CN117299530B - A single-drive energy-saving horizontal elliptical vibrating screen and its parameter determination method - Google Patents

A single-drive energy-saving horizontal elliptical vibrating screen and its parameter determination method

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CN117299530B
CN117299530B CN202310890631.4A CN202310890631A CN117299530B CN 117299530 B CN117299530 B CN 117299530B CN 202310890631 A CN202310890631 A CN 202310890631A CN 117299530 B CN117299530 B CN 117299530B
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vibrating screen
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horizontal elliptical
elliptical vibrating
screen system
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CN117299530A (en
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张学良
张振彪
程壮壮
李子谦
张家鑫
梁坤
段梦娇
闻邦椿
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Northeastern University China
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B07—SEPARATING SOLIDS FROM SOLIDS; SORTING
    • B07B—SEPARATING SOLIDS FROM SOLIDS BY SIEVING, SCREENING, SIFTING OR BY USING GAS CURRENTS; SEPARATING BY OTHER DRY METHODS APPLICABLE TO BULK MATERIAL, e.g. LOOSE ARTICLES FIT TO BE HANDLED LIKE BULK MATERIAL
    • B07B1/00—Sieving, screening, sifting, or sorting solid materials using networks, gratings, grids, or the like
    • B07B1/28—Moving screens not otherwise provided for, e.g. swinging, reciprocating, rocking, tilting or wobbling screens
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B07—SEPARATING SOLIDS FROM SOLIDS; SORTING
    • B07B—SEPARATING SOLIDS FROM SOLIDS BY SIEVING, SCREENING, SIFTING OR BY USING GAS CURRENTS; SEPARATING BY OTHER DRY METHODS APPLICABLE TO BULK MATERIAL, e.g. LOOSE ARTICLES FIT TO BE HANDLED LIKE BULK MATERIAL
    • B07B1/00—Sieving, screening, sifting, or sorting solid materials using networks, gratings, grids, or the like
    • B07B1/46—Constructional details of screens in general; Cleaning or heating of screens
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations

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  • General Engineering & Computer Science (AREA)
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  • Apparatuses For Generation Of Mechanical Vibrations (AREA)
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Abstract

The invention belongs to the technical field of vibration screening devices, and discloses a single-machine-driven energy-saving horizontal elliptical vibrating screen and a parameter determination method thereof. The single-machine driving energy-saving horizontal elliptical vibrating screen comprises a vibration exciter, an outer body, an inner body, a shearing rubber spring and a vibration isolation spring, wherein the vibration isolation spring is connected with a foundation and a main body, the vibration exciter is positioned at the center of mass of the outer body and consists of an eccentric rotor and an induction motor, and the vibration exciter rotates around the center of a rotation axis of the vibration exciter to generate exciting force, so that the inner body generates certain vibration intensity, the movement track of the inner body is elliptical, and a corresponding number of inner bodies can be installed according to the use requirement, so that the productivity is improved, the power consumption is reduced, and the engineering application value of the vibration exciter is realized.

