A resonance energy-saving eccentric vibration mill and its parameter determination method

Abstract

The present invention belongs to the technical field of vibration mill devices, and discloses a resonance energy-saving eccentric vibration mill and a method for determining its parameters. The vibration mill includes: a main vibration spring, an exciter, a driving mass, a main working cylinder, a machine body base, and a vibration isolation spring; the exciter is placed inside the driving mass, and during operation, the motor drives the eccentric rotor to rotate around the center of the rotation axis to generate eccentric excitation, so that the grinding medium in the main working cylinder impacts, frictions, shears, etc. the material, thereby crushing the material. The driving mass is located outside the gravity axis of the main working cylinder, and is connected to the main working cylinder through main vibration springs with relatively large stiffness around it. By using the structural characteristics of the eccentric vibration mill for parameter optimization, the powder efficiency can be improved, the unit volume output can be increased, and the energy consumption can be reduced without affecting the system stability, thereby realizing its engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration mill devices, and particularly to a resonance energy-saving eccentric vibration mill and a method for determining its parameters. Background Art

[0002] Vibration mills are mechanical crushing devices widely used at home and abroad. They use grinding media to impact, friction, shear, etc. on materials in a cylinder with high-frequency vibration, so as to crush the materials. With the increasing progress of modern science and technology, a large amount of raw materials need to be processed by vibration mills every year, and the important position of powder grinding technology is becoming more and more prominent, so higher requirements are put forward for the preparation of powders. However, there are three problems with existing vibration mills:

[0003] 1. Non-eccentric vibration mills have high initial costs, high foundation requirements, and low energy utilization rates.

[0004] 2. The single-machine processing capacity of vibration mills is low, the energy consumption is high, it cannot meet the output requirements of large-scale production, and its stability is poor and the corresponding motor equipment is easily damaged and costly.

[0005] 3. Most existing eccentric vibration mills are of single-mass body structure, such as patent CN201815334U. The working frequency far exceeds the resonance frequency, large vibrations will occur when starting and stopping, and there is still great room for improvement in energy utilization rate.

[0006] Therefore, it is very necessary to design a vibration mill that can not only improve the grinding efficiency but also achieve energy saving. Summary of the Invention

[0007] In order to overcome the problems existing in the prior art, the present invention proposes a resonance energy-saving eccentric vibration mill and a method for determining its parameters. Taking this new type of vibration mill as the research object, a dynamic model is first established, and the Lagrange equation is applied to obtain the differential equation of motion of the system. The response of the system is solved based on the differential equation. Numerical qualitative analysis is carried out based on theoretical derivation. Numerical simulation analysis and discussion are intended to divide the entire frequency range into several regions, and the motion states in different regions, including the motor speed, the motion displacement and trajectory of the mass body, are discussed respectively.

[0008] The technical solution of the present invention is as follows: A resonance energy-saving eccentric vibration mill, comprising: a main vibration spring 1, an exciter 2, a driving mass 3, a main working cylinder 4, a machine body base 5, and a vibration isolation spring 6; the main working cylinder 4 is connected to the machine body base 5, and the machine body base 5 is connected to the foundation through the vibration isolation spring 6; the driving mass 3 is eccentrically arranged on the main working cylinder 4, and the periphery of the driving mass 3 is connected to the main working cylinder 4 through the main vibration spring 1; the exciter 2 is placed inside the driving mass 3, and their central axes coincide; the exciter 2 includes a motor and an eccentric rotor, and during operation, the motor drives the eccentric rotor to rotate around the center of the rotation axis of the motor to generate eccentric excitation. The inside of the main working cylinder 4 is filled with grinding media, and during operation, under the action of the circumferential exciting force, the grinding media and the material inside the cylinder perform a combined movement of elliptical, circular, and linear vibrations, so as to grind and crush the material more efficiently.

[0009] The specific eccentric arrangement of the driving mass 3 is to be arranged at a position outside the gravity axis of the main working cylinder 4, and the axis of the exciter 2 is parallel to the axis of the main working cylinder 4 and located on the same horizontal plane.

