CN109649966B - Double-machine self-synchronous driving three-mass vibrating feeder and parameter determination method thereof - Google Patents

Abstract

The invention belongs to the technical field of vibratory feeding devices, and relates to a double-machine self-synchronous driving three-mass vibratory feeder. The novel feeder is mainly developed by applying a vibration synchronization theory and utilizing vibration states of different resonance types of a vibration system. The vibrating machine comprises a hopper, a machine body, a base, a discharge hole, a vibration exciter, a spring, a conveying belt, a vibrating table and an umbrella-shaped boss. The vibrating feeder is different from a common vibrating feeder, and the vibrating feeder is structurally innovated to a certain extent, and has the characteristics of simple structure, convenience in maintenance, large vibrating force, high working efficiency and the like. Meanwhile, the invention provides a parameter determination method of the vibrating feeder, which provides certain guidance on the structural design and parameter selection of the vibrating feeder.

Description

Double-machine self-synchronous driving three-mass vibrating feeder and parameter determination method thereof

Technical Field

The invention belongs to the technical field of vibratory feeding devices, and relates to a double-machine self-synchronous driving three-mass vibratory feeder and a parameter determination method thereof.

Background

The vibration feeder is a device which can uniformly, regularly and continuously feed block-shaped and granular materials from a storage bin to a receiving device. The method is widely applied to industries such as metallurgy, coal mine, building materials, chemical engineering and the like. The vibrating feeder has the advantages of simple structure, uniform feeding, good continuity, adjustable exciting force and the like. The vibration feeder uses the eccentric block in the vibrator to rotate to generate centrifugal force, so that the movable parts of the sieve box, the vibrator and the like do forced continuous circular or approximate circular motion.

Compared with other vibrating feeders:

(1) at present, a vibration exciter and a gear are mainly combined in a common vibration feeder, the vibration exciter and the gear are required to generate a vibration source, and a triangular belt is required to be connected between a motor and the gear. The self-synchronizing triploid vibrating feeder is a novel vibrating feeder developed according to the vibration self-synchronizing theory, and has the advantages of simple structure and convenience in maintenance because the self-synchronizing triploid vibrating feeder does not need gear and belt transmission compared with a common vibrating motor.

(2) At present, a near (sub) resonance double-mass vibrating feeder is mostly adopted in the self-synchronous feeder, but the feedback vibration amplification of the invention is more excellent than that of a double-mass vibrating feeder, so that larger amplitude can be generated, and the mechanical working efficiency is improved.

Disclosure of Invention

The invention overcomes the defects of the prior art, mainly applies a vibration synchronization theory and develops a novel feeder by utilizing the vibration states of different resonance types of a vibration system. A double-machine self-synchronous driving three-mass vibrating feeder and a parameter determination method thereof are provided.

A double-machine self-synchronous driving three-mass vibrating feeder comprises a hopper, a vibrating table, a vibrating machine body, a base, a vibration exciter, a spring, a conveying belt and an umbrella-shaped boss; the lower part of the vibrating machine body is fixed on the base through a spring, supports the whole equipment and provides necessary elasticity and vibration isolation; two semi-arc vibration tables are symmetrically arranged on two sides above the vibration machine body, the vibration machine body is connected with the vibration tables through springs, and the vibration tables are used for providing exciting force to convey falling materials to the bottom end; an umbrella-shaped boss is arranged in the middle above the vibrating machine body and is positioned under the hopper, and the umbrella-shaped boss is used for guiding the materials to slide down to the cambered surface of the vibrating table; a discharge port is arranged on the vibrating machine body at the bottom end of the semi-arc vibrating table, materials slide into the discharge port from the vibrating table, and a conveying belt is arranged below the discharge port, so that the materials are conveniently conveyed and fed; the vibration exciters are symmetrically arranged on the vibration machine body, and the eccentric rotors of the two vibration exciters reversely and synchronously rotate to serve as power sources; the motion of the vibrating body is limited to the y-direction.

The working principle is as follows: when the material fed into the hopper, at first through umbelliform boss, the material fell along the umbrella wall landing, and on the shaking table, the shaking table reciprocating vibration carried the material to the discharge gate, carried the material to required equipment through conveying platform at last. The exciting force of the vibration table is provided by the two vibration exciters, and the vibration directions and amplitudes of the vibration table and the vibration exciters are ensured by a parameter determination method, so that an ideal effect is achieved.

The invention takes a double-machine three-plastid dynamic model as a research object, establishes a differential equation for the model by applying principles such as an average parameter method, a transfer function method and the like, obtains a system synchronism and stability capability coefficient curve, a dimensionless coupling moment maximum value graph and the like through characteristic analysis of synchronism and stability, finally obtains a plastid speed curve, a displacement curve and a phase difference graph through simulation of a vibration system, and verifies the correctness of the method through comparison of the characteristic analysis and the system simulation.

