WO2020125088A1 - 一种三磨筒高频振动磨机的参数确定方法 - Google Patents

一种三磨筒高频振动磨机的参数确定方法 Download PDF

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WO2020125088A1
WO2020125088A1 PCT/CN2019/105529 CN2019105529W WO2020125088A1 WO 2020125088 A1 WO2020125088 A1 WO 2020125088A1 CN 2019105529 W CN2019105529 W CN 2019105529W WO 2020125088 A1 WO2020125088 A1 WO 2020125088A1
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mass
exciter
exciters
synchronization
displacement
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French (fr)
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张学良
李超
崔世举
高志国
岳红亮
李振民
马辉
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Northeastern University China
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Northeastern University China
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B02—CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
    • B02C—CRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
    • B02C17/00—Disintegrating by tumbling mills, i.e. mills having a container charged with the material to be disintegrated with or without special disintegrating members such as pebbles or balls
    • B02C17/14—Mills in which the charge to be ground is turned over by movements of the container other than by rotating, e.g. by swinging, vibrating, tilting
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B02—CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
    • B02C—CRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
    • B02C17/00—Disintegrating by tumbling mills, i.e. mills having a container charged with the material to be disintegrated with or without special disintegrating members such as pebbles or balls
    • B02C17/18—Details
    • B02C17/24—Driving mechanisms
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B02—CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
    • B02C—CRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
    • B02C25/00—Control arrangements specially adapted for crushing or disintegrating
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling

Definitions

  • the invention belongs to the technical field of a vibration mill device, and relates to a parameter determination method of a three-mill barrel high-frequency vibration mill.
  • Vibration mill is an ultra-fine crushing device with balls or rods as the medium, which can grind 2mm materials to a few microns. It has the advantages of high efficiency, energy saving, space saving, uniform product size, etc. It occupies an important advantage in the field of ultrafine crushing and has been widely used.
  • the working principle of the vibration mill is to use the exciting force generated by the eccentric block to make the cylinder body vibrate at high frequency, and use the grinding medium to crush the material.
  • the invention is a three-mill barrel mill, which can achieve finer grinding under high frequency operation. Ordinary mills use less than three vibrators.
  • the present invention has the following advantages over ordinary mills:
  • a mill with a small number of exciters requires very high requirements for the exciter when driving the entire machine.
  • the technical requirements for the exciter are very high, and the present invention uses three exciters While ensuring that the rated power and standard working requirements are met, the technical requirements of the vibrator are reduced, at the same time the loss of the vibrator is reduced and the service life of the machine is increased.
  • the invention uses three-machine drive, which can work in high frequency state.
  • the three motors resonate, high amplitude can be achieved, so that the material crushing effect is better, and the noise is small, pollution-free, and the reliability is good.
  • the invention takes the three-machine four-mass dynamic model as the research object, uses the average parameter method, the transfer function method and other principles to establish differential equations for the model, and obtains the synchronization stability coefficient curve of the system through the characteristics analysis of synchronization and stability , The maximum dimensionless coupling torque diagram, etc. Finally, through the simulation of the vibration system, the mass velocity curve, displacement curve, phase difference diagram are obtained, and the correctness of the method is verified by the comparison of characteristic analysis and system simulation.
  • a method for determining the parameters of a three-mill barrel high-frequency vibration mill includes three vibrators, four masses, and springs; mass 1, mass 2, and mass 3 are: The three grinding cylinders are connected to the mass body 4 through the spring, and the mass body 4 is connected to the substrate through the spring; the three vibrators are located on the mass body 1, the mass body 2, and the mass body 3; the three vibrators rotate in the same direction, And each vibrator rotates around its own rotation axis; the method of determining the parameters of the vibrator includes the following steps:
  • Step 1 Establish the dynamic model and differential equation of motion of the system
  • the dynamic model of the vibration mill is shown in Figure 1. Two rectangular coordinate systems are established. The three exciters rotate in the same direction. The motion of the body can be divided into vibration in the x and y directions and swing around the center of mass, with x, y and ⁇ respectively Said.
  • M 1 m 1 + m 01
  • M 2 m 2 + m 02
  • M 3 m 3 + m 03
  • M 4 m 4 + m 01 + m 02 + m 03
  • J ⁇ J m4 +(m 01 +m 02 +m 03 )(r 2 +l 2 )——the rotational inertia of the rigid body;
  • phase difference between the exciter 1 and the exciter 2 is 2 ⁇ 1
  • phase difference between the exciter 2 and the exciter 3 is 2 ⁇ 2
  • the average phase difference between the three exciters is
  • M mass coupling matrix
  • K stiffness coupling matrix
  • ⁇ ( ⁇ 2 ) is the eigenvalue equation
  • ⁇ c12 ( ⁇ 1 , ⁇ 2 ) and ⁇ c23 ( ⁇ 1 , ⁇ 2 ) are the dimensionless coupling torques between motors 1 , 2 and 2 , 3 , respectively, and their constraint functions are as follows:
  • Step 3 Stability criteria for synchronization status
  • the kinetic energy T and potential energy V of the whole system are obtained as:
  • the average kinetic energy E T and average potential energy E V can be obtained in a single period
  • the Hesse matrix of I is expressed as H, and
  • H 1 and H 2 are defined as the stability capability coefficient of the system under the synchronous conditions.
  • the above formula is the expression of the stability capability of the system. When the above formula (23) is satisfied, the system is stable.
  • the beneficial effect of the present invention is that the parameters of the high-frequency vibration mill obtained by the method can reduce the technical requirements of the shaker, reduce the loss of the shaker, increase the service life of the machine, and at the same time ensure a better crushing effect and low noise , No pollution, good reliability. It has a great guiding role in the design of the structural parameters of the vibrating feeder equipment and the selection of the working area.