[0010] A method for determining the parameters of a resonance energy-saving eccentric vibration mill includes the following steps:

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

[0012] The motion laws of the driving mass 3 and the main working cylinder 4 are described in three reference systems respectively: The first reference system is a fixed coordinate system o i x i y i , i = 1, 2, with the fixed coordinate system o2x2y2 of the main working cylinder 4 as the main coordinate, and its center O as the centroid of the main working cylinder 4; the second reference system is a translational coordinate system o' i x i y i parallel to the fixed coordinate system o i x′ i y′ i , and the third coordinate system is a rotating coordinate system o' i x″ i y″ i fixed on the centroid of the driving mass 3 and the centroid of the main working cylinder 4 respectively; the vibration system of the entire eccentric vibration mill has six degrees of freedom, namely x1, y1, ψ1, x2, y2, ψ2, where the first three items are the vibration of the driving mass 3 in the x direction, the vibration in the y direction, and the swing around its centroid, and the last three items are the vibration of the main working cylinder 4 in the x direction, the vibration in the y direction, and the swing around its centroid; the exciter 2 rotates around its own rotating shaft, and the angle with the horizontal axis is

[0013] Select x1, x2, y1, y2, ψ1, ψ2, Taking [[ID=]] as the generalized coordinates, based on the Lagrange equation, the differential equations of motion of the vibration system are derived as follows:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] where M1 = m1 + m0; M2 = m2; J o = m0r0 2 ; J1 = J m1 + J0 + m0l1 2 ;

[0022] J2 = J m2 ;

[0023] f ψ12 = f1(l1 2 + Rr m );

[0024] In the formula, m0 is the mass of the eccentric rotor of the exciter; m i includes the masses of the driving mass m1 and the main working cylinder m2, i = 1, 2; J0 is the moment of inertia of the exciter; J mi is the moment of inertia of the driving mass and the main working cylinder, i = 1, 2; r m is the eccentricity of the exciter; R is the distance from the axis of the driving mass to the connection point of the main vibration spring and the main working cylinder; f i is the damping coefficient of the driving mass and the main working cylinder in the x and y directions, i = 1, 2, and the damping coefficients in the two directions are the same; f ψi is the damping coefficient of the driving mass and the main working cylinder in the ψ direction, i = 1, 2; f ψ12 is the damping coupling coefficient of the driving mass and the main working cylinder in the ψ direction; k j is the stiffness coefficient of the main vibration spring and the vibration isolation spring in the x and y directions, j = 1, 2, and the stiffness coefficients in the two directions are the same; k ψj is the stiffness coefficient of the main vibration spring and the vibration isolation spring in the ψ direction, j = 1, 2; f dis the shaft damping coefficient of the motor; T0 is the electromagnetic torque of the motor; l1 is the distance from the axis of the driving mass to the axis of the main working cylinder; l x1 is the horizontal distance from the axis of the main working cylinder to the horizontally placed vibration isolation spring; l x2 is the horizontal distance from the axis of the main working cylinder to the vertically placed vibration isolation spring; l y1 is the vertical distance from the axis of the main working cylinder to the horizontally placed vibration isolation spring; l y2 is the vertical distance from the axis of the main working cylinder to the vertically placed vibration isolation spring; is the first derivative with respect to time; is the second derivative with respect to time;

[0025] Step 2, solve for the natural frequency of the vibration system;

[0026] When the vibration system is in a steady state, the average angular velocity of the exciter 2 does not consider the angular acceleration of the exciter Furthermore, the relationship expressions between the displacements and accelerations of the driving mass and the main working cylinder are obtained,

[0027]

[0028]

[0029] Generally in engineering, the stiffness k2 of the vibration isolation spring between the main working cylinder and the foundation part is much smaller than the stiffness k1 of the assisting spring between the main working cylinder and the driving mass. Therefore, k2 and f2 are ignored, and there is f ψ1 ≈f ψ2 ≈f ψ12 ; Based on the above analysis, the expressions of the first six terms of Equation (1) are changed to,

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] where M′1 = M1, J′1 = J1,

[0037] By using the method of elimination by addition or subtraction to reorganize Equation (2), the differential equations of relative motion of the driving mass and the main working cylinder in the x, y, and ψ directions are expressed as follows:

[0038]

[0039]

[0040]

[0041] Among them, x 12 = x1 - x2,

[0042] y 12 = y1 - y2,

[0043] ψ 12 = ψ1 - ψ2,

[0044] According to the above equations, the two natural frequencies ω0 and ω of the vibration system are obtained ψ0 , and at the same time, the response expressions of the driving mass and the main working cylinder in the x, y, and ψ directions of the two relative motions are as follows:

[0045]

[0046]

[0047]