According to the parameter determination method of the dual-motor self-synchronous driving three-mass vibrating feeder, a dynamic model of the feeder comprises three masses and two vibration exciters; the two vibration exciters rotate in opposite directions; the mass 1 and the mass 2 are two vibration tables and move in opposite directions in the horizontal direction; the mass 3 is a vibrating body which moves up and down and has no movement in the x-axis direction, and the parameter determination method of the vibration exciter comprises the following steps:

the method comprises the following steps: establishing a dynamic model and a kinematic differential equation of a system

The dynamic model of the vibrating feeder is shown in figure 1, two rectangular coordinate systems are established, and a motion differential equation is obtained according to the Lagrange method

In the formula

M₁＝m₁+m₀₁，M₂＝m₂+m₀₂，M₃＝m₃+m₀₁+m₀₂；

m₀₁,m₀₂The mass of the exciters 1 and 2; m is_i-mass of mass (i ═ 1 to 3); f. of_1y，f_2y，f_3y-damping coefficient in y-direction; j. the design is a square_oi＝m_oir_i ²-moment of inertia (i ═ 1-2); r-eccentricity of vibration exciter; k is a radical of_1y,k_2y-spring rate in the y-direction;

-the phase angle of the exciter i (i-1-2);

-angular velocity of exciter i (i-1-2);

-angular acceleration of exciter i (i-1-2);

step two: deriving synchronization conditions

The response of the system obtained by the transfer function method is:

γ_1y-the lag angle of the mass 1 in the y-direction;

γ_2y-the lag angle of the mass 2 in the y-direction;

γ_3y-the lag angle of the mass 3 in the y-direction;

η -mass ratio of rotors 1 and 2;

the average phase angle of the two vibration exciters is

The phase difference of the two exciters is 2 α, and the following components are provided:

masses 1 and 2 being of the same mass, i.e. M₁＝M₂Then there is

So that there are

In mass 1, the spring is assumed to be at an angle β to the horizontal, in mass 2, the spring is assumed to be at an angle π - β to the horizontal, mass 3 is at a displacement of 0 in the x-direction, and with small fluctuations, the system responds in the x-direction as:

in the formula, M is a mass coupling matrix, K is a stiffness coupling matrix, Delta (omega)²) Is an equation of eigenvalues

Let the eigenvalue equation equal 0, i.e. Δ (ω)²)＝0

-M₁M₂M₃ω⁶+(k_1yM₂M₃+k_2yM₁M₃+k_1yM₁M₂+k_2yM₁M₂+k_3yM₁M₂)ω⁴-(k_1yk_2yM₃+k_1yk_2yM₂+k_1yk_3yM₂+k_1yk_2yM₁+k_2yk_3yM₁)ω²+k_1yk_2yk_3y＝0

Let k_1y＝k_2y＝k₀，M₁＝M₂＝M₀To obtain

k₀ ²k₃-k₀ ²ω_m0 ²M₃-2ω_m0 ²M₀k₀ ²-2k₀ω_m0 ²M₀k₃+2k₀ω_m0 ⁴M₀M₃+2ω_m0 ⁴M₀ ²k₀+ω_m0 ⁴M₀ ²k₃-ω_m0 ⁶M₀ ²M₃＝0

When the system is operating in a steady state, i.e.

Derived from formula (2)

And is substituted into the last equation of formula (1), and then let

Integrating, we will get the average differential equation of the two exciters as follows:

in the formula

Representing the kinetic energy, omega, of a standard vibration exciter_m0Indicating the synchronous angular velocity, T, of both motors_e01，T_e01Representing the electromagnetic torque of the two electrical machines,

shows the output torque difference (Delta T) between the two motors (1, 2)₁₂) Comprises the following steps:

the finishing formula (10) is as follows:

in the formula

The dimensionless coupling torque for both exciters is a constraint function on α:

thus, the following steps are obtained:

the synchronous rule of the two exciters is that the absolute value of the dimensionless residual torque difference of any two motors is less than or equal to the maximum value of the dimensionless coupling torque.

Will be provided with

Summed and then divided by 2T_uObtaining the dimensionless load moments of the two vibration exciters as follows:

in the formula

For the dimensionless load moment of the two exciters, the constraint function is as follows:

the coefficients of the synchronicity before the exciters 1 and 2 are as follows:

the larger the synchronization capability coefficient is, the stronger the synchronism of the system is, and the easier the synchronization is to be realized.

Step three: stability criterion for synchronous state

The kinetic energy equation of the system is as follows:

the potential energy equation of the system is as follows:

equation of average kinetic energy in one cycle E_TAnd average is potential energy equation E_VComprises the following steps:

P＝-k_1yF₃ ²cos(2α-β)-k_1yF₃ ²cos(2α+β)-k_1yF₁ ²cos(2α-β)-k_1yF₁ ²cos(2α+β)-k_2yF₃ ²cos(2α-β)-k_2yF₃ ²cos(2α+β)-k_2yF₂ ²cos(2α-β)-k_2yF₂ ²cos(2α+β)-k_2yF₃ ²sin(2α+β)+k_2yF₃ ²sin(2α-β)-k_2yF₂ ²sin(2α+β)+k_2yF₂ ²sin(2α-β)-k_3yF₃ ²sin(2α+β)+k_3yF₃ ²sin(2α-β)-2k_1yF₃ ²cos(β)-2k_1yF₁ ²cos(β)-2k_2yF₃ ²cos(β)-2k_2yF₂ ²cos(β)-2k_1yF₃ ²sin(β)-2k_1yF₁ ²sin(β)-2k_2yF₃ ²sin(β)-2k_2yF₂ ²sin(β)-2k_3yF₃ ²sin(β)

in the formula E_TDenotes the average kinetic energy, E_VRepresents the average potential energy

