the foundation is also about 0. It can be seen in fig. 8 (d) that the four working mass motion trajectories in the test are approximately circular, while the vibration isolation mass remains approximately stationary.

(c) Test results with excitation frequency of 20.0Hz

The power supply frequency of each motor is adjusted to 20.0Hz through the frequency conversion cabinet, and the related test result is shown in figure 9. Similar to the test results when the power supply frequency is 17.4Hz and 18.4Hz, in the initial stage after power-on, the vibration system generates strong vibration, and meanwhile, the rotating speed of the motor is rapidly increased until reaching the synchronous operation speed, and the coupling moment between the motors can enable the system to stably and synchronously operate.

FIG. 9 (e) shows that the power supply frequency is 20.0HzThe synchronous speed of the four motors is 1111r/min, namely 116.34rad/s, according to the motor speed diagram, at the moment, z ₀ ≈0.97，z ₄ Approximately 0.77, corresponding to the system with respect to ω ₀ and ω₄ Is defined as the sub-resonance region of (I) region. FIG. 9 (f) is a graph showing the results of a test on the phase difference between four vibration exciters under the test condition of 20.0Hz, in which the fluctuation range of the phase difference is 2α ₁ ≈178.1°～190.0°，2α ₂ ≈170.8°～177.9°，2α ₃ ≈171.8°～179.4°。

Fig. 9 (a) - (c) are response diagrams of the system: the amplitude of the four working masses is about 1.53mm in the x-direction and about 1.47mm in the y-direction; the vibration isolation body has an amplitude of about 0.17mm in the x direction and about 0.19mm in the y direction; the maximum response of the vibration isolation body in the psi direction is 0.5 deg.. From the enlarged view, it can be seen that the response of the vibration isolation body in the x and y directions is approximately 0, which is consistent with the enlarged view of the system motion trace in fig. 9 (d). In fig. 9 (d), the four working masses approximately exhibit circular motion, and the vibration isolation mass remains approximately stationary as compared to the response of the working masses.

The stable phase differences of the system in the three groups of test results are slightly different from the simulation results, but are consistent in nature. The reason for the deviation may be that even if four motor models are selected to be identical, the output torque thereof may not be identical. It is also possible that inaccuracy in the arrangement of the hall sensors leads to deviations in the measured phase or that the test stand structure is not completely symmetrical due to machining errors. The three groups of test results show that the vibration suppression of the vibration isolation body is realized while the effective vibration intensity of the four working bodies is realized in the resonance region I, which is required in engineering, and can provide reference for the self-balancing function design of self-synchronous vibration screening and ball milling equipment.

Claims

1. The four-machine homodromous driving self-balancing vibrating machine is characterized by comprising: four vibration exciters, five plastids, a spring A (11) and a spring B (8); wherein the four inner plastids are connected with the outer plastid through a spring A (11), and the inner plastids are symmetrically distributed on the outer plastid in a rectangular shape; the exosome is connected with the foundation by a spring B (8)Connecting; the four vibration exciters are respectively arranged at the mass centers of the four inner plastids; the vibration exciter comprises eccentric rotors and induction motors, wherein the eccentric rotors are driven by the respective induction motors and respectively rotate around the rotation axis center o of the respective vibration exciter ₁ ，o ₂ ，o ₃ ，o ₄ Rotating; the four vibration exciters are identical in rotation direction, and are driven in the same direction and self-synchronization mode, so that circular track movement and self-balancing of the inner mass are achieved.

2. The four-machine co-drive self-balancing vibrator according to claim 1, wherein the excitation frequency of the exciter is not greater than the main natural frequency ω ₀ 。

3. A parameter determining method of a four-machine co-drive self-balancing vibrator according to claim 1 or 2, comprising the steps of:

step 1, establishing a dynamic model and a system motion differential equation;

establishing a coordinate system: the four vibration exciters respectively rotate around the central axis o ₁ ,o ₂ ,o ₃ and o₄ Rotating;the rotation angles of the four eccentric rotors respectively; line o between the inner and outer plastid centroids _i The angles between the-O and the positive direction of the x axis are respectively beta ₁ ，β ₂ ，β ₃ and β₄ A representation; the degree of freedom of the five-mass vibration system driven by the whole four machines in the same direction is as follows: the response of five plastids in the x-direction and the y-direction, respectively, i.e. x _i ，y _i I=1, 2,3,4,5, wherein the mass 5 is an exosome, and the wobble response ψ of the exosome, and the rotational phase angles of the four exciters +.>

wherein ,

J _ψ ＝J _m5 +(m ₀₁ +m ₀₂ +m ₀₃ +m ₀₄ )(l ₀ ² +r ² )，

step 3, determining the synchronism condition of the four vibration exciters;