[0048]

[0049] Among them,

[0050] Set the relative motion amplitudes of the driving mass and the main working cylinder in the x and y directions to be equal,

[0051] λ 12 = |A 12 | (6)

[0052] λ 12 is the relative motion amplitude; according to the left part of the first four expressions of the differential equation of motion, the coupling matrix and characteristic equation of the driving mass and the main working cylinder are obtained. M' is the inertial coupling matrix, K' is the stiffness coupling matrix, and Δ(ω 2 ) is the characteristic equation of the eigenvalue of the equation, and its expression is as follows:

[0053]

[0054]

[0055] Let Δ(ω 2 ) = 0, and solve to obtain the four natural frequencies of the vibration system in the x, y, and ψ directions as

[0056]

[0057]

[0058]

[0059]

[0060] Among them, ω inv is the natural frequency of the anti-phase relative motion of the two masses in the x and y directions, while ω sa is the natural frequency of the in-phase relative motion of the two masses, ω ψinv is the natural frequency of the anti-phase relative motion of the two masses in the ψ direction, and ω ψsa is the natural frequency of the in-phase relative motion of the two masses;

[0061] Without considering k2 and k ψ2 , there is ω inv = ω0, ω ψinv = ω ψ0 , and ω sa and ω ψsa are zero; therefore, ω0 and ω ψ0 are the main natural frequencies of the system;

[0062] Step 3, analysis of the motion trajectory of the main working cylinder;

[0063] The driving mass is installed on one side of the center of gravity of the entire working system, that is, the exciter is eccentrically placed; this structure can make the motion form of the internal abrasive particles different from that of the traditional mill. By analyzing the established dynamic model, the relationships between the motion trajectory, velocity, and acceleration of each point on the outer wall of the resonance energy-saving eccentric vibration mill with time are obtained; eight points with a distance of R from the centroid of the main working cylinder are taken on the outer wall of the vibration mill for motion trajectory analysis, and the angles between each point and the positive y-axis direction of the fixed coordinate system are respectively 0, π, According to the positional relationship of each point in the fixed coordinate system, the expressions of the displacement, velocity, and acceleration of each point in the horizontal and vertical directions are obtained:

[0064]

[0065]

[0066]

[0067] Table 1 Eight-point position table for the motion trajectory analysis to be carried out

[0068]

[0069] Advantages of the present invention:

[0070] (1) By adopting the eccentric excitation technology, the driving mass is placed on one side outside the center of gravity of the main working cylinder. On the basis of the ordinary circular vibration mill, the swing vibration is increased. During operation, the main working cylinder body can generate elliptical, circular and linear vibration trajectories, and the motion trajectory of the grinding medium is in a changing state, so that the grinding medium cannot jump, reducing the impact effect, while the friction, shear and rolling grinding become very intense, and the filling speed of the material is accelerated. This not only improves the grinding efficiency of the machine body, but also reduces the energy consumption and increases the output per unit volume.

[0071] (2) The working point of the system is set in the high excitation frequency sub-resonance region. During operation, the power is only 1 / 2 to 1 / 5 of that of other models with the same output, achieving energy conservation;

[0072] (3) The equipment has a simple structure, is convenient to manufacture, reduces the initial cost, and is easy to popularize. Description of the drawings

[0073] Figure 1 It is a dynamic model diagram of the vibration system of the eccentric vibration mill.

[0074] In the figure: 1. Main vibration spring; 2. Exciter; 3. Driving mass; 4. Main working cylinder body; 5. Machine body base; 6. Vibration isolation spring;

[0075] Meanings of the parameters in the figure: O - the center of the whole system; O0 - the rotation center of the exciter; - the rotation phase angle of the exciter; m0 - the mass of the exciter; m1 - the total mass of the driving mass; m2 - the mass of the main working cylinder body; r0 - the eccentricity of the exciter; k x - the spring stiffness coefficient in the x direction; k y - the spring stiffness coefficient in the y direction; l1 - the distance between the rotation center of the exciter and the system center.

[0076] Figure 2(a) is the curve of the amplitude of the driving mass and the main working cylinder body changing with frequency in the x direction;

[0077] Figure 2(b) is the curve of the amplitude of the driving mass and the main working cylinder body changing with frequency in the y direction;

[0078] Figure 2(c) is the curve of the swing amplitude of the driving mass and the main working cylinder body changing with frequency.