  • Figure 8 Area 1 three motor speed
  • Figure 10 the displacement of area 1 in the x direction
  • Figure 11 is a partial enlarged front view of the displacement of area 1 in the x direction;
  • Figure 12 is a partial enlarged view of the area 1 in the x direction
  • Figure 13 Displacement of area 1 in the y direction
  • Figure 14 is a partial enlarged view of the front portion of the area 1 displacement in the y direction;
  • Figure 17 area 2 (a) three motor speed
  • Fig. 20 is a partially enlarged front view of the displacement in the x direction of area 2(a);
  • Figure 21 is a partial enlarged view of the rear part of the displacement in the area 2(a) in the x direction;
  • Figure 22 area 2 (a) y-direction displacement diagram
  • Figure 23 is a partial enlarged view of the front part of the displacement in the area 2(a) in the y direction;
  • Figure 24 is a partial enlarged view of the rear part of the area 2(a) displacement in the y direction;
  • Figure 28 the displacement of area 2(b) in the x direction
  • Figure 29 is a partial enlarged front view of the displacement in the x direction of the area 2(b);
  • Figure 30 is a partially enlarged view of the rear portion of the displacement in the x direction of area 2(b);
  • Figure 32 is a partial enlarged view of the front of the area 2 (b) displacement in the y direction;
  • Figure 33 is a partially enlarged view of the rear portion of the displacement in the y direction of area 2(b);
  • Fig. 36 The phase difference between three exciters in area 3.
  • Figure 37 The displacement of area 3 in the x direction
  • Figure 38 is a partially enlarged front view of the area 3 displaced in the x direction;
  • 39 is a partial enlarged view of the rear portion of the area 3 displaced in the x direction;
  • Figure 40 Displacement of area 3 in the y direction
  • Figure 41 is a partially enlarged front view of the area 3 displaced in the y direction;
  • Figure 42 is a partial enlarged view of the rear portion of the area 3 displaced in the y direction;
  • the model consists of three vibrators and four masses. The three exciters rotate in the same direction, and each exciter rotates around its own axis of rotation to Said.
  • the mass of mass 4 is 2000 kg
  • the masses of the exciters 1, 2, and 3 are equal, making the three excitations
  • k 1 , k 2 , k 3 46000kN/m
  • k 4 10kN/m
  • k ⁇ 4000kN/m
  • Figure 2 shows the phase angle relationship of the two exciters.
  • the phase difference appears two sets of solutions, 0° and 120°, and 120°; in the sub-resonance region relative to ⁇ 3 , 0° and 120°, and 120°; in the over resonance region with respect to ⁇ 3 , 0° and 120°, and 120°.
  • Figure 3 shows the lag angles of the three masses, ⁇ is the lag angle, in the first region, ⁇ 1 is 0, ⁇ 2 and ⁇ 4 are 180; in the second region, ⁇ 2 is 360, ⁇ 1 and ⁇ 4 are 180; In the third region, ⁇ 4 is 360, and ⁇ 1 and ⁇ 2 are 180.
  • Figures 4 and 5 show the stability capability coefficient curve, and it can be seen from the enlarged view of the curve that the stability capability coefficient curve is greater than or equal to 0 in the entire interval. And in zone 1, the stability coefficient increased significantly.
  • Fig. 6 shows the synchronization capability coefficient. It can be seen that the extreme value is obtained at ⁇ ⁇ , and the synchronization capability coefficient is 0 at ⁇ 0 and ⁇ 3
  • Fig. 7 shows the maximum coupling torque curve. It can be seen that the maximum coupling torque takes an extreme value at ⁇ ⁇ and also increases significantly at ⁇ 3 .
  • the simulation of the vibration system mainly uses the fourth-order Rouge-Kutta program for simulation, and the simulation is carried out one by one according to the three areas previously divided.
  • the motor speed corresponding to the simulation result is 894r/min. Through calculation, this time corresponds to 114rad/s in the phase difference diagram of numerical analysis.
  • Figure 8 shows the steady state of the speed of the two shakers.
  • the speed of the two shakers quickly stabilizes, and the synchronization speed is basically stable at about 893r/min.
  • the shaker 2 increases Disturbance, the speed has not changed significantly.
  • FIG 9 shows the stable state of the phase difference. Under the stable state, the phase difference between the exciters 1 and 2, 2 and 3, 1 and 3 is 120°, and interference is added at 30s. After the displacement curve produces small fluctuations, it returns to The original phase difference relationship.
  • Figures 10, 11 and 12 show the displacement of the masses 1, 2 and 3 in the x direction. It can be seen from the magnification diagram of the local displacement that the displacement between the masses 1, 2 and 3 is equal, the mass 4 has no movement in the x direction, and interference is added at 30s, and the displacement curve does not change significantly.
  • Figures 13, 14 and 15 show the displacement of the masses 1, 2 and 3 in the y direction. It can be seen from the partially enlarged view that the displacement between the masses 1, 2, and 3 is equal, and the mass 4 is not displaced in the y direction. The displacement curves of the plastid before and after interference are consistent.
  • Figure 16 shows the system swing. It can be seen that the swing angle is around 0°, and there is no obvious change when the interference is increased.
  • Figure 17 shows the steady state of the speed of the two exciters.
  • the speed of the two exciters quickly stabilizes, and the synchronization speed is basically stable at 870r/min.
  • the exciter 2 increases the interference , No significant change in speed.
  • Fig. 18 shows the stable state of the phase difference, the phase difference between the exciters 1 and 2, the exciters 2 and 3, and the exciters 1 and 3 is 0°; interference is added at 30s, and the phase difference remains unchanged.