Therefore, there are:

the system Hamilton average effect (I) is:

stabilizing the solution of the phase difference in the synchronous state

Corresponding to the minimum Hamiltonian contribution, whose Hessen matrix is positive, which is denoted as H,

F₁＝k_3yF₃ ²sin(2α-3β)-k_3yF₃ ²sin(2α+3β)+k_2yF₂ ²sin(2α-3β)-k_2yF₂ ²sin(2α+3β)-k_1yF₃ ²sin(2α+3β)+k_1yF₃ ²sin(2α-3β)-k_1yF₁ ²sin(2α+3β)+k_1yF₁ ²sin(2α-3β)-k_2yF₃ ²sin(2α+3β)+k_2yF₃ ²sin(2α-3β)-k_2yF₂ ²sin(2α+3β)-k_1yF₃ ²sin(2α-3β)-k_1yF₃ ²cos(2α+3β)-k_1yF₁ ²cos(2α-3β)-k_1yF₁ ²cos(2α+3β)-k_2yF₃ ²cos(2α-3β)-k_2yF₃ ²cos(2α+3β)-k_2yF₂ ²cos(2α+3β)

F₂＝k_1yF₃ ²cos(2α-β)+k_1yF₃ ²cos(2α+β)+k_1yF₁ ²cos(2α-β)+k_1yF₁ ²cos(2α+β)+k_2yF₃ ²cos(2α-β)+k_2yF₃ ²cos(2α+β)+k_2yF₂ ²cos(2α-β)+k_2yF₂ ²cos(2α+β)+3k_1yF₃ ²sin(2α+β)-3k_1yF₃ ²sin(2α-β)+3k_1yF₁ ²sin(2α+β)-3k_1yF₁ ²sin(2α-β)+3k_2yF₃ ²sin(2α+β)-3k_2yF₃ ²sin(2α-β)+3k_2yF₂ ²sin(2α+β)-3k_2yF₂ ²sin(2α-β)+3k_3yF₃ ²sin(2α+β)-3k_3yF₃ ²sin(2α-β)

F₃＝3M₃F₃ ²ω_m0 ²sin(2α-β)-3M₃F₃ ²ω_m0 ²sin(2α+β)+M₃F₃ ²ω_m0 ²sin(2α+3β)-M₃F₃ ²ω_m0 ²sin(2α-3β)-4M₁F₁ ²ω_m0 ²sin(2α+β)+4M₁F₁ ²ω_m0 ²sin(2α-β)-4M₂F₂ ²ω_m0 ²sin(2α+β)+4M₂F₂ ²ω_m0 ²sin(2α-β)

F₄＝cos(γ_1y-γ_3y)[-3k_1yF₁F₃sin(2α+β)+3k_1yF₁F₃sin(2α-β)-k_1yF₁F₃cos(2α-β)-k_1yF₁F₃cos(2α+β)+k_1yF₁F₃cos(2α-3β)+k_1yF₁F₃cos(2α+3β)+k_1yF₁F₃sin(2α+3β)-k_1yF₁F₃sin(2α-3β)]

F₅＝cos(γ_2y-γ_3y)[-3k_1yF₂F₃sin(2α+β)+3k_2yF₂F₃sin(2α-β)-k_2yF₂F₃cos(2α-β)-k_2yF₂F₃cos(2α+β)+k_2yF₂F₃cos(2α-3β)+k_2yF₂F₃cos(2α+3β)+k_2yF₂F₃sin(2α+3β)-k_2yF₂F₃sin(2α-3β)]

thus obtaining

To ensure that the Hessen matrix is positive, the following conditions should be satisfied:

H＞0 (25)

h is defined as the stability factor of the system, and the system is stable when the condition of equation (25) is satisfied.

The invention has the beneficial effects that: the invention provides a novel vibration feeder model which is driven by double vibration exciters and is provided with two material conveying groove bodies (m)₁,m₂) Therefore, when more materials need to be conveyed, the equipment can work normally, and the working efficiency is high. The materials are easy to wear with the groove body in the conveying process, so that when the materials with the same quantity are conveyed, the double-groove-body structure has longer service life than the single-groove-body structure. And when the device works, the amplitude of the machine body is basically 0, and the influence on the surrounding environment is small.