[0079] Figure 3 shows the simulation results for ω m0 = 75.15 rad / s; Fig. 3(a) shows the motor speed; Fig. 3(b) shows the displacement of the driving mass in the x-direction; Fig. 3(c) shows the displacement of the main working cylinder in the x-direction; Fig. 3(d) shows the comparison of the displacements of the driving mass and the main working cylinder in the x-direction; Fig. 3(e) shows the displacement of the driving mass in the y-direction; Fig. 3(f) shows the displacement of the main working cylinder in the y-direction; Fig. 3(g) shows the comparison of the displacements of the driving mass and the main working cylinder in the y-direction; Fig. 3(h) shows the swing angle of the driving mass; Fig. 3(i) shows the swing angle of the main working cylinder; Fig. 3(j) shows the comparison of the swing angles of the driving mass and the main working cylinder; Fig. 3(k) shows the motion trajectories of the driving mass and the main working cylinder.

[0080] Figure 4 shows the simulation results for ω m0 = 189.97 rad / s; Fig. 4(a) shows the motor speed; Fig. 4(b) shows the displacement of the driving mass in the x-direction; Fig. 4(c) shows the displacement of the main working cylinder in the x-direction; Fig. 4(d) shows the comparison of the displacements of the driving mass and the main working cylinder in the x-direction; Fig. 4(e) shows the displacement of the driving mass in the y-direction; Fig. 4(f) shows the displacement of the main working cylinder in the y-direction; Fig. 4(g) shows the comparison of the displacements of the driving mass and the main working cylinder in the y-direction; Fig. 4(h) shows the swing angle of the driving mass; Fig. 4(i) shows the swing angle of the main working cylinder; Fig. 4(j) shows the comparison of the swing angles of the driving mass and the main working cylinder; Fig. 4(k) shows the motion trajectories of the driving mass and the main working cylinder.

[0081] Figure 5 shows the simulation results for ω m0 = 460.84 rad / s; Fig. 5(a) shows the motor speed; Fig. 5(b) shows the displacement of the driving mass in the x-direction; Fig. 5(c) shows the displacement of the main working cylinder in the x-direction; Fig. 5(d) shows the comparison of the displacements of the driving mass and the main working cylinder in the x-direction; Fig. 5(e) shows the displacement of the driving mass in the y-direction; Fig. 5(f) shows the displacement of the main working cylinder in the y-direction; Fig. 5(g) shows the comparison of the displacements of the driving mass and the main working cylinder in the y-direction; Fig. 5(h) shows the swing angle of the driving mass; Fig. 5(i) shows the swing angle of the main working cylinder; Fig. 5(j) shows the comparison of the swing angles of the driving mass and the main working cylinder; Fig. 5(k) shows the motion trajectories of the driving mass and the main working cylinder.

[0082] Figure 6 shows the trajectory diagram of eight points on the main working cylinder; Fig. 6(a) shows the trajectory diagram of the point with coordinates (-R, 0) on the main working cylinder; Fig. 6(b) shows the trajectory diagram of the point with coordinates on the main working cylinder; Fig. 6(c) shows the trajectory diagram of the point with coordinates (0, R) on the main working cylinder; Fig. 6(d) shows the trajectory diagram of the point with coordinates Locus diagram of points; Fig. 6(e) is the locus diagram of the point with coordinates (R, 0) on the main working cylinder; Fig. 6(f) is the locus diagram of the point with coordinates Locus diagram of points; Fig. 6(g) is the locus diagram of the point with coordinates Locus diagram of points; Fig. 6(h) is the locus diagram of the point with coordinates Locus diagram of points. Specific embodiments

[0083] Embodiment 1:

[0084] To further analyze the system characteristics, numerical analysis is carried out on it.

[0085] Assume the parameters of the vibration system: The system parameters are set as follows: M1 = 300 kg, M2 = 1000 kg, m0 = 8 kg, r = 0.15 m, k1 = 4000 kN / m, k ψ1 = 6000 kN / rad, k2 = 100 kN / m, k ψ2 = 244 kN / rad, f1 = f2 = 3.83 kN·s / m, J m1 = 50 kg·m 2 J m2 = 1200 kg·m 2 . According to the above parameters, the natural frequencies of the system can be obtained as: ω0 = 131.75 rad / s, ω ψ0 = 351.79 rad / s. Motor type: Three-phase squirrel-cage, 50 Hz, 380 V, 6-pole, 0.75 kW, rated speed 980 r / min.