  • Figures 19, 20 and 21 show the displacement of the masses 1, 2 and 3 in the x direction. From the displacement magnification diagram, it can be seen that the displacement between the masses 1, 2, and 3 is equal, and the movement displacement of the mass 4 is opposite to the movement direction of the masses 1, 2, 3; interference is added at 30s, and the displacement curve keep it steady.
  • Figures 22, 23 and 24 show the displacement of the masses 1, 2 and 3 in the y direction. It can be seen from the partial enlarged view that the displacement between the masses 1, 2, 3 is equal, and the movement displacement of the mass 4 is opposite to the movement direction of the masses 1, 2, 3; interference is added at 30s, and the displacement curve remains stable .
  • Figure 25 shows the system's swing. It can be seen that the swing angle is around 0°, and there is no obvious change in increasing interference.
  • Figure 26 shows the steady state of the speed of the two exciters.
  • the speed of the two exciters quickly stabilizes, and the synchronization speed is basically stable at 982r/min.
  • the exciter 2 increases the interference , No significant change in speed.
  • Figure 27 shows that the phase difference is stable, the exciter 1 and 2, the exciter 2 and 3, the phase difference between the exciter 1 and 3 is 0°; interference is added at 30s, and the phase difference is abruptly changed to 120° .
  • Figures 28, 29 and 30 show the displacement of plastids 1,2,3 in the x direction. From the displacement magnification diagram, it can be seen that the displacement between the masses 1, 2, 3 is equal, and the movement displacement of the mass 4 is opposite to the movement direction of the masses 1, 2, 3; interference is added at 30s, and the displacement changes The mass 4 is at rest, and the displacements of masses 1, 2, and 3 are equal.
  • Figures 31, 32 and 33 show the displacement of the masses 1, 2 and 3 in the y direction. It can be seen from the displacement magnification diagram that the displacement between the masses 1, 2, and 3 is equal, and the movement displacement of the mass 4 is opposite to the movement direction of the masses 1, 2, 3; interference is added at 330s, and the displacement changes The mass 4 is at rest, and the displacements of masses 1, 2, and 3 are equal.
  • Figure 34 shows the oscillation of the system. It can be seen that the oscillation angle is around 0°, and there is no significant change in increasing interference.
  • Figure 35 shows the steady state of the speed of the two exciters.
  • the speed of the two exciters quickly stabilizes, and the synchronization speed is basically stable at 982r/min.
  • the exciter 2 increases the interference , No significant change in speed.
  • Fig. 36 shows the stable state of the phase difference, the exciters 1 and 2, the exciters 2 and 3, and the phase difference between the exciters 1 and 3 is 0°; interference is added at 30s, and the phase difference changes suddenly, and becomes 120° .
  • Figures 37, 38 and 39 show the displacement of plastids 1,2,3 in the x direction. It can be seen from the displacement magnification diagram that the displacement between the masses 1, 2, and 3 is equal, and the movement displacement of the mass 4 is opposite to the movement direction of the masses 1, 2, 3; interference is added at 30s, and the mass 4 At rest, the displacements of masses 1, 2, and 3 are equal.
  • Figures 40, 41 and 42 show the displacement of the masses 1, 2 and 3 in the y direction. From the displacement magnification diagram, it can be seen that the displacement between the masses 1, 2, 3 is equal, and the movement displacement of the mass 4 is opposite to the movement direction of the masses 1, 2, 3; interference is added at 30s, and the displacement changes The mass 4 is at rest, and the displacements of masses 1, 2, and 3 are equal.
  • Figure 43 shows the system's swing. It can be seen that the swing angle is around 0°, and there is no obvious change in increasing interference.
  • the system simulation results show that the phase difference of the second half of Zone 1, Zone 3, and Zone 2 does not return to the original state after interference, while in the first half of Zone 2, the system is still stable after being interfered with.
  • the working state of the working area that is, the first half of area 2
  • the displacements of mass 1, mass 2, and mass 3 in the x and y directions are equal and the same
  • the displacement of mass 4 in the x and y directions is large And with reverse vibration.
  • the present invention provides a new model of the vibrating mill. It uses two machines to drive the four masses. According to the establishment of differential equations, numerical analysis and simulation, the vibrating feeder of the present invention is obtained in zone 1, zone 3 and working area. The phase difference of the second half of 2 cannot be restored to the original state after the interference, and the stability is insufficient. Therefore, the working area is the second half of the second zone, and the motion state of the vibrating mill during operation can be analyzed.
  • the research content of the present invention has an important guiding role in the design of the structural parameters of the vibrating feeder equipment and the selection of the working area.
  • Example 3 Example data parameters of a vibrating feeder. The invention is not limited to this design parameter.
  • the two motors have the same model, three-phase squirrel-cage type (model VB-1082-W, 380V, 50Hz, 6-pole, ⁇ -connected, 0.75kw, speed 980r/min, 39kg).

