A four-machine co-directional drive self-balancing vibrator and parameter determination method

Abstract

The present invention belongs to the technical field of vibration devices, and discloses a four-machine co-rotating drive self-balancing vibrator and a parameter determination method. In this vibration system, four inner masses are connected to the outer mass through spring A and are symmetrically distributed on the outer mass; the outer mass is connected to the ground through spring B; four exciters are respectively installed at the centers of mass of the four working masses, and the four exciters rotate in the same direction to drive the equipment to work by self-synchronous vibration; parameters are determined through the parameter determination method to achieve the synchronization condition and stability condition for synchronous and stable operation, and finally find the stable region where the system realizes the self-balancing function, define the self-balancing stable operation interval of the system, and complete experimental verification. The present invention can effectively improve the working efficiency of vibration equipment; solve the vibration isolation problem of the system from the aspects of self-synchronization and self-balancing of the system itself, thereby eliminating the additional vibration isolation strategy, reducing noise pollution, saving energy and protecting the environment, and increasing the system stability and service life.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration devices, and particularly to a four-machine co-directional drive self-balancing vibrator and a parameter determination method. Background Art

[0002] Self-synchronous vibration equipment is one of the important material processing equipment in industrial production, and realizes functions such as vibration crushing, conveying, feeding, screening, dewatering, ball milling, grinding, polishing, drying, cooling, forming, densifying, aging, separating, ramming, stirring, shakeout, etc. of materials. For example, a vibrating screening device is a device that classifies materials by vibration, and is mainly applicable to the screening and classification of materials such as coal, ore, metal, and chemical industry; in industries such as cement, building materials, and non-ferrous metal beneficiation, it is necessary to crush or finish the surface of the original ore and other rough products after crushing. A vibrating ball mill can achieve these functions. As a high-fineness grinding and processing machine with a high usage rate in industrial production, the vibrating ball mill has a large product application market. The above traditional vibration equipment has many problems as follows:

[0003] 1. While realizing its own vibration function requirements, traditional vibration equipment will have problems such as excessive noise and excessive load transmitted to the foundation. These drawbacks will cause vibrations in the buildings within the surrounding area of the plant centered on the equipment, affecting the surrounding environment and ultimately affecting human health and normal life.

[0004] 2. When traditional vibration equipment is in operation, its components will be damaged more quickly due to vibration, which will further lead to unstable operation and reduced function of the equipment, increasing the processing and maintenance costs of the equipment.

[0005] 3. Most traditional vibration equipment is single-machine or double-machine driven single-mass or double-mass bodies, with low working efficiency, low production capacity, high energy consumption, and poor process effects of the equipment.

[0006] With the continuous in-depth research on the synchronous theory of exciters and the application of advanced vibration synchronization technology, it is imperative to design a vibrating machine that can not only meet the equipment function and performance requirements but also achieve the self-balancing function of the equipment, making it have high productivity, energy conservation, vibration suppression, and noise reduction, so as to meet the environmental protection requirements, etc. This patent innovatively proposes a new self-balancing theory for a self-synchronous system for the first time, which is one of the effective ways to realize the functional advantages of the above vibration equipment. Summary of the Invention

[0007] The present invention belongs to vibration conveying / feeding / screening / dewatering / ball milling / grinding / polishing / drying / cooling / separating / stirring / shakeout and other equipment with self-synchronous drive and self-balancing function. In order to overcome the problems existing in the prior art, the present invention is realized through the following technical solutions:

[0008] The technical solution of the present invention is as follows: A four-machine co-rotating self-balancing vibrator, which includes: four exciters, five masses, spring A and spring B; among them, four inner masses are connected to the outer mass through spring A, and the inner masses are symmetrically distributed in a rectangle on the outer mass; the outer mass is connected to the ground through spring B; four exciters are respectively installed at the centers of mass of the four inner masses; the exciter includes an eccentric rotor and an induction motor, and the eccentric rotor is driven by its respective induction motor and rotates around the centers o1, o2, o3, o4 of the rotation axes of their respective exciters; the four exciters rotate in the same direction, and the four-machine co-rotating self-synchronizing drive is used to realize the circular trajectory movement and self-balancing of the inner masses.

[0009] The excitation frequency of the exciter is not greater than the main natural frequency ω0. When the excitation frequency of the exciter is designed in the sub-resonance region of the main natural frequency ω0 and ω4 of the system, the system can realize the self-suppression vibration function, and at the same time realize the circular motion trajectory of the four working masses to improve the output of the system. The working area is selected in the first sub-resonance region. In this working area, the excitation force required for the system to excite the same amplitude is 1 / 5 to 1 / 3 of that under the condition of super-far resonance, reducing the driving motor power required for the vibration system.

[0010] A method for determining the parameters of a four-machine co-rotating self-balancing vibrator includes the following steps:

[0011] Step 1, establish a dynamic model and the system's differential equation of motion;

[0012] Establish a coordinate system: The four exciters rotate around their own rotation center axes o1, o2, o3, and o4 respectively; are the rotation angles of the four eccentric rotors respectively; the angles between the connection lines o i -O between the centers of mass of the inner mass and the outer mass and the positive direction of the x-axis are represented by β1, β2, β3, and β4 respectively; the four exciters are respectively installed at the centers of mass of each working mass, so the swing angles of the four working masses are ignored, and only the swing response ψ of the vibration isolation mass is considered. The degrees of freedom of the entire four-machine co-rotating five-mass vibration system are: the responses of the five masses in the x direction and the y direction respectively, that is, x i , y i , i = 1, 2, 3, 4, 5, where mass 5 is the outer mass, and the swing response ψ of the outer mass, as well as the rotation phase angles of the four exciters n = 1, 2, 3, 4;

[0013] According to the Lagrange equation, the differential equation of motion of the four-machine co-rotating five-mass vibration system is as follows:

[0014]

[0015]

[0016] In the formula, l0 is the distance between the rotation center of each exciter and the centroid O of the four-machine co-directional drive five-mass vibration system; r is the eccentric radius of the four exciters; m 0n is the eccentric rotor mass of exciter n, where n = 1, 2, 3, 4; m i is the mass of inner mass body i, where i = 1, 2, 3, 4; M i is the sum of the mass of inner mass body i and the eccentric rotor installed on it, where i = 1, 2, 3, 4; m5 is the mass of the outer mass body; J 0n is the moment of inertia of the induction motor of exciter n, where n = 1, 2, 3, 4, J 0n = m 0n r 2 ; J m5 is the moment of inertia of the outer mass body; J ψ is the moment of inertia of the entire four-machine co-directional drive five-mass vibration system; T en is the electromagnetic torque of the induction motor of exciter n, where n = 1, 2, 3, 4; f w is the damping coefficient of spring k w in the x and y directions, where w = 1, 2, 3, 4, 5; k w is the stiffness coefficient of spring k w in the x and y directions, where w = 1, 2, 3, 4, 5; among them, k w , where w = 1, 2, 3, 4 is spring A, and k5 is spring B; the stiffness and damping coefficients of spring A and B in the x and y directions are respectively equal; f ψ is the damping coefficient of the four-machine co-directional drive five-mass vibration system in the ψ direction; k ψ is the stiffness coefficient of the four-machine co-directional drive five-mass vibration system in the ψ direction; f dn is the damping coefficient of the motor shaft of the induction motor of exciter n, where n = 1, 2, 3, 4;