[0086] Embodiment 2:

[0087] To better describe the dynamic characteristics of the driving mass and the main working cylinder in different resonance regions, the Runge-Kutta program can be applied to simulate the system's differential equation of motion. The vibration system parameters and motor parameters are given. According to the results in the numerical analysis, ω m0 is divided into three regions, each region corresponding to different motion states. By changing k1 and k ψ1 , and then affecting the value of ω m0 , the simulation results of the three regions are discussed.

[0088] (a) Simulation result diagram under the condition of ω m0 = 75.15 rad / s;

[0089] Fig. 3 is when k1 = 6000 kN / m, k ψ1The simulation results obtained with = 9000 kN·m / rad. Combining the system parameters, the natural frequency ω′0 = 161.32 rad / s can be calculated. As shown in Fig. 3(a), the rotational speed of the motor stabilizes at 880.2 r / min, that is, the operating frequency ω I ≈ 75.14 rad / s. Then the ratio z0 between the operating frequency ω I and the natural frequency ω′0 is 0.57. Since the frequency ratio in the numerical characteristic analysis is the same as that in the simulation analysis, i.e., z0 = ω m0 / ω0 = ω I / ω′0, the simulation result of ω m0 = 75.15 rad / s can be obtained. In addition, at 30 s, a disturbance with a magnitude of π / 3 phase is applied to the exciter. After receiving the disturbance, the exciter quickly returns to the original stable state, indicating that the motion state of the system is stable. Figures 3(b) - 3(j) They respectively represent the displacement curves of the mass body in the x, y, and ψ directions. It can be seen that the vibration state of the system reaches stability after about 3 s. According to the enlarged view, the motion forms of the mass body in the x, y, and ψ directions at the steady state can be clearly seen. Among them, the main working cylinder has obvious displacements in all directions, which is exactly what is required in engineering and can be better applied to the design of the new vibration mill. The motion trajectory diagram at its steady state is shown in Fig. 3(k). The trajectory shape of the driving mass body is an ellipse, and the trajectory shape of the center of the main working mass body can be approximated as a circle.

[0090] (b) Simulation result diagram under the condition of ω m0 = 189.97 rad / s;

[0091] Fig. 4 shows the simulation results obtained when k1 = 500 kN / m, k ψ1 = 750 kN·m / rad. According to the above parameters, ω′ ψ0 = 125.39 rad / s can be calculated. In Fig. 4(a), it can be seen that the rotational speed of the motor is basically stable at 631.08 r / min, that is, the operating frequency ω II ≈ 65.19 rad / s. Then the ratio z II between the operating frequency ω ψ0 and the natural frequency ω′ ψ0 is 0.54. Then the simulation result of ω m0 = 189.97 rad / s can be obtained. Similarly, at 30 s, a π / 3 phase disturbance is applied to the motor. After a slight fluctuation in the phase difference, it quickly returns to the original stable state, indicating that the disturbance does not affect the stability of the system. The displacement curve diagrams of the system in the x, y, and ψ directions are respectively as Figures 4(b) - 4(j)As shown, it can be seen that the amplitude reaches stability after about 3 s, and the motion form can be obtained from the displacement magnification diagram. By comparing the motion trajectory diagram in the stable state in Figure 3, it can be seen that the motion trajectory shape of the driving mass is still an ellipse, and the motion trajectory of the centroid position of the main working cylinder body is still a circle, indicating that the change in spring stiffness will not change the overall shape of the motion trajectory, but the motion amplitudes in each direction will change.

[0092] (c) ω m0 Simulation result diagram under the condition of ω = 460.84 rad / s;

[0093] In this resonance region, the spring stiffness of the system is k1 = 100 kN / m, k ψ1 = 150 kN·m / rad. Figure 6 is the simulation result obtained when ω m0 = 460.84 rad / s. The obtained motor speed diagram is shown in Figure 5(a). It can be seen that the speed of motor 1 during stable operation is about 631.08 r / min, that is, the operating frequency ω III ≈ 65.19 rad / s. According to the equal-frequency theory, z ψ0 = 1.31. At the same time, a disturbance of π / 3 is applied to the exciter at 30 s, and the phase difference between the two exciters quickly returns to the original stable state soon after the disturbance, indicating that the motion state of the system is stable. Figures 5(b) - 5(j) They respectively represent the displacement curves of the mass in the x, y, and ψ directions. It can be seen that the system vibration reaches stability after about 3 s. According to the magnification diagram, the motion forms of the mass in the x, y, and ψ directions at the steady state can be clearly seen. The motion trajectory at the steady state is shown in Figure 5(k), and the planar motion trajectory shape can be clearly seen.