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Abstract

一种三磨筒高频振动磨机的参数确定方法，通过应用平均参数法、传递函数法等原理对模型建立微分方程，通过同步性和稳定性的特性分析得到系统的同步性稳定能力系数曲线，无量纲耦合力矩最大值图等，最后通过振动系统的仿真，得到质体的速度曲线，位移曲线，相位差图，通过特性分析和系统仿真的对比验证方法的正确性。高频振动磨机参数能够降低激振器的技术要求，减少激振器的损耗，提高机器的使用寿命，同时保证粉碎的效果更好，噪声小、无污染、可靠性好，对于振动给料机设备的结构参数设计以及工作区域的选择具有重大指导作用。

Description

一种三磨筒高频振动磨机的参数确定方法 技术领域
本发明属于振动磨机装置技术领域，涉及一种三磨筒高频振动磨机的参数确定方法。
背景技术
振动磨机是以球或棒为介质的超微粉碎设备，可以使2mm物料磨碎至数微米。它具有高效、节能、节省空间、产品粒度均匀等优点，在超微粉碎领域内占有重要优势，得到了广泛的应用。振动磨机工作原理是利用偏心块产生的激振力使筒体作高频振动，利用研磨介质使物料粉碎。
本发明是三磨筒磨机，能够在高频工作下达到更精细的研磨。普通的磨机使用的是激振器数量一般少于三个，本发明相对于普通的研磨机有以下优点：
1.激振器数量少的磨机，驱动整个机器工作时，对激振器的要求很高，为了保证达到额定功率，需要激振器的技术要求很高，而本发明使用三个激振器，在保证达到额定功率和标准工作要求同时，降低了激振器的技术要求，同时减少激振器的损耗，提高机器的使用寿命。
2.本发明使用三机驱动，能在高频状态下工作，当三个电机共振，可以达到很高的振幅，从而使物料粉碎效果更好，且噪声小、无污染、可靠性好。
发明内容
本发明是以三机四质体动力学模型为研究对象，应用平均参数法、传递函数法等原理对模型建立微分方程，通过同步性和稳定性的特性分析得到系统的同步性稳定能力系数曲线，无量纲耦合力矩最大值图等，最后通过振动系统的仿真，得到质体的速度曲线，位移曲线，相位差图，通过特性分析和系统仿真的对比验证方法的正确性。
本发明的具体技术方案为：
一种三磨筒高频振动磨机的参数确定方法，该振动磨机的动力学模型包括三个激振器、四个质体、弹簧；质体1、质体2、质体3分别为三个磨筒通过弹簧与质体4相连，质体4通过弹簧与基底相连；三个激振器分别位于质体1、质体2、质体3上；三个激振器同向旋转，并且每个激振器绕自身回转轴旋转；所述激振器的参数确定方法，包括如下步骤：
步骤一：建立系统的动力学模型和运动微分方程
振动磨机的动力学模型如图1所示，建立两个直角坐标系，三激振器同向旋转，机体运动可分为x,y方向振动及绕质心摆动，分别以x,y和ψ表示。
选择x，y，ψ，
Figure PCTCN2019105529-appb-000001
为广义坐标，求解系统的动能、势能、能量散逸函数，将其带入拉格朗日方程，得系统的微分方程。
Figure PCTCN2019105529-appb-000002
式中
m 0i——激振器的质量(i＝1～3)；m i——质体的质量(i＝1～4)；
M 1＝m 1+m 01，M 2＝m 2+m 02，M 3＝m 3+m 03，M 4＝m 4+m 01+m 02+m 03
J ψ＝J m4+(m 01+m 02+m 03)(r 2+l 2)——振动刚体的转动惯量；
Figure PCTCN2019105529-appb-000003
——激振器转动惯量(i＝1～3)；
Figure PCTCN2019105529-appb-000004
k i(i＝1～4)——弹簧刚度系数；
Figure PCTCN2019105529-appb-000005
f i(i＝1～4)——阻尼系数；
Figure PCTCN2019105529-appb-000006
——激振器i的相位角(i＝1～3)；
Figure PCTCN2019105529-appb-000007
——激振器i的角速度(i＝1～3)；
Figure PCTCN2019105529-appb-000008
——激振器i的角加速度(i＝1～3)；
步骤二：同步性分析
设激振器1和激振器2之间的相位差为2α 1，激振器2和激振器3之间的相位差为2α 2，三激振器之间的平均相位差为
Figure PCTCN2019105529-appb-000009
Figure PCTCN2019105529-appb-000010
重新整理上式有
Figure PCTCN2019105529-appb-000011
通过传递函数法，可求得系统的响应：
Figure PCTCN2019105529-appb-000012
定中间参量：
Figure PCTCN2019105529-appb-000013
Figure PCTCN2019105529-appb-000014
Figure PCTCN2019105529-appb-000015
Figure PCTCN2019105529-appb-000016
Figure PCTCN2019105529-appb-000017
Figure PCTCN2019105529-appb-000018
Figure PCTCN2019105529-appb-000019
Figure PCTCN2019105529-appb-000020
Figure PCTCN2019105529-appb-000021
Figure PCTCN2019105529-appb-000022
c 2＝e 1，d 2＝f 1，e 2＝c 1，f 2＝d 1，h 2＝e 1，p 2＝f 1，u 2＝u 1，z 2＝z 1，
c 3＝e 1，d 3＝f 1，e 3＝e 1，f 2＝f 1，h 3＝c 1，p 3＝d 1，u 3＝u 1，z 3＝z 1
Figure PCTCN2019105529-appb-000023
γ 5＝γ 2，γ 6＝γ 1，γ 7＝γ 2，γ 8＝γ 4，γ 9＝γ 2，γ 10＝γ 2，γ 11＝γ 1，γ 12＝γ 4
式中γ i(i＝1～4)——滞后角；
Figure PCTCN2019105529-appb-000024
Figure PCTCN2019105529-appb-000025
式中，M——质量耦合矩阵，K——刚度耦合矩阵，Δ(ω 2)为特征值方程
令特征值方程等于0，即Δ(ω 2)＝0：
Figure PCTCN2019105529-appb-000026