Drawings

FIG. 1 (a) is a diagram of a dual-motor self-synchronous driving three-mass structure, and (b) a dynamic model;

in the figure: 1, a hopper; 2, vibrating a table; 3 vibrating the machine body; 4, a vibration exciter; 5, discharging a material outlet; 6, a base; 7, a spring;

the meaning of the parameters in fig. 1:

m₁-mass of the mass 1;

m₂the mass of the mass 2;

m₃-mass of mass 3;

m₀₁the mass of the exciter rotor 1;

m₀₂the mass of the exciter rotor 2;

-the rotation angle of the exciter rotor 1;

-the rotation angle of the exciter rotor 2;

o₁the center of mass of exciter 1;

o₂the center of mass of exciter 2;

k_ii is 0-3-spring stiffness coefficient;

β -the angle between the springs of the mass 1 and the horizontal;

pi- β -the angle between the spring of mass 2 and the horizontal;

FIG. 2 is a phase difference diagram between exciters;

figure 3 lag angle diagrams of three masses;

FIG. 4 synchronization performance capability factor graph;

FIG. 5 is a dimensionless maximum coupling torque diagram;

FIG. 6 stability performance force coefficient plot;

FIG. 7 is a plot of motor speed for region 1;

FIG. 8 is a phase difference diagram of region 1;

FIG. 9 is a graph of the displacement of region 1 in the x-direction;

FIG. 10 is a partial enlarged view of the displacement of region 1 in the x-direction;

FIG. 11 is a graph of the displacement of region 1 in the y-direction;

FIG. 12 is a partial enlarged view of the displacement of region 1 in the y-direction;

FIG. 13 is a plot of motor speed at region 2;

FIG. 14, region 2 phase difference diagram;

FIG. 15 is a graph of displacement of region 2 in the x-direction;

FIG. 16 is an enlarged partial front view of the displacement of region 2 in the x-direction;

FIG. 17 is a rear enlarged partial view of the displacement of region 2 in the x-direction;

FIG. 18 is a graph of displacement of region 2 in the y-direction;

FIG. 19 is an enlarged partial front view of region 2 displacement in the y-direction;

FIG. 20 is a rear enlarged partial view of the displacement of region 2 in the y-direction;

FIG. 21, region 3, a motor speed map;

FIG. 22, region 3 phase difference diagram;

FIG. 23 is a graph of displacement of region 3 in the x-direction;

fig. 24 is a displacement diagram of region 3 in the y-direction.

Detailed Description

A double-machine self-synchronous driving three-mass vibrating feeder. The kinetic model is shown in figure 1 and comprises: vibration exciter m_0i(i 1-2); plasmid m_i(i 1-3), spring k_i(i is 1 to 3). The model consists of two exciters and three masses. The masses 1 and 2 move in opposite directions horizontally and the mass 3 is not displaced in the x direction. And each exciter is rotated about its own rotation axis to

And (4) showing.

Example 1: numerical analysis

The steady state phase relationship of the system consists of three phase relationships, namely the phase difference between the vibration exciters, the phase relationship between the system response and the vibration exciters, and the phase relationship between the system response.

Assume a vibration system parameter of k_1y＝k_2y＝20000kN/m，k_3y＝10kN/m，m₁＝m₂＝1500kg，m₃＝2000kg，m₀₁＝m₀₂＝10kg，M₃＝m₃+m₀₁+m₀₂The natural frequency of the system is calculated as 2020kg, point a: omega₁116rad/s, point B: omega₂＝182rad/s。

Thus according to ω₁116rad/s and ω₂182rad/s can be divided into three zones: region 1 is ω_m0＜ω₁Region 2 is ω₁＜ω_m0＜ω₂Region 3 is ω₂＜ω_m0。

Fig. 2 shows the phase angle relationship between the two exciters, 2 α shows the phase difference between the exciters 1 and 2, the phase difference between the two exciters being 180 ° and 0 ° when the excitation frequency is in region 1, 0 ° when the excitation frequency is in region 2, and 0 ° and 180 ° when the excitation frequency is in region 3.

Figure 3 shows the lag angle for three masses, gamma for the lag angle, and 180 ° for the system in zone 1; in region 2, the hysteresis angles of masses 1 and 2 are 180 °, and the hysteresis angle of mass 3 is 0 °; in region 3, the hysteresis angles of masses 1 and 2 are 0 °, and the hysteresis angle of mass 3 is 180 °.

ζ₁₂And the larger the synchronous coefficient between the two vibration exciters is, the larger the relative coupling quantity is. The easier the two exciters are synchronized, the better the system is synchronized. As shown in fig. 4, in the region 1 and the region 2, the system synchronization capability coefficient curve starts to increase and then decreases as the excitation frequency increases, and in the region 3, the system synchronization capability coefficient curve increases as the excitation frequency increases.

By adjusting the phase difference between the two vibration exciters, the coupling torque achieves the energy distribution of the system, thereby ensuring the stability of the system. As can be seen from fig. 5, in the region 1, the maximum coupling torque τ curve decreases as the excitation frequency increases. In the regions 2 and 3, the curve of the maximum coupling torque τ increases first and then decreases as the excitation frequency increases.

As shown in fig. 6, the stability factor is 0 in the region 1, and is greater than 0 as the excitation frequency increases, and the stability factor is significantly increased in the region 2, indicating that the system is stable.