[0017] Among them,

[0018] M1 = m1 + m 01 , M2 = m2 + m 02 , M3 = m3 + m 03 , M4 = m4 + m 04 , M5 = m5,

[0019]

[0020]

[0021] l x1 -- The horizontal distance from the connection point of spring A connected to the left side of the inner mass body to the center of the inner mass body;

[0022] lx2 -- The horizontal distance from the connection point of spring A connected to the left side of the inner mass to the center of the inner mass;

[0023] l x3 -- The horizontal distance from the connection point of spring B connected to the right side of the outer mass to the center of the outer mass;

[0024] l y1 -- The vertical distance from the connection point of spring A connected to the right side of the inner mass to the center of the inner mass;

[0025] l y2 -- The vertical distance from the connection point of spring A connected to the left side of the inner mass to the center of the inner mass;

[0026] l y3 -- The vertical distance from the connection point of spring A connected to the lower side of the inner mass to the center of the inner mass;

[0027] l y4 -- The vertical distance from the connection point of spring A connected to the lower side of the inner mass to the center of the outer mass;

[0028] l y5 -- The vertical distance from the connection point of spring B connected to the lower side of the outer mass to the center of the outer mass;

[0029] Step 2, determine the response of the four-machine co-rotating five-mass vibration system;

[0030] Step 3, determine the synchronism condition of the four exciters;

[0031] Step 4, determine the stability condition of the four-machine co-rotating five-mass system.

[0032] The determination of the response of the four-machine co-rotating five-mass vibration system is a steady-state response, including obtaining the phase, instantaneous angular velocity and instantaneous angular acceleration of the eccentric rotor and the steady-state response of each degree of freedom of the four-machine co-rotating five-mass vibration system;

[0033] During the stable operation of the four-machine co-rotating five-mass vibration system, the average phase of the four eccentric rotors is set as The instantaneous average angular velocity is ; The phase differences between adjacent eccentric rotors are set as 2α1, 2α2, 2α3 in sequence, then there is

[0034]

[0035] The phases of the four eccentric rotors and The expressions are

[0036]

[0037] In the formula, θ n is the difference between the phase of the eccentric rotor in the exciter n and the average phase, where n = 1, 2, 3, 4;

[0038] When the system operates stably, the exciting forces applied to the system by the four exciters change periodically. Therefore, the vibration of the system is also periodic. Take the least common multiple of the change periods of the four exciting forces as T0, and assume that the average value of ω m0 (t) within T0 is ω m ; Let ε0 and ε h represent the instantaneous fluctuation coefficient of ω m , where h = 1, 2, 3, then there is

[0039]

[0040] Substitute Equation (3) into Equation (4) to obtain the expressions for the instantaneous angular velocity and instantaneous angular acceleration of the four eccentric rotors as

[0041]

[0042]

[0043] The steady-state responses of each degree of freedom of the four-machine co-rotating five-mass vibration system are obtained as follows;

[0044] During the stable operation of the four-machine co-rotating five-mass vibration system, the change in the angular acceleration of the four exciters is not considered. At the same time, to ensure the structural symmetry of the four-machine co-rotating five-mass vibration system, the masses of the masses m i i = 1, 2, 3, 4 and the masses of the eccentric rotors of the four exciters are kept consistent respectively, and the design parameters of the four groups of springs A are the same, that is

[0045]

[0046] Based on the transfer function method, the steady-state response of the four-machine co-rotating five-mass vibration system is

[0047]

[0048] Among them,

[0049]

[0050] z ψ = ω m / ω nψ ,

[0051] r l = l0 / le , M = 4M0 + M5 + 4m0,

[0052]

[0053]

[0054]

[0055] γ7 = γ 13 = γ 19 = γ1, γ 10 = γ 15 = γ 20 = γ5

[0056] γ3 = γ4 = γ6 = γ8 = γ9 = γ 11 = γ 12 = γ 14 = γ 16 = γ 17 = γ 18 = γ2

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] M —— The total mass of the entire vibration system; l e —— The equivalent radius of rotation of the entire vibration system about its center of mass; r m —— The mass ratio of the standard eccentric rotor to the entire vibration system; ω nψ —— The natural frequency of the vibration system in the ψ direction; ξ nψ —— The damping ratio of the entire vibration system in the ψ direction; γ i —— The lag angle between the mass body response and the exciter, i = 1, 2,..., 21;

[0067] The specific condition for determining the synchronism of the four exciters is to calculate the natural frequencies of the four-machine co-directionally driven five-mass vibration system in the x-direction and the y-direction; calculate for the main natural frequencies, and finally obtain the synchronism criterion of the four-machine co-directionally driven five-mass system.

[0068] Ignoring the influence of system damping, from Equation (1), the stiffness matrix K, mass matrix M, and characteristic equation of the four-machine co-directionally driven five-mass vibration system in the x-direction and the y-direction are as follows:

[0069]

[0070] When Δ(ω 2 ) = 0, the natural frequencies of the four-machine co-directionally driven five-mass vibration system in the x-direction and the y-direction are calculated as

[0071]

[0072]

[0073] The main natural frequencies are determined as follows. The value of the natural frequency ω5 is very small, and the system has captured it during the start-up stage before achieving steady-state operation. Therefore, it has no practical significance for the study of the system's synchronous stability, and the natural frequency ω5 is not considered. After that, only the main natural frequencies ω0 and ω4 of the four-machine co-directionally driven five-mass vibration system are studied.

[0074] Differentiate the equation in Equation (7) to obtain and Substitute them into the last equation of Equation (1), and considering Equation (5), when the four-machine co-directionally driven five-mass vibration system is operating stably, ignore the high-order terms of ν1, ν2, ν3, ν4, and then integrate both sides of the obtained equation on to obtain the single-period average differential equations of the four eccentric rotors as

[0075]

[0076] where

[0077]

[0078]

[0079]

[0080]

[0081] In the formula, T e0n is the electromagnetic torque output by the four induction motors operating at a steady state with a frequency of ω m , and k e0nFor four motors with frequency ω m The stiffness coefficient during steady-state operation;

[0082] During the above integration process, the phase differences 2α1, 2α2, and 2α3 are respectively replaced by their integral mean values and to replace;

[0083] Select four motors of the same model with the same parameters, i.e., J 01 = J 02 = J 03 = J 04 = m0r 2 , f d1 = f d2 = f d3 = f d4 = f d0 ; Equation (10) is written in the following form,

[0084]

[0085] where,

[0086] A = [a nq 4×4 , u = [u1 u2 u3 u4] T

[0087]

[0088]

[0089]

[0090] Equation (11) is the dimensionless coupling equation of the eccentric rotors of four motors; where, is the dimensionless average perturbation parameter of the instantaneous average angular velocity of the four excitator induction motors with respect to during the operating period T0, n = 1, 2, 3, 4; The matrices A and B are respectively the dimensionless inertial coupling matrix and the dimensionless stiffness coupling matrix of the four eccentric rotors, u n , representing the dimensionless load torque of the eccentric rotors of the four excitators, n = 1, 2, 3, 4;

[0091] The dimensionless average perturbation parameter of the instantaneous average angular velocity of the four eccentric rotors during the operating period T0 is 0, which is used to ensure the synchronous operation of the four eccentric rotors. At this time, u = 0 is obtained in Equation (11), and its expression is sorted out as

[0092]