Description

Single-machine driving energy-saving horizontal elliptical vibrating screen and parameter determination method thereof
Technical Field
The invention relates to the technical field of vibration screening devices, in particular to a single-machine-driven energy-saving horizontal elliptical vibrating screen and a parameter determination method thereof.
Background
The technology of the vibrating screen at the present stage gradually tends to be mature, and is widely applied to the sand and aggregate industry, mines, steel mills, foods, chemical industry, petroleum, tunnel engineering and the like, and classification of various materials is realized. Accordingly, there are many kinds of shakers including those that screen in a single frequency drive, those that employ a single body far super resonance technique, and the like, but these shakers suffer from various drawbacks. For example, the operating frequency of the single-body vibrating screen in CN102744203a is far beyond the resonance frequency, the required exciting force is large, so that the power consumption is also increased, and when the vibrating screen is started and stopped to pass through the resonance region, the equipment can generate large vibration, so that the machine can be operated unstably and is easy to damage, and the service life of the machine is reduced. Thereby causing the waste of resources and improving the production cost. In addition, the existing material screening mode mostly needs to be screened for multiple times, materials with different granularity can be separately collected, screening efficiency is low, the situation that coarse and fine materials are mixed after screening is still generated, and production requirements cannot be met. Therefore, it is necessary to design a vibrating screen device to improve the screening quality and to allow efficient production.
Disclosure of Invention
The invention aims to solve the technical problem of providing a single-machine-driven energy-saving horizontal elliptical vibrating screen and a parameter determination method thereof, and a double-mass high-frequency vibrating fine screen utilizing a sub-resonance technology is used, so that the screening area of the whole machine can be increased, the energy consumption can be reduced, and the screening efficiency can be improved.
The vibration exciter on the exosome is used as a research object, a dynamic model is firstly established, and a Lagrange equation is applied to calculate a motion differential equation of the system. Because the system is driven by a single machine, the system is stable, and then the natural frequency of the main vibration system is obtained. And solving steady-state responses of the inner and outer plastids in the x and y directions and an elliptic orbit equation of the inner plastid. And finally, the high-order natural frequency and the low-order natural frequency of the system under the action of external excitation are obtained, so that the working range of the machine is determined. And simulating corresponding working parameters and motion tracks through simulation.
The technical scheme is that the single-machine-driven energy-saving horizontal elliptical vibrating screen comprises a vibration exciter 5, an outer body 2, an inner body 3, shearing springs 4 and vibration isolation springs 1, wherein the vibration isolation springs 1 are symmetrically distributed and connected with a foundation 6 and the outer body 2, the vibration exciter 5 comprises an eccentric rotor and an induction motor which are positioned at the center of mass of the outer body 2, the vibration exciter 5 rotates around the center of a rotation axis of the vibration exciter 5 to generate exciting force, a horizontal elliptical vibrating screen system is driven to generate vibration intensity, the inner body 3 is driven to realize elliptical motion, the inner body comprises a plurality of bodies, each body is connected to an inner base of the outer body 3 through a plurality of shearing springs 4, the inclination angles of all the shearing springs 4 are identical, and adjacent bodies are equidistant.
The outer body 2 is a vibrating screen body, and the inner body 3 is a screen; the shearing springs 4 are distributed at two ends of the plastid, and the feed inlet and the discharge outlet of the vibrating screen body are symmetrically distributed at the origin of the body center of the vibrating screen body.
When the inclination angle of the shearing spring 4 is 0-90 degrees, the vibration exciter 5 rotates anticlockwise, the feeding port is positioned at the upper right side of the vibrating screen body, the discharging port is positioned at the lower left side of the vibrating screen body, and when the inclination angle of the shearing spring is 90-180 degrees, the vibration exciter 5 rotates clockwise, the feeding port is positioned at the upper left side of the vibrating screen body, and the discharging port is positioned at the lower right side of the vibrating screen body.
A single machine driving energy-saving type horizontal elliptical vibrating screen parameter determining method comprises the following steps:
step 1, establishing a dynamic model and a system motion differential equation;
setting a fixed coordinate Oxy, the rotation center of the exciter 5 being O, the corresponding phase being expressed as The whole horizontal elliptic vibrating screen system has three degrees of freedom, which are divided into x-direction vibration, y-direction vibration and swinging psi around the mass center;
the number of x, y, ψ, For generalized coordinates, based on Lagrange's equation, the differential equation of motion of the horizontal elliptical vibrating screen system is derived as follows:
Wherein;
M1＝m1+m2+m3+...+mn,M2＝m0+mv,M＝M1+M2
β=0°-90°
lx＝l1·cosβ,ly＝l2·cosβ
Wherein M is the total mass of the horizontal elliptical vibrating screen system, M v is the mass of an outer body, M 0 is the eccentric rotor mass of the vibration exciter, M i is the mass of a screen, i=1, 2, 3..n, J is the moment of inertia of the whole horizontal elliptical vibrating screen system, J 0 is the moment of inertia of the vibration exciter, J m is the moment of inertia of the inner body, the outer body and an induction motor of the vibration exciter, l e is the equivalent radius of gyration of the horizontal elliptical vibrating screen system, r is the eccentric distance of the vibration exciter, f 0 is the shaft damping coefficient of the induction motor, T 0 is the electromagnetic output torque of the induction motor, beta is the installation angle of a shear spring, k x,kψ is the spring stiffness of the horizontal elliptical vibrating screen system in the x and psi directions, k y is the spring stiffness of the inner body and the outer body in the y directions, f x,fψ is the damping coefficient of the horizontal elliptical vibrating screen system in the x and psi directions, f 1y,f2y is the damping coefficient of the inner body and the outer body in the y directions, l 1 is the linear vibration isolation distance from the connecting point of the vibration screen to the outer body to the vibration center of mass of the vibration screen 1, and the linear vibration isolation distance between the connecting point of the linear vibration screen and the vibration screen is 2; Is a first order time derivative; Is the second time derivative;