The numerical analysis results show that: when the system is in the relative to ω₁And relative to ω₂In the super-resonance state of (1), i.e., region (ω)_m0＜ω₁) And region 3(ω)₂＜ω_m0) The phase difference between the two vibration exciters has a plurality of groups of stability solutions, and the diversity condition of a nonlinear system occurs; when the system is in the relative to ω₂Or relative to ω₁In the super-resonance state of (c), i.e., region 2(ω)₁＜ω_m0＜ω₂) The stability capability coefficient of the system is obviously increased.

Example 2: simulation of a vibration system

In practical engineering application, the same vibration exciter is generally adopted, parameters of four motors are the same, namely η is 1.0, and the overall parameters of the system are as follows, namely rotor resistance R_r3.40 Ω, stator resistance R_s3.35 Ω, rotor inductance L_r170mH, stator inductance L_s170mH, mutual inductance L_m＝164mH，f_1y＝f_2y0.05. Other parameters of the vibration system: r is 0.15m, m₁＝m₂＝1500kg，m₃＝2000kg，m₀₁＝m₀₂＝10kg，M₃＝m₃+m₀₁+m₀₂The parameters were adjusted to give a sub-resonance state and a super-resonance state, respectively, for a system of 2020 kg.

Simulation for region 1, assume k_1y＝k_2y＝60000kN/m，k_3y＝10kN/m，z₁＝0.52：

Fig. 7 shows the steady state of the speeds of the two exciters, the speeds of the two exciters are quickly stabilized in a short time, the synchronous speed is basically stabilized at about 983r/min, at 40s, the exciters 2 increase interference, the speed fluctuates, but the speed is still about 983r/min after stabilization.

Fig. 8 shows the phase difference steady state, with the first 20s phase difference of 0 °, after which the phase difference between exciters 1 and 2 is stabilized at 180 °, at 40s the interference of exciter 2 increases, and the phase difference after stabilization is still 180 °, consistent with the phase difference of the signature analysis.

Figures 9 and 10 show the displacement of the masses 1,2,3 in the x-direction. The masses 1 and 2 move in opposite directions in the horizontal direction. At 40s later, the vibration exciter 2 increased the disturbance, the displacement curve fluctuated, and the displacement of the mass 3 in the horizontal direction was always 0.

Figures 11 and 12 show the displacement of the masses 1,2,3 in the y-direction. The displacement of the first 25s masses 1 and 2 is equal to or slightly greater than that of mass 3 and the 3 masses move in the same direction. At 40s, the vibration exciter 2 increases interference, the displacement curves of the three masses fluctuate, and then the displacement curves are restored to 0, so that the characteristic analysis of the lag angle is met.

Region 2 was simulated, assuming k_1y＝k_2y＝10000kN/m，k_3y＝10kN/m，z₁＝0.8：

Fig. 13 shows the steady state of the speeds of the two exciters, the speeds of the two exciters are fast stabilized in a short time, the synchronous speed is basically stabilized at 790 r/min-811 r/min, at 30s, the exciters 2 increase interference, the speed fluctuates, but the speeds are still 790 r/min-811 r/min after stabilization.

Fig. 14 shows a phase difference steady state, in which the phase difference between exciters 1 and 2 is stabilized at 0 °, interference is increased in 30s type exciter 2, and the phase difference after stabilization is still 0 °, which corresponds to the phase difference of the characteristic analysis.

Figures 15, 16 and 17 show the displacement of the masses 1,2 and 3 in the x-direction. Masses 1 and 2 move in opposite directions in the horizontal direction and mass 3 has a displacement of 0. Then, at 30 seconds, the vibration exciter 2 increases the disturbance, the displacement curve fluctuates, and then the state returns to the original state.

Figures 18, 19 and 20 show the displacement of the masses 1,2 and 3 in the y-direction. The displacement of masses 1 and 2 is equal to or slightly less than that of mass 3 and the 3 masses move in the same direction. Then, at 30 seconds, the vibration exciter 2 increases the disturbance, the displacement curve fluctuates, and then the state returns to the original state. The characteristic analysis of the lag angle is met.

Region 3 was simulated, assuming k_1y＝k_2y＝4000kN/m，k_3y＝10kN/m，z₁＝1.27：

Fig. 21 shows a steady state of the speeds of the two exciters, in which the speeds of the two exciters rapidly stabilize and the synchronous speed substantially stabilizes at about 983.23r/min, and at 30s, the speed of the exciter 2 increases with disturbance and fluctuates, but after stabilization, it is 983.23 r/min.

Fig. 22 shows a phase difference steady state in which the phase difference between exciters 1 and 2 is steady at 0 °, and becomes 180 ° at 5s, and at 30s, the disturbance of exciter 2 increases, and the phase difference after stabilization returns to 180 °, and matches the phase difference of the characteristic analysis.

Figure 23 shows the displacement of the masses 1,2,3 in the x-direction. Before 30s, the three masses are stable, at 30s, the vibration exciter 2 increases interference, the displacement curve fluctuates, the mass 1 and the mass 2 move reversely in the horizontal direction, the mass 3 is displaced to 0, and then the system returns to the original state and remains stable again.

Figure 24 shows the displacement of the masses 1,2,3 in the y-direction. Before 30s, all three masses were stable, at 30s, the exciter 2 increased the disturbance, the displacement curve fluctuated, the displacements of the three masses were identical, and then the system again remained stable.