[0093] ​In Equation (12), is the kinetic energy of the standard exciter, represents the effective load torque of the four motors when the eccentric rotors of the four exciters achieve synchronous operation, where n = 1, 2, 3, 4; Substitute and in Equation (12) and take the difference to obtain

[0094]

[0095] where,

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] In Equation (13), (T e0n -f dn ω m )-(T e0q -f dq ω m ) represents the difference in the effective electromagnetic output torque between the n-th motor and the q-th motor of the exciter when they achieve synchronous operation; represents the difference in the effective load torque between the n-th motor and the q-th motor of the exciter when they achieve synchronous operation;

[0103] Let 1 ≤ n < q ≤ 4 be a bounded function of and . Rearrange Equation (13) to obtain

[0104]

[0105] Equation (14) is a dimensionless equation. The right side of the equal sign is the dimensionless load torque difference between the four motors, and the left side of the equal sign is the dimensionless effective electromagnetic output torque difference between any two motors; The right side of Equation (14) is a constraint equation of and . Obtain

[0106]

[0107] where, τ cnqmax is the maximum value;

[0108] According to equations (14) and (15), the synchronization criterion of the four-machine co-directional drive five-mass system is obtained, that is

[0109]

[0110] Equation (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.

[0111] The specific determination of the stability condition of the four-machine co-directional drive five-mass system is as follows;

[0112] Linearize equation (12) at the synchronous solution of the phase difference between the eccentric rotors and , without considering the motor shaft damping coefficient f dn , n = 1, 2, 3, 4, and considering equation (5) at the same time, we get

[0113]

[0114] where

[0115] In the formula is the value of the function in the brackets at and ;

[0116] After arranging equation (17), we get

[0117]

[0118] h = 1, 2, 3, rewrite equation (18) into the following form, and the generalized system of phase difference perturbation parameters is obtained

[0119]

[0120] In the formula, C = [c nh 3×3 , and the parameters are

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] ​

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138] According to det(C - λI)=0, the characteristic equation of the phase difference perturbation system is

[0139] λ 3 + d1λ 2 + d2λ + d3 = 0 (20)

[0140] According to the Routh - Hurwitz criterion, the parameters in the characteristic equation (20) satisfy the following conditions, and the zero solution of equation (20) with respect to is stable,

[0141] d1 > 0, d3 > 0, d1d2 > d3 (21)

[0142] Among them,

[0143] d1 = - c 11 - c 22 - c 33 , d2 = - c 12 c 21 - c 23 c 32 - c 13 c 31 + c 11 c 22 + c 22 c 33 + c 33 c 11

[0144] d3 = -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

[0145] Satisfied That is h = 0, 1, 2, 3. It can be seen from Equation (5) that At this time, the four-machine co-directional drive five-mass system satisfies the Routh-Hurwitz criterion, so the four-machine co-directional drive five-mass system is stable. Equation (21) is the condition for the system to achieve synchronous and stable operation; from Equation (21), the system stability ability coefficients H1, H2, and H3 are as follows

[0146] H1 = d1 > 0, H2 = d3 > 0, H3 = d1d2 - d3 > 0 (22).

[0147] The structural parameters and motor parameters of the system need to satisfy the synchronous condition and the stable condition to obtain the corresponding characteristic curves under different parameters, and then reasonably determine the parameter matching for the system to achieve the self-suppression vibration function. After each set of parameters satisfies the two major theoretical conditions, a phase-frequency curve can be obtained. Through this curve, the resonance region for realizing the equipment function can be determined. Further adjust the excitation frequency to make it work in the resonance region for realizing the equipment function.

[0148] Advantages of the present invention: The present invention selects four working masses and one vibration isolation mass. The four working masses are symmetrically installed on the vibration isolation mass, and the four-machine co-directional self-synchronization drive is adopted. While improving the system output, the vibration isolation problem of the system is effectively solved. The circular motion trajectories of the four working masses can be realized, which can effectively improve the processing efficiency and working quality of the equipment, such as improving the processing capacity and efficiency of the screening machine, and the vibration grinding effect of the vibration mill. The working area is selected in the first sub-resonance region. In this working area, the excitation force required for the system to generate the same amplitude is 1 / 5 to 1 / 3 of that under the ultra-far resonance condition, reducing the driving motor power required for the vibration system. At the same time, the system can achieve the self-balancing function in this region, effectively reducing the amplitude of the vibration isolation mass, reducing energy consumption, and achieving energy conservation. Description of the Drawings

[0149] Figure 1 It is the dynamic model diagram of a five-mass vibration system driven by four machines in the same direction.

[0150] In the figure: 1. Vibration isolation mass; 2. Second working mass; 3. Second exciter; 4. First exciter; 5. First working mass; 6. Fourth exciter; 7. Fourth working mass; 8. Spring B; 9. Third exciter; 10. Third working mass; 11. Spring A.

[0151] Oxy - Absolute coordinate system; O - Center of the whole system; O1 - Rotation center of the first exciter; O2 - Rotation center of the second exciter; O3 - Rotation center of the third exciter; O4 - Rotation center of the fourth exciter; - Rotation phase angle of the first exciter; - Rotation phase angle of the second exciter; - Rotation phase angle of the third exciter; - Rotation phase angle of the fourth exciter; m 01 - Mass of the first exciter; m 02 - Mass of the second exciter; m 03 - Mass of the third exciter; m 04 - Mass of the fourth exciter; m1 - Mass of the first working mass; m2 - Mass of the second working mass; m3 - Mass of the third working mass; m4 - Mass of the fourth working mass; m5 - Mass of the vibration isolation mass; r - Eccentric distance of the exciter; k1 - Stiffness coefficient of spring A, k1 = k2 = k3 = k4; k5 - Stiffness coefficient of spring B; β1 - Angle between the line o1 - O connecting the centroid of working mass 1 and the vibration isolation mass and the positive x-axis; β2 - Angle between the line o2 - O connecting the centroid of working mass 2 and the vibration isolation mass and the positive x-axis; β3 - Angle between the line o3 - O connecting the centroid of working mass 3 and the vibration isolation mass and the positive x-axis; β4 - Angle between the line o4 - O connecting the centroid of working mass 4 and the vibration isolation mass and the positive x-axis; l0 - Distance between the rotation center of each exciter and the centroid O of the system; l x1 - Horizontal distance from the connection point of spring A connected to the left side of the working mass to the center of the working mass; l x2 - Horizontal distance from the connection point of spring A connected to the left side of the working mass to the center of the vibration isolation mass; l x3 - Horizontal distance from the connection point of spring B connected to the right side of the vibration isolation mass to the center of the vibration isolation mass; l y1 - Vertical distance from the connection point of spring A connected to the right side of the working mass to the center of the working mass; l y2 - Vertical distance from the connection point of spring A connected to the left side of the working mass to the center of the working mass; l y3-- The vertical distance from the connection point of spring A connected below the working mass to the center of the working mass; l y4 -- The vertical distance from the connection point of spring A connected below the working mass to the center of the vibration isolation mass; l y5 -- The vertical distance from the connection point of spring B connected below the vibration isolation mass to the center of the vibration isolation mass; ψ - The angle of swing of the vibration isolation mass around the central axis.

[0152] Figure 2 It is the diagram of the system stability ability coefficient.