[0094] Example 3:

[0095] The trajectory analysis of the main eight working points of the main working cylinder body is carried out through the simulation program, so as to more intuitively and clearly analyze the working state of the whole system; the motion trajectories of each point at the steady state are shown in Figure 6.

[0096] According to the three examples, finally, when the working point is in the working state at ω m0 = 75.15 rad / s, the system is in the high-excitation-frequency sub-resonance region, and the operating frequency ω m0 is close to the natural frequency ω0. The required exciting force is small, and the sub-resonance state has a more stable amplitude than the super-resonance state. Therefore, when the vibrator works in the sub-resonance state, the best energy-saving effect can be achieved.

Claims

1. A method for determining the parameters of a resonance energy-saving eccentric vibration mill, characterized in that The resonance energy-saving eccentric vibration mill includes: a main vibration spring (1), an exciter (2), a driving mass (3), a main working cylinder (4), a machine body base (5), and a vibration isolation spring (6); the main working cylinder (4) is connected to the machine body base (5), and the machine body base (5) is connected to the foundation through the vibration isolation spring (6); the driving mass (3) is eccentrically arranged on the main working cylinder (4), and the periphery of the driving mass (3) is connected to the main working cylinder (4) through the main vibration spring (1); the exciter (2) is placed inside the driving mass (3), and their central axes coincide; the exciter (2) includes a motor and an eccentric rotor. During operation, the motor drives the eccentric rotor to rotate around the center of the motor rotation axis to generate eccentric excitation. The parameter determination method described above includes the following steps: Step 1, establish a dynamic model and a system motion differential equation; The kinetic model is established as follows: The driving mass (3) and the main working cylinder (4) describe their motion laws in three reference systems respectively: The first reference system is the fixed coordinate system o i x i y i , i = 1, 2. Taking the fixed coordinate system o2x2y2 of the main working cylinder (4) as the main coordinate, with its center O being the mass center of the main working cylinder (4); The second reference system is a translational coordinate system o i x i y i parallel to the fixed coordinate system o i ′x i ′y i ′. The third coordinate system is a rotational coordinate system o i ′x i ″y i ″ fixed on the mass centers of the driving mass (3) and the main working cylinder (4) respectively; The vibration system of the entire eccentric vibration mill has six degrees of freedom, namely x1, y1, ψ1, x2, y2, ψ2. The first three items are the vibration of the driving mass (3) in the x direction, the vibration in the y direction, and the swing around its mass center. The last three items are the vibration of the main working cylinder (4) in the x direction, the vibration in the y direction, and the swing around its mass center; The vibrator (2) rotates around its own rotating shaft, and the angle with the horizontal axis is The establishment of the system motion differential equation is as follows: Select \(x_1\), \(x_2\), \(y_1\), \(y_2\), \(\psi_1\), \(\psi_2\), as the generalized coordinates. Based on the Lagrange equation, the differential equation of motion of the vibration system is derived as follows: where M1 = m1 + m0; M2 = m2; J o = m0r0 2 ; J1 = J m1 + J0 + m0l1 2 ; J2 = J m2 ; f ψ12 = f1(l1 2 + Rr m )); where m0 is the mass of the eccentric rotor of the exciter; m i includes the masses of the driving mass body m1 and the main working cylinder m2, i = 1, 2; J0 is the moment of inertia of the exciter; J mi is the moment of inertia of the driving mass body and the main working cylinder, i = 1, 2; r m is the eccentricity of the exciter; R is the distance from the axis of the driving mass body to the connection point of the main vibration spring and the main working cylinder; f i is the damping coefficient of the driving mass body and the main working cylinder in the x and y directions, i = 1, 2, and the damping coefficients in the two directions are the same; f ψi is the damping coefficient of the driving mass body and the main working cylinder in the ψ direction, i = 1, 2; f ψ12 is the damping coupling coefficient of the driving mass body and the main working cylinder in the ψ direction; k j is the stiffness coefficient of the main vibration spring and the vibration isolation spring in the x and y directions, j = 1, 2, and the stiffness coefficients in the two directions are the same; k ψj is the stiffness coefficient of the main vibration spring and the vibration isolation spring in the ψ direction, j = 1, 2; f d is the shaft damping coefficient of the motor; T0 is the electromagnetic torque of the motor; l1 is the distance from the axis of the driving mass body