The system simulation result shows that: when the system is before and after the interference, the phase difference and the numerical analysis result are consistent, namely, the diversity of the nonlinear system exists between the area 1 and the area 3, and the system can be still stable after the interference in the area 2. The working area of the vibrating feeder under this parameter therefore selects the area 2.

(1) As is clear from comparison of the results of example 1 and example 2, the numerical verification and the system simulation results were the same. The parameter determination method of the present invention is therefore correct.

(2) The invention is a new model of the vibrating feeder, uses a double-machine driving three-mass body, and obtains two groups of solutions of phase difference of a region 1 and a region 3 of the vibrating feeder according to establishment, numerical analysis and simulation of a differential equation, namely the diversity of a nonlinear system, so that a working region is a region 2.

(3) From the simulation result of the area 2, it can be known that the phase difference between the two vibration exciters is 0 °, and the vibrating body has no vibration in the x direction and is opposite to the vibration of the mass 1 and the mass 2 in the y direction, so the vibration feeder of the present invention can generate great vibration and has high working efficiency.

(4) The research content of the invention has important guiding function for the design of the structural parameters of the vibrating feeder equipment and the selection of the working area.

Example 3 example data parameters for one of the vibrating feeders designed by the present invention were utilized. The present invention is not limited to this design parameter.

Spring rate: k is a radical of_1y＝k_2y＝10000kN/m，k_3y＝10kN/m；

Damping coefficient: f. of_1y＝f_2y＝0.05

Mass of plastid: m is₁＝m₂＝1500kg，m₃＝2000kg；

r＝0.15m；z₁0.8; synchronous rotating speed: omega_m0＝790r/min—811r/min

The eccentric rotor mass of the vibration exciter is as follows: m is₀₁＝m₀₂＝10kg，M₃＝m₃+m₀₁+m₀₂＝2020kg；

Motor parameters: rotor resistance R_r3.40 Ω, stator resistance R_s3.35 Ω, rotor inductance L_r170mH, stator inductance L_s170mH, mutual inductance L_m＝164mH。

The two motors are in the same model, and the three-phase squirrel-cage type (model VB-1082-W, 380V, 50Hz, 6-pole, delta-connection, 0.75kw, rotating speed 980r/min, 39kg) is adopted.

Claims (3)

1. A double-machine self-synchronous driving three-mass vibrating feeder is characterized by comprising a hopper, a vibrating table, a vibrating machine body, a base, a vibration exciter, a spring, a conveying belt and an umbrella-shaped boss; the lower part of the vibrating machine body is fixed on the base through a spring, supports the whole equipment and provides necessary elasticity and vibration isolation; two semi-arc vibration tables are symmetrically arranged on two sides above the vibration machine body, the vibration machine body is connected with the vibration tables through springs, and the vibration tables are used for providing exciting force to convey falling materials to the bottom end; an umbrella-shaped boss is arranged in the middle above the vibrating machine body and is positioned under the hopper, and the umbrella-shaped boss is used for guiding the materials to slide down to the cambered surface of the vibrating table; a discharge port is arranged on the vibrating machine body at the bottom end of the semi-arc vibrating table, materials slide into the discharge port from the vibrating table, and a conveying belt is arranged below the discharge port, so that the materials are conveniently conveyed and fed; the vibration exciters are symmetrically arranged on the vibration machine body, and the eccentric rotors of the two vibration exciters reversely and synchronously rotate to serve as power sources; the motion of the vibrating body is limited to the y-direction.

2. The dual-motor self-synchronizing driven three-mass vibrating feeder parameter determination method of claim 1, characterized in that the dynamic model of the feeder comprises three masses and two vibration exciters; the two vibration exciters rotate in opposite directions; the mass 1 and the mass 2 are two vibration tables and move in opposite directions in the horizontal direction; the mass 3 is a vibrating body which moves up and down and has no movement in the x-axis direction, and the parameter determination method of the vibration exciter comprises the following steps:

the method comprises the following steps: establishing a dynamic model and a kinematic differential equation of a system

Establishing two rectangular coordinate systems, and obtaining a motion differential equation according to a Lagrange method

In the formula

M₁＝m₁+m₀₁，M₂＝m₂+m₀₂，M₃＝m₃+m₀₁+m₀₂；

m₀₁,m₀₂The mass of the exciters 1 and 2; m is_i-mass of mass (i ═ 1 to 3); f. of_1y，f_2y，f_3y-damping coefficient in y-direction;

-moment of inertia (i ═ 1-2); r-eccentricity of vibration exciter; k is a radical of_1y,k_2y-spring rate in the y-direction;

-the phase angle of the exciter i (i-1-2);

-angular velocity of exciter i (i-1-2);

-angular acceleration of exciter i (i-1-2);

step two: determining synchronization conditions

The response of the system obtained by the transfer function method is:

γ_1y-the lag angle of the mass 1 in the y-direction;

γ_2y-the lag angle of the mass 2 in the y-direction;

γ_3y-the lag angle of the mass 3 in the y-direction;