[0153] Figure 3(a) is the diagram of the stable phase difference relationship among the four exciters in the system steady state;

[0154] Figure 3(b) is the diagram of the phase difference relationship between the exciter and the mass in the system steady state.

[0155] Figure 4 It is the diagram of the system steady state response.

[0156] Figure 5(a) is the simulation result of the displacement of each mass in the x direction in resonance region I;

[0157] Figure 5(b) is the simulation result of the displacement of each mass in the y direction in resonance region I;

[0158] Figure 5(c) is the simulation result of the displacement of each mass in the ψ direction in resonance region I;

[0159] Figure 5(d) is the simulation result of the motion trajectory of the mass in resonance region I;

[0160] Figure 5(e) is the rotational speed of the four motors in resonance region I;

[0161] Figure 5(f) is the phase difference between the exciters in resonance region I.

[0162] Figure 6(a) is the simulation result of the displacement of each mass in the x direction in resonance region III;

[0163] Figure 6(b) is the simulation result of the displacement of each mass in the y direction in resonance region III;

[0164] Figure 6(c) is the simulation result of the displacement of each mass in the ψ direction in resonance region III;

[0165] Figure 6(d) is the simulation result of the motion trajectory of each mass in resonance region III;

[0166] Figure 6(e) is the rotational speed of the four motors in resonance region III;

[0167] Figure 6(f) is the phase difference between the exciters in resonance region III.

[0168] Figure 7(a) shows the test results of the displacement of each mass in the x direction when the power supply frequency is 17.4 Hz;

[0169] Figure 7(b) shows the test results of the displacement of each mass in the y direction when the power supply frequency is 17.4 Hz;

[0170] Figure 7(c) shows the test results of the displacement of each mass in the ψ direction when the power supply frequency is 17.4 Hz;

[0171] Figure 7(d) shows the test results of the enlarged view of the movement trajectory of each mass when the power supply frequency is 17.4 Hz;

[0172] Figure 7(e) shows the test results of the rotational speeds of the four motors when the power supply frequency is 17.4 Hz;

[0173] Figure 7(f) shows the test results of the phase difference between the exciters when the power supply frequency is 17.4 Hz.

[0174] Figure 8(a) shows the test results of the displacement of each mass in the x direction when the power supply frequency is 18.4 Hz;

[0175] Figure 8(b) shows the test results of the displacement of each mass in the y direction when the power supply frequency is 18.4 Hz;

[0176] Figure 8(c) shows the test results of the displacement of each mass in the ψ direction when the power supply frequency is 18.4 Hz;

[0177] Figure 8(d) shows the test results of the enlarged view of the movement trajectory of each mass when the power supply frequency is 18.4 Hz;

[0178] Figure 8(e) shows the test results of the rotational speeds of the four motors when the power supply frequency is 18.4 Hz;

[0179] Figure 8(f) shows the test results of the phase difference between the exciters when the power supply frequency is 18.4 Hz.

[0180] Figure 9(a) shows the test results of the displacement of each mass in the x direction when the power supply frequency is 20.0 Hz;

[0181] Figure 9(b) shows the test results of the displacement of each mass in the y direction when the power supply frequency is 20.0 Hz;

[0182] Figure 9(c) shows the test results of the displacement of each mass in the ψ direction when the power supply frequency is 20.0 Hz;

[0183] Figure 9(d) shows the test results of the enlarged view of the movement trajectory of each mass when the power supply frequency is 20.0 Hz;

[0184] Figure 9(e) shows the test results of the rotational speeds of the four motors when the power supply frequency is 20.0 Hz;

[0185] Figure 9(f) shows the test results of the phase difference between exciters when the power supply frequency is 20.0 Hz. Detailed implementation

[0186] In the dynamic model of the four-machine co-rotating self-synchronous drive five-mass vibrator, the inner mass is the working mass, and the outer mass is the vibration isolation mass 1; the first exciter 4, the second exciter 3, the third exciter 9, and the fourth exciter 6 are respectively arranged on the first working mass 5, the second working mass 2, the third working mass 10, and the fourth working mass 7. The four working masses are respectively connected to the vibration isolation mass through the main vibration springs A11, and the working masses are symmetrically distributed on the vibration isolation mass; the vibration isolation mass is connected to the foundation through the vibration isolation spring B8; the four exciters are respectively installed at the centers of mass of the four working masses. Each exciter has an eccentric rotor, and the eccentric rotor is driven by its respective induction motor and rotates around the center of the rotation axis. The four exciters rotate in the same direction, and the four-machine co-rotating self-synchronous drive realizes the self-balancing function of the equipment and the circular trajectory movement function of the four working masses.

[0187] Example 1: Numerical qualitative analysis of the four-machine co-rotating five-mass mechanical system

[0188] Assume the parameters of the vibration system: m 0i =10 kg (i = 1, 2, 3, 4), m1 = m2 = m3 = m4 = m0 = 1000 kg, m5 = 10000 kg, J m5 =1430 kg·m 2 , k1 = k2 = k3 = k4 = k0 = 18000 kN / m, k5 = 200 kN / m, k ψ =2000 kN·m / rad, r = 0.15 m, β1 = π / 4, β2 = 3π / 4, β3 = -3π / 4, β4 = -π / 4. According to the parameters of the vibration system, it is easy to calculate the main natural frequencies: ω0 = 133.5 rad / s, ω4 = 158.2 rad / s. The type of the motor: three-phase squirrel-cage, 50 Hz, 380 V, 6-pole, 0.75 kW, rated speed: 980 r / min. Set the motor parameters: rotor resistance R r =3.40 Ω, stator resistance R s =3.35 Ω, mutual inductance coefficient L m =164 mH, rotor inductance L r =170 mH, stator inductance L s =170 mH.

[0189] According to the ratios z0 and z4 of the operating frequency to the natural frequency, the entire frequency domain is divided into three resonance regions, where z0 = ω m / ω0, z4 = ω m / ω4. The three resonance regions are respectively: (1) Region I: the sub-resonance region of ω0 and ω4, that is, z0 < 1 and z4 < 1; (2) Region II: the over-resonance region of ω0 and the sub-resonance region of ω4, that is, z0 > 1 and z4 < 1; (3) Region III: the over-resonance regions of ω0 and ω4, that is, z0 > 1 and z4 > 1.

[0190] (a) The stability ability of the system

[0191] According to H i (i = 1, 2, 3), the expression can obtain Figure 2 The stability ability coefficient diagram of the system as shown. From Figure 2 It can be seen that the stability ability coefficient values of the system in the three resonance regions are all greater than 0, satisfying Equation (22), indicating that the system can achieve synchronous and stable operation in the entire frequency domain. H i increases with the increase of ω m until ω m increases to near ω0, H i increases sharply and then decreases. When ω m increases to near ω4, H i increases sharply again and then decreases. After that, H i continues to increase with the increase of ω m . H i has the minimum value in Region I and reaches the maximum value near the resonance points ω0 and ω4. The larger the value of H i , the stronger the stability ability of the system.