4. The method for determining parameters of a four-machine co-driven self-balancing vibration machine according to claim 3, wherein determining that the four-machine co-driven five-mass vibration system response is a steady-state response comprises obtaining a phase, an instantaneous angular velocity and an instantaneous angular acceleration of an eccentric rotor and a steady-state response of each degree of freedom of the four-machine co-driven five-mass vibration system;

In the stable operation process of the four-machine homodromous driving five-mass vibration system, the average phase of the four eccentric rotors is set asInstantaneous average angular velocity of +.>The phase difference between adjacent eccentric rotors is set to 2 alpha in turn ₁ ，2α ₂ ，2α ₃ Then there is

Phase of four eccentric rotors and />The expression of (2) is

the least common multiple of four exciting force change periods is taken as T ₀ Let T be ₀ Inner omega _m0 (t) average value of omega _m The method comprises the steps of carrying out a first treatment on the surface of the Setting epsilon ₀ and ε_h Representation ofFor omega _m The instantaneous fluctuation coefficient of (1, 2, 3) h=h, then there is

5. the method for determining parameters of a four-machine co-drive self-balancing vibration machine according to claim 4, wherein steady-state responses of degrees of freedom of the four-machine co-drive five-mass vibration system are obtained as follows;

wherein ,

z _ψ ＝ω _m /ω _nψ ，

r _l ＝l ₀ /l _e ，/>M＝4M ₀ +M ₅ +4m ₀ ，

6. the method for determining parameters of a four-machine co-driven self-balancing vibrator according to claim 5, wherein the condition for determining the synchronism of the four-vibration exciter is specifically that the natural frequencies of a four-machine co-driven five-mass vibration system in the x direction and the y direction are calculated; calculating aiming at the main natural frequency, and finally obtaining the synchronicity criterion of the four-machine homodromous driving five-mass system;

the rigidity matrix K, the mass matrix M and the characteristic equation of the four-machine co-drive five-mass vibration system in the x direction and the y direction are obtained by the method (1) as follows:

7. The method for determining parameters of four-machine co-drive self-balancing vibrator according to claim 6, wherein the main natural frequency is determined without consideration of natural frequency ω ₅ Then only drive the main natural frequency omega of the five-mass vibration system in the same direction for four machines ₀ and ω₄ Unfolding the study;

wherein ,

wherein

A＝[a _nq ] _4×4 ，u＝[u ₁ u ₂ u ₃ u ₄ ] ^T

in the operation period T ₀ Dimensionless average disturbance parameter of instantaneous average angular velocity of inner four eccentric rotors0 for ensuring synchronous operation of four eccentric rotors, where u=0 in formula (11) is obtained, the expression is set as follows;

In the formula (12), the amino acid sequence of the compound,is the kinetic energy of a standard vibration exciter, < >>When the eccentric rotors of the four vibration exciters realize synchronous operation, the effective load moment of the four motors is represented, and n=1, 2,3 and 4; in formula (12)> and />The interaction difference is obtained;

wherein ,

is provided withIs about-> and />Is obtained by sorting the bounded functions of formula (13)

in the formula ,τ_cnqmax Is thatIs the maximum value of (2);

8. The method for determining parameters of a four-machine co-drive self-balancing vibrator according to claim 6 or 7, wherein the determining conditions of stability of a four-machine co-drive five-mass system are specifically as follows;

wherein ,

in the formula ,is a function in parentheses-> and />A value at;

the finishing type (17) is carried out to obtain,

Wherein C= [ C ] _nh ] _3×3 Each parameter is

/>

λ ³ +d ₁ λ ² +d ₂ λ+d ₃ ＝0 (20)

d ₁ ＞0,d ₃ ＞0,d ₁ d ₂ ＞d ₃ (21)

wherein ,

satisfy the following requirementsI.e. < ->h=0, 1,2,3, from formula (5)>At the moment, the four-machine homodromous driving five-plastid system meets the Routh-Hurwitz criterion, so that the four-machine homodromous driving five-plastid system is stable, and the formula (21) realizes synchronization for the systemStable operating conditions; obtaining the system stability capability coefficient H from (21) ₁ ，H ₂ and H₃ The following are listed below