η -mass ratio of rotors 1 and 2;

the average phase angle of the two vibration exciters is

The phase difference of the two exciters is 2 α, and the following components are provided:

masses 1 and 2 being of the same mass, i.e. M₁＝M₂Then there is

a＝-M₁M₂M₃ω⁶ _m0+(f_1yf_2yM₁+f_1yf_2yM₂+f_1yf_2yM₃+f_1yf_3yM₂+f_2yf_3yM₁+M₁M₂k_1y+M₁M₂k_2y+M₁M₂k_3y+M₂M₃k_1y+M₁M₃k_2y)ω_m0 ⁴-(k_1yk_2yM₁+k_1yk_2yM₂+k_1yk_2yM₃+k_1yk_3yM₂+k_2yk_3yM₁+f_1yf_3yk_2y+f_2yf_3yk_1y+f_1yf_2yk_3y)ω_m0 ²+k_1yk_2yk_3y

b＝(M₁M₂f_1y+M₁M₂f_2y+M₁M₂f_3y+M₁M₃f_2y+M₂M₃f_1y)ω_m0 ⁵-(f_1yk_2yM₁+f_1yk_2yM₂+f_1yk_2yM₃+f_1yk_3yM₂+f_2yk_3yM₁+f_2yk_1yM₁+f_2yk_1yM₂+f_2yk_1yM₃+f_3yk_1yM₂+f_3yk_2yM₁+f_1yf_2yf_3y)ω_m0 ³+(f_1yk_2yk_3y+f_2yk_1yk_3y+f_3yk_1yk_2y)ω_m0

c＝-(f_1yf_2y+k_1yM₂)ω_m0 ²+k_1yk_2y，d＝-f_1yM₂ω_m0 ³+(f_1yk_2y+f_2yk_1y)ω_m0(4)

e＝-(k_2yM₁+f_1yf_2y)ω_m0 ²+k_1yk_2y，g＝-f_2yM₁ω_m0 ³+(k_2yf_1y+k_1yf_2y)ω_m0

h＝M₁M₂ω_m0 ⁴-(f_1yf_2y+k_1yM₂+k_2yM₁)ω_m0 ²+k_1yk_2y

p＝-(f_1yM₂+f_2yM₁)ω_m0 ³+(f_1yk_2y+f_2yk_1y)ω_m0

So that there are

In mass 1, the spring is assumed to be at an angle of β with the horizontal direction, in mass 2, the spring is assumed to be at an angle of pi- β with the horizontal direction, the displacement of mass 3 in the x direction is 0, and the response of the system in the x direction under small fluctuation is as follows:

in the formula, M is a mass coupling matrix, K is a stiffness coupling matrix, Delta (omega)²) When the eigenvalue equation is made equal to 0 for the eigenvalue equation, i.e., Δ (ω)²)＝0

-M₁M₂M₃ω⁶+(k_1yM₂M₃+k_2yM₁M₃+k_1yM₁M₂+k_2yM₁M₂+k_3yM₁M₂)ω⁴

-(k_1yk_2yM₃+k_1yk_2yM₂+k_1yk_3yM₂+k_1yk_2yM₁+k_2yk_3yM₁)ω²+k_1yk_2yk_3y＝0

Let k_1y＝k_2y＝k₀，M₁＝M₂＝M₀To obtain

k₀ ²k₃-k₀ ²ω_m0 ²M₃-2ω_m0 ²M₀k₀ ²-2k₀ω_m0 ²M₀k₃+2k₀ω_m0 ⁴M₀M₃+2ω_m0 ⁴M₀ ²k₀+ω_m0 ⁴M₀ ²k₃-ω_m0 ⁶M₀ ²M₃＝0

When the system is operating in a steady state, i.e.

Derived from formula (2)

And is substituted into the last equation of formula (1), and then let

Integration will result in an average differential equation for the two exciters as follows:

in the formula

Representing the kinetic energy, omega, of a standard vibration exciter_m0Indicating the synchronous angular velocity, T, of both motors_e01，T_e01Representing the electromagnetic torque of the two electrical machines,

shows the output torque difference (Delta T) between the two motors (1, 2)₁₂) Comprises the following steps:

the finishing formula (10) is as follows:

in the formula

The dimensionless coupling torque for both exciters is a constraint function on α:

thus, the following steps are obtained:

the synchronism condition of the two vibration exciters is that the absolute value of the dimensionless residual torque difference of any two motors is less than or equal to the maximum value of the dimensionless coupling torque;

step three: stability criterion for synchronous state

The kinetic energy equation of the system is as follows:

the potential energy equation of the system is as follows:

equation of average kinetic energy in one cycle E_TAnd average is potential energy equation E_VComprises the following steps:

P＝-k_1yF₃ ²cos(2α-β)-k_1yF₃ ²cos(2α+β)-k_1yF₁ ²cos(2α-β)-k_1yF₁ ²cos(2α+β)-k_2yF₃ ²cos(2α-β)-k_2yF₃ ²cos(2α+β)-k_2yF₂ ²cos(2α-β)-k_2yF₂ ²cos(2α+β)-k_2yF₃ ²sin(2α+β)+k_2yF₃ ²sin(2α-β)-k_2yF₂ ²sin(2α+β)+k_2yF₂ ²sin(2α-β)-k_3yF₃ ²sin(2α+β)+k_3yF₃ ²sin(2α-β)-2k_1yF₃ ²cos(β)-2k_1yF₁ ²cos(β)-2k_2yF₃ ²cos(β)-2k_2yF₂ ²cos(β)-2k_1yF₃ ²sin(β)-2k_1yF₁ ²sin(β)-2k_2yF₃ ²sin(β)-2k_2yF₂ ²sin(β)-2k_3yF₃ ²sin(β)

in the formula E_TDenotes the average kinetic energy, E_VRepresents the average potential energy

Therefore, there are:

the system Hamilton average effect (I) is:

stabilizing the solution of the phase difference in the synchronous state

Corresponding to the minimum Hamiltonian contribution, whose Hessen matrix is positive, which is denoted as H,

F₁＝k_3yF₃ ²sin(2α-3β)-k_3yF₃ ²sin(2α+3β)+k_2yF₂ ²sin(2α-3β)-k_2yF₂ ²sin(2α+3β)-k_1yF₃ ²sin(2α+3β)+k_1yF₃ ²sin(2α-3β)-k_1yF₁ ²sin(2α+3β)+k_1yF₁ ²sin(2α-3β)-k_2yF₃ ²sin(2α+3β)+k_2yF₃ ²sin(2α-3β)-k_2yF₂ ²sin(2α+3β)-k_1yF₃ ²sin(2α-3β)-k_1yF₃ ²cos(2α+3β)-k_1yF₁ ²cos(2α-3β)-k_1yF₁ ²cos(2α+3β)-k_2yF₃ ²cos(2α-3β)-k_2yF₃ ²cos(2α+3β)-k_2yF₂ ²cos(2α+3β)

F₂＝k_1yF₃ ²cos(2α-β)+k_1yF₃ ²cos(2α+β)+k_1yF₁ ²cos(2α-β)+k_1yF₁ ²cos(2α+β)+k_2yF₃ ²cos(2α-β)+k_2yF₃ ²cos(2α+β)+k_2yF₂ ²cos(2α-β)+k_2yF₂ ²cos(2α+β)+3k_1yF₃ ²sin(2α+β)-3k_1yF₃ ²sin(2α-β)+3k_1yF₁ ²sin(2α+β)-3k_1yF₁ ²sin(2α-β)+3k_2yF₃ ²sin(2α+β)-3k_2yF₃ ²sin(2α-β)+3k_2yF₂ ²sin(2α+β)-3k_2yF₂ ²sin(2α-β)+3k_3yF₃ ²sin(2α+β)-3k_3yF₃ ²sin(2α-β)

F₃＝3M₃F₃ ²ω_m0 ²sin(2α-β)-3M₃F₃ ²ω_m0 ²sin(2α+β)+M₃F₃ ²ω_m0 ²sin(2α+3β)-M₃F₃ ²ω_m0 ²sin(2α-3β)-4M₁F₁ ²ω_m0 ²sin(2α+β)+4M₁F₁ ²ω_m0 ²sin(2α-β)-4M₂F₂ ²ω_m0 ²sin(2α+β)+4M₂F₂ ²ω_m0 ²sin(2α-β)

F₄＝cos(γ_1y-γ_3y)[-3k_1yF₁F₃sin(2α+β)+3k_1yF₁F₃sin(2α-β)-k_1yF₁F₃cos(2α-β)-k_1yF₁F₃cos(2α+β)+k_1yF₁F₃cos(2α-3β)+k_1yF₁F₃cos(2α+3β)+k_1yF₁F₃sin(2α+3β)-k_1yF₁F₃sin(2α-3β)]

F₅＝cos(γ_2y-γ_3y)[-3k_1yF₂F₃sin(2α+β)+3k_2yF₂F₃sin(2α-β)-k_2yF₂F₃cos(2α-β)-k_2yF₂F₃cos(2α+β)+k_2yF₂F₃cos(2α-3β)+k_2yF₂F₃cos(2α+3β)+k_2yF₂F₃sin(2α+3β)-k_2yF₂F₃sin(2α-3β)]

thus obtaining

To ensure that the Hessen matrix is positive, the following conditions should be satisfied:

H＞0 (25)

h is defined as the stability factor of the system, and the system is stable when the condition of equation (25) is satisfied.

3. The method for determining the parameters of the dual-machine self-synchronous driving three-mass vibrating feeder according to claim 2, characterized in that the method comprises the step of determining the parameters of the dual-machine self-synchronous driving three-mass vibrating feeder according to the parameters

Summed and then divided by 2T_uObtaining the dimensionless load moments of the two vibration exciters as follows:

in the formula

For the dimensionless load moment of the two exciters, the constraint function is as follows:

the coefficients of the synchronicity before the exciters 1 and 2 are as follows:

the larger the synchronization capability coefficient is, the stronger the synchronism of the system is, and the easier the synchronization is to be realized.

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