[0192] (b) The phase relationship during the steady-state operation of the system

[0193] According to Equation (16) and Equation (22), the steady-state phase difference between the four exciters is obtained varying with the operating frequency ω m The curve is shown in Figure 3(a). In the resonance regions I and III, the value is ±180°. In engineering, and correspond to the same operating states of the four exciters. Therefore, in these two regions, the system is in a single equilibrium point state, that is, . In this case, the motion trajectories of the masses m i (i = 1, 2, 3, 4) are circular. The vibration forces transmitted by the masses m5 from the masses m i (i = 1, 2, 3, 4) cancel each other out. Theoretically, the vibration isolation mass m5 remains stationary, and the dynamic load transmitted by the mass m5 to the foundation is zero. At this time, the system has a strong self-balancing ability. In the resonance region II, , the corresponding motion form of the system is the circular motion of the four working masses. At this time, the exciters pass through the masses m i(i = 1, 2, 3, 4), the vibration forces transmitted to the vibration isolation mass m5 are superimposed on each other, and the vibration isolation mass also exhibits circular motion. In region I, the vibration isolation effect of the system is good, the self-balancing ability is high, the stability ability is strong, and the operating frequency of the motor is small, which can reduce the energy consumption of the system. It is an ideal working region to meet the requirements of engineering practice.

[0194] Figure 3(b) shows the response x of the mass i (i = 1, 2, 3, 4, 5), y i (i = 1, 2, 3, 4, 5) and ψ and the lag angle γ of the exciting force i (i = 1, 2,..., 21) varying with the operating frequency ω m The curve relationship diagram of the change, γ i The expression of is shown in Equation (7). It can be seen from Figure 3(b) that in the resonance region I, γ1 is stable near 0°. When the operating frequency ω m operates near the resonance point ω0, γ1 gradually rises until ω m enters region II, γ1 is stable at about 180°. Near ω4, γ1 suddenly drops to about 2π / 3, then returns to 180°, and remains in this state in region III. γ2, γ3, γ4 are stable at about 180° in region I, suddenly drop near ω0 until they are stable near 0° in region II, then continue to rise near ω4 and are stable at about 180°, and remain stable at 180° in region III. Similarly, γ5 and γ 21 are close to 180° when ω m < ω4 until the operating frequency ω m operates near the resonance point ω4, γ5 gradually drops to 0° and remains at this value in region III, while γ 21 does not change near the resonance point and is stable at 180° throughout the frequency domain. γ i (i = 1, 2,..., 5) all show obvious resonance effects near the resonance point. In engineering applications, the exciting frequency of the equipment is usually set far from the natural frequencies ω0 and ω4.

[0195] (c) Steady-state response of the system

[0196] Substitute the system parameters into Equation (7) to obtain the amplitudes in the x and y directions of the system. It can be seen from Equation (7) that the amplitudes in the x and y directions of the system are the same, that is, λ xi = λ yi = λ i (i = 1, 2, 3, 4, 5). Figure 4 is the curve graph of the system amplitude varying with the operating frequency. λ i corresponds to the amplitudes of the five masses respectively. It can be seen from the figure that the amplitudes of the four working masses are the same. In region I (ω m < ω0), λi (i=1,2,3,4) with ω m The increase shows an upward trend and suddenly rises to the maximum value at ω0; Zone II (ω0<ω m <ω4), the amplitudes of the four working masses are relatively large until ω m =ω4 and starts to decrease; Zone III (ω m >ω4), as ω m Gradually increase, λ i (i=1,2,3,4) gradually decreases, but the amplitude is greater than 0. The amplitude λ5 of the vibration isolation mass is always 0 in zones I and III, and the system has good self-balancing ability, which is consistent with the vibration exciter in zones I and III shown in Figure 3(a). The situation is consistent with that when When plastid m i (i=1,2,3,4) The vibration forces transmitted to mass m5 cancel each other out, the force on mass m5 is 0, and the corresponding amplitude is also 0. When the excitation frequency is close to the natural frequency ω0 and ω4, a resonance effect occurs, and λ5 quickly rises to the maximum value, corresponding to the amplitude of zone II.

[0197] Example 2: Simulation analysis of a five-mass mechanical system driven by four machines in the same direction

[0198] In order to further analyze and verify the results of numerical qualitative analysis, the simulation results of different resonance regions are given by the Runge-Kutta method. In engineering practice, the resonance regions I and III can achieve both effective vibration and effective vibration isolation of the equipment, so only regions I and III are simulated and analyzed. The vibration system parameters and motor parameters are given above. In order to obtain the motion state of the system in different regions, the values of ω0 and ω4 are generally adjusted by changing the spring stiffness k0.

[0199] (a) Simulation results of region I

[0200] The system parameters and motor parameters are consistent with those of Example 1. The natural frequency of the system corresponding to this set of parameters is: and . Four identical exciters are powered at the same frequency at the same time. As can be seen in Figure 5(e), about 25 seconds after the system is powered on, due to the generation of coupling torque between the exciters, the speeds of the four motors simultaneously drop to about 819r / min (corresponding to an operating frequency of 85.8rad / s). At this time, the system is in a new synchronous state. When the system runs for 150s, a π / 2 interference is applied to the second exciter 3. After a short fluctuation, the speed of the system returns to the speed before the interference, indicating that the synchronous state of the system is stable. The frequency ratio between the operating frequency and the natural frequency corresponding to this set of dynamic parameters is and , the operating frequency corresponding to the system in the numerical characteristic analysis is calculated by the equivalent frequency ratio as ω m = z0ω0 ≈ z4ω4 ≈ 85.4 rad / s, corresponding to l1 in Fig. 3(a), located in resonance region I.

[0201] In Fig. 5(f), when the system is in a new synchronous state after running for about 25 s, the phase differences between the four exciters are 2α1 = 2α2 = 2α3 = 2α4 = 180°. At this time, the vibration forces exerted on the outer mass by any two adjacent exciters are the same in magnitude and opposite in direction, and the four vibration forces cancel each other out, showing that the force on the outer mass is 0. After the system is disturbed, the phase differences between the four exciters quickly return to the steady-state value before the disturbance after a short fluctuation, which indicates that the system has strong anti-interference ability, consistent with the analysis in Fig. 3(a).

[0202] Figs. 5(a) and (b) respectively describe the responses of the five masses in the x and y directions. It can be seen from the figures that the amplitudes of the four working masses in the x and y directions are almost the same, both about 8.5 mm, and the amplitude of the vibration isolation mass is 0. After the disturbance is applied at 150 s, the response of the system can recover to the stable value before the disturbance. In Fig. 5(c), the swing angle of the system is about 0°, indicating that the vibration isolation mass has little response in the x, y, and ψ directions and is basically in a stationary state.

[0203] Fig. 5(d) is the motion trajectory diagram of the five masses. It can be seen that the four working masses show circular motion, and the vibration isolation mass is almost stationary. If the working area of this vibration system is selected in resonance region I, the four screening boxes or grinding cylinders that achieve circular motion can perform good screening and grinding on the filled materials. At the same time, the load transmitted by the system to the foundation through the vibration isolation mass can be greatly reduced, and it is 0 in the ideal state. The above results show that the system has good vibration intensity and self-balancing ability in resonance region I.

[0204] (b) Simulation results in region III

[0205] Adjust the spring stiffness k0 = 6000 kN / m, keep other parameters unchanged, and calculate the corresponding It can be seen from Fig. 6(e) that the corresponding rotational speed when the four motors run synchronously and stably is 981 r / min, and the operating frequency is The corresponding frequency ratios are The ω corresponding to the system in the characteristic analysis is calculated by the equivalent frequency ratio m=z0ω0≈z4ω4≈177rad / s, which has the same dynamic characteristics as l2 in zone III in Figure 3(a). Figure 6(e) shows that the motor runs to the synchronous state and remains stable about 60s after power-on. When 150s after power-on, a π / 2 interference is applied to the exciter 2, and the stable state of the system before and after the interference is applied is consistent, indicating that the system has strong anti-interference ability.