求得固有频率：
Figure PCTCN2019105529-appb-000027
当三个激振器能够同步运转时，有
Figure PCTCN2019105529-appb-000028
对x 1、x 2、x 3、y 1、y 2、y 3、ψ关于时间t进行二阶求导，并带入式，在0～2π上对
Figure PCTCN2019105529-appb-000029
进行积分，取均值并整理后，得到三激振器的平衡方程如下：
Figure PCTCN2019105529-appb-000030
其中
Figure PCTCN2019105529-appb-000031
在上述积分过程中，对比
Figure PCTCN2019105529-appb-000032
随时间t的变化程度，2α 1和2α 2的变化很小，可将两个参数视为其慢变参数，根据直接运动分离法，在积分过程中2α 1和2α 2以其积分中值
Figure PCTCN2019105529-appb-000033
和
Figure PCTCN2019105529-appb-000034
表示。
各激振器间输出力矩之差为：
Figure PCTCN2019105529-appb-000035
Figure PCTCN2019105529-appb-000036
对上述两式进行整理，得
Figure PCTCN2019105529-appb-000037
其中，
Figure PCTCN2019105529-appb-000038
Figure PCTCN2019105529-appb-000039
在上述推导中，τ c12(α 1,α 2)，τ c23(α 1,α 2)分别为1、2电机之间和2、3电机之间无量纲耦合力矩，其约束函数如下：
Figure PCTCN2019105529-appb-000040
综上，结合上式，可得三激振器的同步性判据
Figure PCTCN2019105529-appb-000041
通过上式，可以看出任意两个激振器的无量纲残余力矩之差的绝对值小于或等于无量纲耦合力矩的最大值。
对
Figure PCTCN2019105529-appb-000042
求和，并除以3T u，即可以得到三激振器平均无量纲负载力矩，表示为τ a(α 1,α 2)。
Figure PCTCN2019105529-appb-000043
三激振器平均无量纲负载力矩的约束函数如下
|τ a(α 1,α 2)|≤τ amax                       (17)
定义同步能力系数为ζ ij(i,j＝1,2,3,4)，可得，
Figure PCTCN2019105529-appb-000044
同步能力系数越大，系统的同步能力越强，越容易达到同步。
步骤三：同步状态的稳定性判据
求得整个系统动能T和势能V分别为：
Figure PCTCN2019105529-appb-000045
Figure PCTCN2019105529-appb-000046
单周期内可求得平均动能E T与平均势能E V
在一个周期内系统的Hamilton平均作用量(I)为
Figure PCTCN2019105529-appb-000047
I的Hesse矩阵表示为H，得
Figure PCTCN2019105529-appb-000048
其中
Figure PCTCN2019105529-appb-000049
Figure PCTCN2019105529-appb-000050
Figure PCTCN2019105529-appb-000051
令
H 1＝d 11
H 2＝d 11d 22-d 12d 21
为了使I的Hesse矩阵正定，即H矩阵正定，应满足
H 1＞0，H 2＞0                     (23)
将H 1与H 2定义为系统的同步条件下的稳定能力系数，上式即为系统的稳定性能力的表达式，当满足上式(23)时，系统稳定。
本发明的有益效果为，该方法得到的高频振动磨机参数，能够降低激振器的技术要求，减少激振器的损耗，提高机器的使用寿命，同时保证粉碎的效果更好，噪声小、无污染、可靠性好。对于振动给料机设备的结构参数设计以及工作区域的选择具有重大指导作用。
附图说明
图1中系统动力学模型，各参数的含义：
m 1——质体1的质量；
m 2——质体2的质量；
m 3——质体3的质量；
m 4——质体4的质量；
m 01——激振器转子1的质量；
m 02——激振器转子2的质量
m 03——激振器转子2的质量；
Figure PCTCN2019105529-appb-000052
——激振器转子1的转角；
Figure PCTCN2019105529-appb-000053
——激振器转子2的转角；
Figure PCTCN2019105529-appb-000054
——激振器转子3的转角
k i,i＝0～4——弹簧刚度系数；
β i(i＝1～3)——激振器i的质心和振动刚体的质心的连线与水平方向之间的夹角；
l 0--激振器质心到振动刚体质心的距离；
l x3--质体4的弹簧到振动槽质心的水平距离；
l y3--质体4的弹簧到振动槽质心的竖直距离；
l x1--三个质体的弹簧近端点到其质心的水平距离；
l x2--三个质体的弹簧远端点到其质心的水平距离；
l y1--三个质体的弹簧近端点到其质心的竖直距离；
l y2--三个质体的弹簧远端点到其质心的竖直距离；
图2三激振器之间的相位差；
图3相位滞后角；
图4稳定性能力系数H 1；
图5稳定性能力系数H 2；
图6同步性能力系数曲线；
图7最大耦合力矩曲线；
图8区域1三电机转速；
图9区域1三激振器之间的相位差；
图10区域1在x方向的位移；
图11区域1在x方向的位移前面局部放大图；
图12区域1在x方向的后面局部放大图；
图13区域1在y方向的位移；
图14区域1在y方向位移前部的局部放大图；
图15区域1在y方向位移后部的局部放大图；
图16区域1摆动位移；
图17区域2(a)三电机转速；
图18区域2(a)三激振器之间的相位差；
图19区域2(a)在x方向的位移；
图20区域2(a)x方向的位移前部局部放大图；
图21区域2(a)x方向的位移后部局部放大图；
图22区域2(a)y方向位移图；
图23区域2(a)y方向的位移前部的局部放大图；
图24区域2(a)y方向位移后部的局部放大图；
图25区域2(a)摆动位移；
图26区域2(b)三电机转速；
图27区域2(b)三激振器之间的相位差；