to the axis of the main working cylinder; l x1 is the horizontal distance from the axis of the main working cylinder to the horizontally placed vibration isolation spring; l x2 is the horizontal distance from the axis of the main working cylinder to the vertically placed vibration isolation spring; l y1 is the vertical distance from the axis of the main working cylinder to the horizontally placed vibration isolation spring; l y2 is the vertical distance from the axis of the main working cylinder to the vertically placed vibration isolation spring; is the first derivative with respect to time; is the second derivative with respect to time; Step 2, solve the natural frequency of the vibration system based on the established dynamic model and system motion differential equation; The specific solution of the natural frequency of the vibration system is as follows: When the vibration system is in a steady state, the average angular velocity of the exciter (2) Without considering the angular acceleration of the exciter Furthermore, the relationship expressions between the displacements and accelerations of the driving mass and the main working cylinder are obtained. Ignoring the vibration isolation spring stiffness k2 and damping coefficient f2 of the main working cylinder body and the base part, f ψ1 = f ψ2 = f ψ12 ; Based on the above analysis, the expressions of the first six terms of Equation (1) are changed to where, M1′ = M1, J1′ = J1, By using the method of elimination by addition or subtraction to reorganize Equation (2), the differential equations of relative motion of the driving plastid and the main working cylinder in the x, y, and ψ directions are expressed as: wherein, x 12 = x1 - x2, y 12 = y1 - y2, ψ 12 = ψ1 - ψ2, According to the above formula, the two natural frequencies ω0 and ω of the vibration system are obtained. ψ0 Meanwhile, the response expressions of the two relatively moving drive masses and the main working cylinder in the x, y, and ψ directions are as follows: Among them, Set the relative motion amplitudes of the driving mass and the main working cylinder in the x and y directions to be equal. λ 12 = |A 12 | (6) λ 12 is the relative motion amplitude; According to the left parts of the equalities of the first four expressions of the kinematic differential equations, the coupling matrix and characteristic equation of the driving mass and the main working cylinder are obtained. M' is the inertia coupling matrix, K' is the stiffness coupling matrix, and Δ(ω 2 ) is the characteristic equation of the eigenvalues of the equation, and its expression is as follows: Let Δ(ω 2 ) = 0, and the four natural frequencies of the vibration system in the x, y, and ψ directions are obtained as where ω inv is the natural frequency of the anti-phase relative motion of the two masses in the x and y directions, and ω sa is the natural frequency of the in-phase relative motion of the two masses, ω ψinv is the natural frequency of the anti-phase relative motion of the two masses in the ψ direction, and ω ψsa is the natural frequency of the in-phase relative motion of the two masses; Disregarding k2 and k ψ2 After that, there is ω inv = ω0, ω ψinv = ω ψ0 and ω sa and ω ψsa are zero; thus ω0 and ω ψ0 are the main natural frequencies of the system; Step 3, analyze the motion trajectory of the main working cylinder.

2. The parameter determination method of the resonance energy-saving type eccentric vibration mill according to claim 1, characterized in that, The eccentric arrangement of the driving mass (3) is specifically to be arranged at a position outside the gravity axis of the main working cylinder (4).

3. The method for determining the parameters of the resonance energy-saving eccentric vibration mill according to claim 1, characterized in that The specific analysis of the motion trajectory of the main working cylinder is as follows: The driving mass is installed on one side of the center of gravity of the entire working system, that is, the exciter is eccentrically placed; by analyzing the established dynamic model, the relationships between the motion trajectories, velocities, and accelerations of each point on the outer wall of the resonance energy-saving eccentric vibration mill with time are obtained; eight points with a distance of R from the centroid of the main working cylinder are taken on the outer wall of the vibration mill for motion trajectory analysis; according to the position relationships of each point in the fixed coordinate system, the displacement, velocity, and acceleration expressions in the horizontal and vertical directions are obtained:

4. The parameter determination method of the resonance energy-saving eccentric vibration mill according to claim 3, characterized in that, Among the eight points selected at a distance R from the centroid of the main working cylinder body, the angles between each point and the positive direction of the y-axis of the fixed coordinate system are respectively

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