[0206] In Figure 6(f), due to the coupling torque and load torque between the motors, the phase difference between the four exciters is stabilized at 180°, which is similar to the dynamic characteristics of zone I. The force on the vibration isolation mass is 0, and the dynamic load transmitted to the foundation is 0, which has a good vibration isolation effect. In addition, Figures 6(a)-(d) show that the amplitudes of the four working masses in the x and y directions are the same, both about 0.8 mm. At the same time, the motion trajectories of the four working masses are approximately circular, and the vibration isolation mass responds to 0 in the ψ direction and remains stationary. In the resonance zone III, the system can also achieve a good vibration isolation and noise reduction effect. However, the equipment in zone I can operate at a frequency lower than that in zone III, so that the sub-working mass can achieve a larger amplitude, reduce energy consumption, and increase power.

[0207] Example 3: Experimental analysis of a five-mass mechanical system driven by four machines in the same direction

[0208] In order to further verify the correctness of the theoretical and numerical analysis, a test bench was built according to the model for experimental research. The parameters of the four motors selected are: 380V, 50Hz, 0.22kW, exciting force 0-2.5kN, rated speed 2720r / min. The parameters of the vibration synchronization test system are: m1=m2=m3=m4=m0=17.71kg, m5=128.70kg, m 0i =1.23kg, J m5 =2.34kg·m 2, k1 = k2 = k3 = k4 = k0 = 256.90 kN / m, k5 = 139.38 kN / m, r = 0.025 m. According to the parameters of the vibration system, the main natural frequencies can be easily obtained: ω0 = 120.44 rad / s, ω4 = 151.28 rad / s. The four working masses are symmetrically installed on the vibration isolation mass, and the four motors are respectively installed at the centers of mass of the four working masses, and their rotation directions are the same. In the experiment, the supply frequency of the motors is adjusted by the frequency converter to obtain different motor speeds, and the exciting force of the exciter can be adjusted by adjusting the angle of the eccentric block. Generally, the larger the angle, the greater the eccentric force. The rotation speed and phase of the motor are measured by using the pulse trigger point of the Hall sensor, and the displacement of the mass can be indirectly measured by the acceleration sensor. The displacement curve can be obtained by performing a second integral on the obtained acceleration curve. The data collected by the intelligent signal analyzer is imported into the Matlab software for programming processing, and finally, the images are obtained through OriginPro 8.5, and the rotation speed, phase difference, displacement response diagram, etc. can be obtained. Synchronization test measurements are respectively carried out on the five-mass vibration test bench driven by four motors in the same direction corresponding to the supply frequencies of 17.4 Hz, 18.4 Hz, and 20.0 Hz.

[0209] (a) Test results with an exciting frequency of 17.4 Hz

[0210] Before the start of the test, the supply frequencies of each motor are adjusted to 17.4 Hz through the frequency conversion cabinet, and then power is supplied to the four vibration motors simultaneously. The test results are shown in Figure 7. The test bench vibrates violently for a period of time after the vibration system is powered on because at this time, the operating frequencies of the four exciters will pass through the low-order natural frequencies of the system during the increasing process, resulting in resonance. Under the action of damping, the resonance response gradually decreases. As the operating frequency of the motors continues to increase, the coupling torque between the motors enables the four exciters to achieve synchronous operation, and the vibration system finally reaches a synchronous stable state.

[0211] As shown in Figure 7(e), when the system operates stably and synchronously, the motor speed is stable at around 955 r / min (99.96 rad / s). At this time, z0 ≈ 0.83 and z4 ≈ 0.66, corresponding to the resonance region I (the first sub-resonance region) of the system. Figure 7(f) shows the test results of the phase difference between each exciter. After the initial violent vibration, the phase differences between the four exciters are 2α1 ≈ 178.9° - 186.4°, 2α2 ≈ 174.2° - 182.7°, and 2α3 ≈ 170.6° - 180.4° at the steady state.

[0212] Figures 7(a), (b), and (c) respectively show the responses of the five masses in the x and y directions and the swing angle of the vibration isolation mass in the ψ direction. It can be seen from the figures that when the system operates stably and synchronously, the responses are as follows: in the x direction, the maximum single amplitude of the four working masses is approximately 0.90 mm, and that of the vibration isolation mass is approximately 0.05 mm; in the y direction, the maximum single amplitude of the four working masses is approximately 0.85 mm, and that of the vibration isolation mass is approximately 0.07 mm; in the ψ direction, the maximum swing angle of the vibration isolation mass is 0.3°. It can be seen from the enlarged view that the vibration waveforms of each mass are all periodically changing, and the first working mass and the third working mass, the second working mass and the fourth working mass are respectively close to being in the same phase change, and the first working mass and the fourth working mass, the second working mass and the third working mass are respectively approximately in the opposite phase change, and the phase differences with the exciters are approximately kept consistent. In this case, the exciting forces transmitted by the exciters to the working masses cancel each other out in both the x and y directions, making the force transmitted from the working masses to the vibration isolation mass approximately 0, and the foundation is almost not loaded. Figure 7(d) is an enlarged view of the movement trajectory of the masses. It can be seen that during the test, the four inner masses are approximately in circular motion, and the vibration isolation mass is approximately stationary.

[0213] (b) Test results with an exciting frequency of 18.4 Hz

[0214] The power supply frequencies of each motor are adjusted to 18.4 Hz, and the relevant test results are shown in Figure 8. Similar to the test results at a power supply frequency of 17.4 Hz, after the vibration system experiences strong vibrations for a period of time after being powered on, as the operating frequency and operating time increase, the generation of the coupling torque between the motors causes the system to gradually reach a stable synchronous operating state.

[0215] As shown in Figure 8(e), when the system operates stably and synchronously, the motor speed is approximately 1015 r / min (106.29 rad / s). At this time, z0≈0.88 and z4≈0.70, corresponding to the resonance region I (the first sub-resonance region) of the system. Figure 8(f) shows the test results of the phase differences between the exciters. The corresponding values of the system at steady state are 2α1≈177.6° - 188.3°, 2α2≈170.8° - 180.5°, and 2α3≈170.0° - 180.0°.

[0216] As can be seen from Figs. 8(a), (b), and (c), the steady-state response of the system is as follows: in the x direction, the amplitudes of the four working masses are approximately equal, about 1.18 mm, and the amplitude of the vibration isolation mass is about 0.08 mm; in the y direction, the amplitudes of the four working masses are about 1.14 mm, and the vibration isolation mass is about 0.11 mm; in the ψ direction, the maximum response of the vibration isolation mass is 0.3°. From the enlarged view, it can be seen that the first and third working masses, and the second and fourth working masses are approximately in-phase in the x and y directions, while the lag angles of the responses of the first and fourth working masses, and the second and third working masses in the x and y directions differ by about 180°. Under this steady state, the exciting force on the vibration isolation mass is about 0, and its response and the load transmitted to the foundation are also about 0. As can be seen from Fig. 8(d), the motion trajectories of the four working masses in the experiment are approximately circular, while the vibration isolation mass remains almost stationary.