图28区域2(b)在x方向的位移；
图29区域2(b)x方向的位移的前部局部放大图；
图30区域2(b)x方向的位移的后部局部放大图；
图31区域2(b)y方向的位移；
图32区域2(b)y方向位移的前部局部放大图；
图33区域2(b)y方向的位移的后部局部放大图；
图34区域2(b)摆动位移；
图35区域3三电机转速；
图36区域3三激振器之间的相位差；
图37区域3在x方向的位移；
图38区域3在x方向位移的前部局部放大图；
图39区域3在x方向位移的后部局部放大图；
图40区域3在y方向的位移；
图41区域3在y方向位移的前部局部放大图；
图42区域3在y方向位移的后部局部放大图；
图43区域3摆动位移。
具体实施方式
一种三磨筒高频振动磨机，其动力学模型见图1，包括：激振器m 0i(i＝1～3)；质体m i(i＝1～4)，弹簧k i(i＝1～4)。该模型由三个激振器和四个质体组成。三个激振器同向旋转，并且每个激振器绕自身回转轴旋转，以
Figure PCTCN2019105529-appb-000055
表示。
实施例1：数值验证
给定参数，质体1、2、3的质量相等，m 1＝m 2＝m 3＝1400kg，质体4的质 量为2000kg，激振器1、2、3的质量相等，令三激振器的质量为m 0＝10kg，l 0＝1.1m。设定弹簧刚度k 1，k 2，k 3相等，k 1＝k 2＝k 3＝46000kN/m，k 4＝10kN/m，k ψ＝4000kN/m，根据给定的数据，可求得ω ψ＝52rad/s，ω 0＝179rad/s，ω 3＝319rad/s。
因此根据ω 0＝179rad/和ω 3＝319rad/s可划分成三个区：1区为ω m0＜ω 0，2区为ω 0＜ω m0＜ω 3，3区为ω 3＜ω m0。
图2表示两个激振器的相位角关系，在相对于ω 0的亚共振区域，相位差出现两组解，0°和120°，以及120°；在相对于ω 3的亚共振区域，0°和120°，以及120°；在相对于ω 3的过共振区域，0°和120°，以及120°。
图3表示三个质体的滞后角，γ为滞后角，在第一区域，γ 1为0，γ 2、γ 4为180；在第二区域，γ 2为360，γ 1、γ 4为180；在第三区域，γ 4为360，γ 1、γ 2为180。
图4和图5表示稳定性能力系数曲线，且通过曲线的放大图可以看出，稳定性能力系数曲线在整个区间大于等于0。且在1区内，稳定性系数明显增大。
图6表示同步性能力系数，可以看出，在ω ψ处取得极值，在ω 0，ω 3处同步性能力系数为0
图7表示最大耦合力矩曲线，可以看出，最大耦合力矩在ω ψ处取得极值，在ω 3也有明显的增大。
数值分析结果表明：当系统在相对于ω 0的亚共振状态和相对于ω 3的超共振状态下，即区域1(ω m0＜ω 0)与区域3(ω 3＜ω m0)，两个激振器之间的相位差存在两组稳定解，出现了非线性系统多样性情况；当系统在相对于ω 3的亚共振状态或相对于ω 0的超共振状态下，即区域2(ω 0＜ω m0＜ω 3)，以ω m0＝250rad/s为中点将区域2分成前半部分和后半部分。在前半部分中系统有一组稳定解，而在后半部中，系统出现两组稳定解，之后又变成一组稳定解。
实施例2：振动系统的仿真
振动系统的仿真主要使用四阶Rouge-Kutta程序进行仿真，根据之前划分的三个区域逐一进行仿真。实际工程应用中，一般取相同的激振器，四电机的参数相同，即η＝1.0。系统整体参数选用如下：转子电阻R r＝3.40Ω，定子电阻R s＝3.35Ω，转子电感L r＝170mH，定子电感L s＝170mH，互感L m＝164mH，f 1y＝f 2y＝0.05。振动系统的其他参数：r＝0.15m，m 1＝m 2＝m 3＝1400kg，m 0＝10kg，k 1＝k 2＝k 3＝k 0，调整参数，使系统分别处于亚共振状态和超共振状态。
对区域1进行仿真，假定k 0＝30000KN/m，k 4＝30KN/m，k ψ＝4000KN/m：
仿真结果对应的电机转速为894r/min,通过计算，此时对应于数值分析相位差图中114rad/s。
图8表示两个激振器速度的稳定状态，在短时间内，两个激振器的速度很快稳定下来，并且同步速度基本稳定在893r/min左右，在30s时，激振器2增加干扰，转速未发生明显变化。
图9表示相位差稳定状态，稳定状态下，激振器1和2，2和3，1和3之间的相位差为120°，30s处加干扰，位移曲线产生小的波动后又恢复为原来的相位差关系。
图10，11和12表示质体1,2,3在x方向的位移。由局部位移放大关系图可以看出，质体1、2、3之间的位移大小相等，质体4在x方向没有运动，在30s处加干扰，位移曲线未发生明显变化。
图13，14和15表示质体1,2,3在y方向的位移。由局部放大图可以看出，质体1、2、3之间的位移大小相等，质体4处于在y方向没有位移。质体在加干扰前后的位移曲线保持一致。
图16为系统摆动情况，可以看出，摆动角度在0°附近，增加干扰并未发生明显变化。
对区域2(a部分)进行仿真，假定k 0＝9000KN/m，k 4＝30KN/m，k ψ＝3000KN/m，仿真结果对应的电机转速为870r/min,通过计算，此时对应于数值分析相位差图中205rad/s.：
图17表示两个激振器速度的稳定状态，在短时间内，两个激振器的速度很快稳定下来，并且同步速度基本稳定在870r/min，在30s时，激振器2增加干扰，转速未发生明显变化。
图18表示相位差稳定状态，激振器1和2，激振器2和3，激振器1和3之间的相位差为0°；30s处加干扰，相位差保持不变。
图19，20和21表示质体1,2,3在x方向的位移。由位移放大关系图可以看出，质体1、2、3之间的位移量大小相等，质体4的运动位移与质体1、2、3的运动方向相反；30s处加干扰，位移曲线保持稳定。
图22，23和24表示质体1,2,3在y方向的位移。由局部放大图可以看出，质体1、2、3之间的位移大小相等，质体4的运动位移与质体1、2、3的运动方向相反；30s处加干扰，位移曲线保持稳定。
图25表示系统的摆动情况，可以看出，摆动角度在0°附近，增加干扰并未发生明显变化。
对区域2(b部分)进行仿真，假定k 0＝9000KN/m，k 4＝30KN/m，k ψ＝3000KN/m，仿真结果对应的电机转速为982r/min,通过计算，此时对应于数值分析相位差图中264rad/s.：
图26表示两个激振器速度的稳定状态，在短时间内，两个激振器的速度很快稳定下来，并且同步速度基本稳定在982r/min，在30s时，激振器2增加干扰，转速未发生明显变化。