[0217] (c) Test results with an exciting frequency of 20.0 Hz

[0218] The power supply frequencies of each motor are adjusted to 20.0 Hz through the frequency conversion cabinet, and the relevant test results are shown in Fig. 9. Similar to the test results when the power supply frequencies are 17.4 Hz and 18.4 Hz, during the initial stage after power-on, the vibration system generates strong vibrations, and at the same time, the motor speeds rise rapidly until they reach the synchronous operating speed. At this time, the coupling torque between the motors can make the system operate stably in synchronization.

[0219] Fig. 9(e) is the motor speed diagram when the power supply frequency is 20.0 Hz. The synchronous speeds of the four motors are 1111 r / min, that is, 116.34 rad / s. At this time, z0≈0.97 and z4≈0.77, corresponding to the sub-resonance regions of the system with respect to ω0 and ω4, that is, Region I. Fig. 9(f) is the test result of the phase difference between the four exciters under the test conditions of 20.0 Hz. The fluctuation range of the phase difference is 2α1≈178.1° - 190.0°, 2α2≈170.8° - 177.9°, and 2α3≈171.8° - 179.4°.

[0220] Figs. 9(a)-(c) are the response diagrams of the system: the amplitudes of the four working masses are about 1.53 mm in the x direction and about 1.47 mm in the y direction; the amplitude of the vibration isolation mass is about 0.17 mm in the x direction and about 0.19 mm in the y direction; the maximum response of the vibration isolation mass in the ψ direction is 0.5°. From the enlarged view, it can be seen that the response of the vibration isolation mass in the x and y directions is approximately 0, which is consistent with the enlarged view of the system motion trajectory in Fig. 9(d). In Fig. 9(d), the four working masses approximately show circular motion. Compared with the response of the working masses, the vibration isolation mass remains almost stationary.

[0221] In the three groups of test results, the stable phase difference of the system has a slight deviation compared with the simulation results, but they are qualitatively consistent. The reason for the deviation may be that even if four motors with exactly the same model are selected, their output torques cannot be exactly the same. It is also possible that the inaccurate arrangement of Hall sensors leads to deviation in the measured phase or the test bench structure is not completely symmetric due to machining errors. The three groups of test results show that the system can achieve effective vibration intensity of four working masses and vibration suppression of the vibration isolation mass within the resonance region I, which is exactly what is required in engineering and can provide reference for the design of the self-synchronizing vibration screening and self-balancing functions of ball milling equipment.

Claims

1. A method for determining the parameters of a four-machine co-directionally driven self-balancing vibrator, characterized in that, The four-machine co-rotating self-balancing vibrator includes: four exciters, five masses, spring A (11) and spring B (8); among them, the four inner masses are connected to the outer mass through spring A (11), and the inner masses are symmetrically distributed in a rectangle on the outer mass; the outer mass is connected to the ground through spring B (8); the four exciters are respectively installed at the mass centers of the four inner masses; the exciter includes an eccentric rotor and an induction motor, and the eccentric rotor is driven by its respective induction motor and rotates around the centers o1, o2, o3, o4 of the rotation axes of their respective exciters; the four exciters rotate in the same direction, and the four-machine co-rotating self-synchronizing drive is used to realize the circular trajectory motion and self-balancing of the inner masses. The parameter determination method described above includes the following steps: Step 1, establish a dynamic model and a system motion differential equation; Establish a coordinate system: The four exciters rotate around their own rotation center axes o1, o2, o3, and o4 respectively; They are the rotation angles of the four eccentric rotors respectively; The angle between the line o connecting the center of mass of the endoplasm and the center of mass of the ectoplasm and the positive direction of the x-axis is represented by β1, β2, β3, and β4 respectively; The degrees of freedom of the entire four-machine co-directional drive five-mass vibration system are: The responses of the five masses in the x-direction and the y-direction respectively, that is, x i , y i , y i , i = 1, 2, 3, 4, 5, where mass 5 is the ectoplasm, and the swing response ψ of the ectoplasm, and the rotation phase angles of the four exciters According to the Lagrange equation, the motion differential equation of the four-machine co-rotating five-mass vibration system is as follows: Where, l0 is the distance between the rotation center of each exciter and the centroid O of the five-mass vibration system driven by four motors in the same direction; r is the eccentric radius of the four exciters; m 0n is the mass of the eccentric rotor of exciter n, n = 1, 2, 3, 4; m i is the mass of the inner mass body i, i = 1, 2, 3, 4; M i is the sum of the mass of the inner mass body i and the eccentric rotor installed on it, i = 1, 2, 3, 4; m5 is the mass of the outer mass body; J 0n is the moment of inertia of the induction motor of exciter n, n = 1, 2, 3, 4, J 0n = m 0n r 2 ; J m5 is the moment of inertia of the outer mass body; J ψ is the moment of inertia of the entire five-mass vibration system driven by four motors in the same direction; T en is the electromagnetic torque of the induction motor of exciter n, n = 1, 2, 3, 4; f w is the damping coefficient of spring k w in the x and y directions, w = 1, 2, 3, 4, 5; k w is the spring k w in the x and y directions, w = 1, 2, 3, 4, 5; where k w , w = 1, 2, 3, 4 are spring A, k5 is spring B; the stiffness and damping coefficients of spring A and B in the x and y directions are respectively equal; f ψ is the damping coefficient of the five-mass vibration system driven by four motors in the same direction in the ψ direction; k ψ is the stiffness coefficient of the five-mass vibration system driven by four motors in the same direction in the ψ direction; f dn is the motor shaft damping coefficient of the induction motor of exciter n, n = 1, 2, 3, 4; Where, M1 = m1 + m 01 ,M2 = m2 + m 02 ,M3 = m3 + m 03 ,M4 = m4 + m 04 ,M5 = m5 l x1 -- The horizontal distance from the connection point of the spring A connected to the left side of the endoplasmic reticulum to the center of the endoplasmic reticulum; l x2 -- The horizontal distance from the connection point of spring A connected to the left side of the endoplasm to the center of the endoplasm; l x3 -- The horizontal distance from the connection point of spring B connected to the right side of the ectoplast to the center of the ectoplast; l y1 -- The vertical distance from the connection point of the spring A connected to the right side of the endoplasmic reticulum to the center of the endoplasmic reticulum; l y2 -- The vertical distance from the connection point of spring A connected to the left side of the endoplasmic body to the center of the endoplasmic body; l y3 -- The vertical distance from the connection point of the spring A connected to the lower part of the endoplasmic body to the center of the endoplasmic body; l y4 -- The vertical distance from the connection point of spring A connected to the lower part of the inner body to the center of the inner body; l y5 -- The vertical distance from the connection point of spring B connected to the lower part of the ectoplast to the center of the ectoplast; Step 2, determine the response of the four-machine co-rotating five-mass vibration system; Step 3, determine the synchronism condition of the four exciters; Step 4, determine the stability condition of the four-machine co-rotating five-mass system.

2. The method for determining the parameters of the four-machine co-directional drive self-balancing vibrator according to claim 1, characterized in that, The excitation frequency of the exciter is not greater than the main natural frequency ω0.