图27表示相位差稳定状态，激振器1和2，激振器2和3，激振器1和3之间的相位差为0°；30s处加干扰，相位差突变，变为120°。
图28，29和30表示质体1,2,3在x方向的位移。由位移放大关系图可以看出，质体1、2、3之间的位移大小相等，质体4的运动位移与质体1、2、3的运动方向相反；30s处加干扰，位移发生改变，质体4处于静止状态，质体1、2、3的位移量大小相等。
图31，32和33表示质体1,2,3在y方向的位移。由位移放大关系图可以看出，质体1、2、3之间的位移大小相等，质体4的运动位移与质体1、2、3的运动方向相反；330s处加干扰，位移发生改变，质体4处于静止状态，质体1、2、3的位移量大小相等。图34表示系统的摆动情况，可以看出，摆动角度在0°附近，增加干扰并未发生明显变化。
对区域3进行仿真，假定k 0＝3200KN/m，k 4＝30KN/m，k ψ＝2000KN/m，仿真结果对应的电机转速为982r/min,通过计算，此时对应于数值分析相位差图中376rad/s.：
图35表示两个激振器速度的稳定状态，在短时间内，两个激振器的速度很快稳定下来，并且同步速度基本稳定在982r/min，在30s时，激振器2增加干扰，转速未发生明显变化。
图36表示相位差稳定状态，激振器1和2，激振器2和3，激振器1和3之间的相位差为0°；30s处加干扰，相位差突变，变为120°。
图37，38和39表示质体1,2,3在x方向的位移。由位移放大关系图可以看出，质体1、2、3之间的位移大小相等，质体4的运动位移与质体1、2、3的运动方向相反；30s处加干扰，质体4处于静止状态，质体1、2、3的位移量大小相等。
图40，41和42表示质体1,2,3在y方向的位移。由位移放大关系图可以看出，质体1、2、3之间的位移大小相等，质体4的运动位移与质体1、2、3的运动方向相反；30s处加干扰，位移发生改变，质体4处于静止状态，质体1、2、3的位移量大小相等。
图43表示系统的摆动情况，可以看出，摆动角度在0°附近，增加干扰并未发生明显变化。
系统仿真结果表明：区域1，区域3和区域2的后半部分的相位差在干扰后并未恢复到原状态，而在区域2前半部分，系统受到干扰后仍然稳定，同时可以看到系统在工作区域(即区域2的前半部分)的工作状态，质体1、质体2和质体3在x和y方向的位移大小相等且同向，质体4在x和y方向的位移较大且与反向振动。
结论
(1)根据步骤四的结果和步骤五的结果对比可知，数值验证和系统仿真结果相同。因此本发明的参数确定方法正确。
(2)本发明给出了振动磨机新的模型，使用双机驱动四质体，根据微分方程的建立、数值分析和仿真得到本发明的振动给料机的区域1，区域3和工作区域2的后半部分相位差在干扰后并不能恢复到原状态，稳定性不足，因此工作区域为2区的后半部分，并可以分析出该振动磨机的工作时的运动状态。
(3)从仿真结果得知，质体1，2，3与质体4(机体)反向运动，且机体振幅较大，从而使介质和物料充分研磨，提高研磨精度，从而证明本发明的模型合理性。
(4)本发明的研究内容对于振动给料机设备的结构参数设计以及工作区域的选择具有重大指导作用。
实施例3：一款振动给料机的示例数据参数。本发明并不仅限于此设计参数。
弹簧刚度：k 0＝9000KN/m，k 4＝30KN/m，k ψ＝3000KN/m，k 1＝k 2＝k 3＝k 0；
阻尼系数：f 1y＝f 2y＝0.05
质体质量：m 1＝m 2＝m 3＝1400kg，m 4＝2000kg；
r＝0.15m；l 0＝1.1m；同步转速：ω m0＝790r/min—811r/min
激振器偏心转子质量：m 01＝m 02＝m 03＝10kg；
电机参数：转子电阻
Figure PCTCN2019105529-appb-000056
定子电阻
Figure PCTCN2019105529-appb-000057
转子电感L r＝170mH，定子电感L s＝170mH，互感L m＝164mH。
两个电机型号一致，三相鼠笼式(型号VB-1082-W，380V，50Hz，6-极，Δ-连接，0.75kw，转速980r/min，39kg)。

Claims (2)

  1. 一种三磨筒高频振动磨机的参数确定方法，其特征在于，该振动磨机的动力学模型包括三个激振器、四个质体、弹簧；质体1、质体2、质体3分别为三个磨筒且均通过弹簧与质体4相连，质体4通过弹簧与基底相连；三个激振器分别位于质体1、质体2、质体3上；三个激振器同向旋转，并且每个激振器绕自身回转轴旋转；所述激振器的参数确定方法，包括如下步骤：
    步骤一：建立系统的动力学模型和运动微分方程
    建立两个直角坐标系，三个激振器同向旋转，机体运动分为x,y方向振动及绕质心摆动，分别以x,y和ψ表示；
    选择x，y，ψ，
    Figure PCTCN2019105529-appb-100001
    为广义坐标，求解系统的动能、势能、能量散逸函数，将其带入拉格朗日方程，得系统的运动微分方程；
    Figure PCTCN2019105529-appb-100002
    式中
    m 0i——激振器的质量(i＝1～3)；m i——质体的质量(i＝1～4)；
    M 1＝m 1+m 01，M 2＝m 2+m 02，M 3＝m 3+m 03，M 4＝m 4+m 01+m 02+m 03
    J＝J m4+(m 01+m 02+m 03)(r 2+l 2)——振动刚体的转动惯量；
    Figure PCTCN2019105529-appb-100003
    ——激振器转动惯量(i＝1～3)；
    Figure PCTCN2019105529-appb-100004
    k i(i＝1～4)——弹簧刚度系数；
    Figure PCTCN2019105529-appb-100005
    f i(i＝1～4)——阻尼系数；
    Figure PCTCN2019105529-appb-100006
    ——激振器i的相位角(i＝1～3)；
    Figure PCTCN2019105529-appb-100007
    ——激振器i的角速度(i＝1～3)；
    Figure PCTCN2019105529-appb-100008
    ——激振器i的角加速度(i＝1～3)；
    步骤二：同步性分析
    设激振器1和激振器2之间的相位差为2α 1，激振器2和激振器3之间的相位差为2α 2，三个激振器之间的平均相位差为
    Figure PCTCN2019105529-appb-100009
    Figure PCTCN2019105529-appb-100010
    重新整理上式有
    Figure PCTCN2019105529-appb-100011
    通过传递函数法，可求得系统的响应：
    Figure PCTCN2019105529-appb-100012
    定中间参量：
    Figure PCTCN2019105529-appb-100013
    Figure PCTCN2019105529-appb-100014
    Figure PCTCN2019105529-appb-100015
    Figure PCTCN2019105529-appb-100016
    Figure PCTCN2019105529-appb-100017
    Figure PCTCN2019105529-appb-100018
    Figure PCTCN2019105529-appb-100019
    Figure PCTCN2019105529-appb-100020
    Figure PCTCN2019105529-appb-100021
    Figure PCTCN2019105529-appb-100022
    c 2＝e 1，d 2＝f 1，e 2＝c 1，f 2＝d 1，h 2＝e 1，p 2＝f 1，u 2＝u 1，z 2＝z 1，
    c 3＝e 1，d 3＝f 1，e 3＝e 1，f 2＝f 1，h 3＝c 1，p 3＝d 1，u 3＝u 1，z 3＝z 1
    Figure PCTCN2019105529-appb-100023
    γ 5＝γ 2，γ 6＝γ 1，γ 7＝γ 2，γ 8＝γ 4，γ 9＝γ 2，γ 10＝γ 2，γ 11＝γ 1，γ 12＝γ 4
    式中γ i(i＝1～4)——滞后角；
    Figure PCTCN2019105529-appb-100024
    式中，M——质量耦合矩阵，K——刚度耦合矩阵，Δ(ω 2)为特征值方程，
    令特征值方程等于0，即Δ(ω 2)＝0：
    Figure PCTCN2019105529-appb-100025
    求得固有频率：
    Figure PCTCN2019105529-appb-100026
    当三个激振器能够同步运转时，有
    Figure PCTCN2019105529-appb-100027
    对x 1、x 2、x 3、y 1、y 2、y 3、ψ关于时 间t进行二阶求导，并带入式，在0～2π上对
    Figure PCTCN2019105529-appb-100028
    进行积分，取均值并整理后，得到三个激振器的平衡方程式如下：
    Figure PCTCN2019105529-appb-100029
    其中
    Figure PCTCN2019105529-appb-100030
    各激振器间输出力矩之差为：
    Figure PCTCN2019105529-appb-100031
    Figure PCTCN2019105529-appb-100032
    对上述两式进行整理，得
    Figure PCTCN2019105529-appb-100033
    其中，
    Figure PCTCN2019105529-appb-100034
    Figure PCTCN2019105529-appb-100035
    在上述推导中，τ c12(α 1,α 2) ，τ c23(α 1,α 2)分别为电机1、电机2之间和电机2、电机3之间无量纲耦合力矩，其约束函数如下：
    Figure PCTCN2019105529-appb-100036
    综上，结合上式，可得三个激振器的同步性判据
    Figure PCTCN2019105529-appb-100037
    上式表示任意两个激振器的无量纲残余力矩之差的绝对值小于或等于无量纲耦合力矩的最大值；
    步骤三：同步状态的稳定性判据
    求得整个系统动能T和势能V分别为：
    Figure PCTCN2019105529-appb-100038
    Figure PCTCN2019105529-appb-100039
    单周期内可求得平均动能E T与平均势能E V，在一个周期内系统的Hamilton平均作用量I为
    Figure PCTCN2019105529-appb-100040
    I的Hesse矩阵表示为H，得
    Figure PCTCN2019105529-appb-100041
    其中
    Figure PCTCN2019105529-appb-100042
    Figure PCTCN2019105529-appb-100043
    Figure PCTCN2019105529-appb-100044
    令
    H 1＝d 11
    H 2＝d 11d 22-d 12d 21
    H矩阵正定，满足
    H 1＞0，H 2＞0          (23)
    将H 1与H 2定义为系统的同步条件下的稳定能力系数，上式即为系统的稳定性能力的表达式，当满足上式(23)时，系统稳定。
  2. 根据权利要求1所述的三磨筒高频振动磨机的参数确定方法，其特征在于，对
    Figure PCTCN2019105529-appb-100045
    求和，并除以3T u，即得到三个激振器平均无量纲负载力矩，表示为τ a(α 1,α 2)；
    Figure PCTCN2019105529-appb-100046
    三个激振器平均无量纲负载力矩的约束函数如下
    |τ a(α 1,α 2)|≤τ amax           (17)
    定义同步能力系数为ζ ij(i,j＝1,2,3,4)，可得，
    Figure PCTCN2019105529-appb-100047
    同步能力系数越大，系统的同步能力越强，越容易达到同步。
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