3. The method for determining the parameters of the four-machine co-directionally driven self-balancing vibrator according to claim 1, characterized in that, The determination of the response of the four-machine co-rotating five-mass vibration system as a steady-state response includes obtaining the phase, instantaneous angular velocity and instantaneous angular acceleration of the eccentric rotor and the steady-state response of each degree of freedom of the four-machine co-rotating five-mass vibration system; During the stable operation of the five-mass vibration system driven by four machines in the same direction, the average phase of the four eccentric rotors is set to The instantaneous average angular velocity is The phase differences between adjacent eccentric rotors are set to 2α1, 2α2, 2α3 in sequence, then there is Phase of four eccentric rotors and The expression is where θ n is the difference between the phase of the eccentric rotor in the exciter n and the average phase, n = 1, 2, 3, 4; Take the least common multiple of four excitation force change periods as T0, and let the average value of ω m0 (t) within T0 be ω m ; Let ε0 and ε h represent the instantaneous fluctuation coefficient of ω m , h = 1, 2, 3, then there is Substituting Equation (3) into Equation (4), the expressions of the instantaneous angular velocity and instantaneous angular acceleration of the four eccentric rotors are obtained as, 4. The method for determining the parameters of the four-machine co-directional drive self-balancing vibrator according to claim 3, characterized in that, The steady-state response of each degree of freedom of the four-machine co-rotating five-mass vibration system is obtained as follows; During the stable operation of the four-machine co-directional drive five-mass vibration system, the angular acceleration changes of the four exciters are not considered. At the same time, to ensure the structural symmetry of the four-machine co-directional drive five-mass vibration system, the masses of the masses m i i = 1, 2, 3, 4 and the eccentric rotor masses of the four exciters are kept consistent respectively, and the design parameters of the four groups of springs A are consistent, that is Based on the transfer function method, the steady-state response of the four-machine co-rotating five-mass vibration system is Among them, z ψ = ω m / ω nψ , r l = l0 / l e , M = 4M0 + M5 + 4m0, γ7 = γ 13 = γ 19 = γ1, γ 10 = γ 15 = γ 20 = γ5 γ3 = γ4 = γ6 = γ8 = γ9 = γ 11 = γ 12 = γ 14 = γ 16 = γ 17 = γ 18 = γ2 5. The method for determining the parameters of the four-machine co-directional drive self-balancing vibrator according to claim 4, characterized in that, The determination of the synchronism condition of the four exciters is specifically as follows: calculate the natural frequencies of the four-machine co-rotating five-mass vibration system in the x direction and the y direction; calculate for the main natural frequency, and finally obtain the synchronism criterion of the four-machine co-rotating five-mass system; From Equation (1), the stiffness matrix K, mass matrix M and characteristic equation of the four-machine co-rotating five-mass vibration system in the x direction and the y direction are as follows: When Δ(ω 2 ) = 0, the natural frequencies of the four-machine co-directional drive five-mass vibration system in the x-direction and y-direction are calculated to be 6. The method for determining the parameters of the four-machine co-directional drive self-balancing vibrator according to claim 5, characterized in that, The main natural frequency is determined as follows: without considering the natural frequency ω5, and then only study the main natural frequencies ω0 and ω4 of the four-machine co-rotating five-mass vibration system; Differentiate the equation in Equation (7) to obtain and Substitute them into the last equation of Equation (1), and considering Equation (5), when the four-machine co-rotating five-mass vibration system is operating stably, neglect the high-order terms of ν1, ν2, ν3, ν4, and then integrate both sides of the resulting equation over to obtain the single-period average differential equations of the four eccentric rotors as Where, Where, T e0n is the electromagnetic torque output during the steady-state operation of four induction motors at a frequency ω m , and k e0n is the stiffness coefficient during the steady-state operation of four motors at a frequency ω m ; During the above integration process, the phase differences 2α1, 2α2, and 2α3 are respectively replaced by their integration mean values and ; Select four motors of the same model, with the same parameters, i.e., J 01 = J 02 = J 03 = J 04 = m0r 2 , f d1 = f d2 = f d3 = f d4 = f d0 ; Equation (10) is written in the following form: Where A = [a nq 4×4 , B = [b nq 4×4 u = [u1 u2 u3 u4] T ​​ Equation (11) is the dimensionless coupling equation of the eccentric rotors of four motors; among them, is the dimensionless average perturbation parameter of the instantaneous average angular velocity of the four exciters induction motors within the operating period T0 with respect to , where n = 1, 2, 3, 4; matrices A and B are the dimensionless inertia coupling matrix and the dimensionless stiffness coupling matrix of the four eccentric rotors respectively, and u n represents the dimensionless load torque of the eccentric rotors of the four exciters, where n = 1, 2, 3, 4; The dimensionless average perturbation parameter of the instantaneous average angular velocity of the four eccentric rotors within the operating cycle T0 is 0, which is used to ensure the synchronous operation of the four eccentric rotors. At this time, u = 0 in Equation (11), and its expression is arranged as follows; In Equation (12), is the kinetic energy of the standard vibrator, represents the effective load torques of the four motors when the eccentric rotors of the four vibrators achieve synchronous operation, where n = 1, 2, 3, 4; Subtracting and from each other gives; Where, In formula (13), (T e0n -f dn ω m )-(T e0q -f dq ω m ) represents the difference in the effective electromagnetic output torque between the exciting motor n and the exciting motor q when they achieve synchronous operation; represents the difference in the effective load torque between the exciting motor n and the exciting motor q when they achieve synchronous operation; Let be a bounded function with respect to and . Rearranging Equation (13) gives Equation (14) is a dimensionless equation. The right-hand side of the equal sign is the difference in dimensionless load torques between four motors, and the left-hand side of the equal sign is the difference in dimensionless effective electromagnetic output torques between any two motors. The right-hand side of Equation (14) is a constraint equation regarding and , and we obtain where τ cnqmax is the maximum value; According to Equations (14) and (15), the synchronism criterion of the four-machine co-rotating five-mass system is obtained, that is Equation (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.

7. The method for determining the parameters of the four-machine co-directional drive self-balancing vibrator according to claim 5 or 6, characterized in that The determination of the stability condition of the four-machine co-rotating five-mass system is specifically as follows; Synchronously solve the phase difference between eccentric rotors in Equation (12) and Perform first-order linearization at this point, without considering the motor shaft damping coefficient f dn , where n = 1, 2, 3, 4, and considering Equation (5) simultaneously, we get Among them, wherein, is the value of the function in the brackets at and ; After arranging Equation (17), Rewrite Equation (18) into the following form to obtain the generalized system of phase difference perturbation parameters as where C = [c nh 3×3 , and each parameter is​ According to det(C - λI) = 0, the characteristic equation of the phase difference perturbation system is obtained as λ 3 +d1λ 2 +d2λ + d3 = 0 (20) According to the Routh-Hurwitz criterion, the parameters in the characteristic equation (20) satisfy the following conditions, and the zero solution of equation (20) with respect to is stable. d1>0, d3>0, d1d2>d3 (21) Where, d1 = -c 11 -c 22 -c 33 , d2 = -c 12 c 21 -c 23 c 32 -c 13 c 31 +c 11 c 22 +c 22 c 33 +c 33 c 11 d3 = -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 Meet That is h = 0, 1, 2, 3. It can be seen from Equation (5) that At this time, the four-machine co-directional drive five-mass system meets the Routh-Hurwitz criterion, so the four-machine co-directional drive five-mass system is stable. Equation (21) is the condition for the system to achieve synchronous and stable operation. The system stability ability coefficients H1, H2, and H3 are as follows from Equation (21) H1 = d1>0, H2 = d3>0, H3 = d1d2 - d3>0 (22).

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