Step 2, calculating the natural frequency, steady-state response and trajectory equation of the horizontal elliptical vibrating screen system;
And step 3, calculating the high-order natural frequency and the low-order natural frequency of the horizontal elliptical vibrating screen system.
The natural frequency, steady-state response and trajectory equation of the horizontal elliptical vibrating screen system are calculated as follows;
In steady state, consider nothing in equation (2) K x and k y are both less than k, irrespective of the damping constant f 2y of the exosomes;
in summary, the formulas (1) and (2) are simplified to
In the middle of
M1′＝M1,
Neglecting k y, therefore
M2′＝M2
Finishing (6) and (7) to obtain:
in the formula,
y3＝y1-y2
Wherein M 3 is the induction mass of the horizontal elliptical vibrating screen system, and y 3 is the relative displacement of y 1、y2;
The natural frequency omega n of the horizontal elliptic vibrating screen system is deduced according to the formula (8);
in the formula,
From the above equation, when ω m0/ωn =1, the horizontal elliptical vibrating screen system resonates at this point, and y 12 has a maximum value, i.e., the amplitude is at this point
The absolute motion response of the horizontal elliptical shaker system in the x, y and ψ directions is derived by transfer function methods as follows:
When epsilon aεcj+εbεd is >0,
When epsilon aεcj+εbεd is <0,
From the above, the maximum displacement of the endosome in the x-direction isMaximum displacement in the y direction is
The elliptic orbit equation of the endosome is as follows:
in the formula,
Where x 1,y1,ψ1 is the absolute motion response of the endosome in the x, y, ψ directions, respectively.
The calculated high-order natural frequency and low-order natural frequency of the horizontal elliptical vibrating screen system are specifically as follows;
The eigenvalue equation of the horizontal elliptical vibrating screen system obtained by the formulas (1) and (2) and the two corresponding higher-order natural frequencies and the lower-order natural frequencies are respectively expressed as
(k-ω2M1)(k+ky-ω2M2)-k2=0 (14)
The solution is carried out,
In the formula,b＝M1(ky+k)+M2k,c＝[M1(k+ky)]2+(M2k)2+2M1M2k(k-ky);
Ignoring the parameter k 1y to obtain omega 1＝ω0, knowing the two frequencies of the horizontal elliptical vibrating screen system and omega 2＜ω1＝ω0 by the method, and adjusting the running frequency of the motor to be smaller than the inherent frequency omega 0 of the horizontal elliptical vibrating screen system to realize the sub-resonance operation of the vibrating screen.
The invention has the beneficial effects that:
(1) The invention adopts the single-machine driven double-plastid horizontal elliptic vibrating screen, has unique high efficiency and working performance, and compared with the traditional direct driving design, the double-plastid vibrating screen can lead the movement amplitude of the screen to be larger under the same condition, thereby being capable of reducing the power consumption better. Furthermore, the elliptical screening movement has a higher screening efficiency than the horizontal screening movement. In addition, different numbers of screens with different granularities can be arranged according to requirements to realize the simultaneous screening of multiple granularities, and the working efficiency is improved;
(2) The sub-resonance double-mass vibrating screen adopts the sub-resonance technology, the vibration frequency is smaller than the natural frequency of a vibration system, sub-resonance occurs when the equipment works, and compared with the single-mass vibrating screen, the sub-resonance double-mass vibrating screen has the advantages of smaller required exciting force and low power consumption. The starting and stopping processes do not pass through a high-order resonance area, so that the damage to the machine is reduced, and the service life is longer;
(3) Through the vibration exciting shear rubber spring and the vibration isolation spring that set up, can realize driving bigger screen frame with very little exciting force, enlarge working amplitude through the vibration excitation spring system to can not influence the performance of screening performance along with the change of material load, vibration isolation spring not only can support the vibration source box, can reduce the dynamic load who gives foundation or structure frame moreover.
Drawings
FIG. 1 is a diagram of a dynamic model of a horizontal elliptical vibrating screen system.
In the figure, the vibration isolation spring is 1, the outer plastid is 2, the inner plastid is 3, the shearing spring is 4, the vibration exciter is 5, and the foundation is 6.
The meaning of each parameter in the figure is O, namely the center of the whole system; The vibration exciter comprises a vibration exciter rotation phase angle, m 0, the mass of the vibration exciter, r, the eccentricity of the vibration exciter, k x, the spring rate in the x direction, k y, the spring rate in the y direction, the stiffness of a shearing rubber spring, beta, the inclination angle of the shearing rubber spring and n, and the number of screens.
FIG. 2 (a) is a diagram of motor speed simulation results;
FIG. 2 (b) is a diagram showing the simulation result of the motion trail of the inner and outer plastids;
FIG. 2 (c) is a graph showing the results of the y-direction displacement simulation of the inner and outer masses;
fig. 2 (d) is a graph showing the result of the displacement simulation in the x direction of the liposome.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in figure 1, the vibration exciter 5 is composed of a motor-driven eccentric rotor and is arranged at the mass center of the vibrating screen body, and the vibration exciter 5 rotates at a fixed speed when working. The vibration exciter 5 is connected with the vibrating screen body so as to enable the vibrating screen body to move circularly, the inner screen 3 is fixed on the outer box body through shearing rubber springs 4 inclined at a certain angle, different numbers of screens 3 can be arranged according to different use requirements, and the distance between each two screens 3 is equal and symmetrically distributed in the vertical direction so as to keep overall balance. The feed inlet of shale shaker is located the upper right side of outside screen cloth 2, and the discharge gate is located the lower left side of outside screen cloth 2. The vibration isolation springs 1 are 4 in number, are installed at the bottom of the outer box body 2 in the front-back and left-right mode, and are installed on the foundation 6.
The vibration exciter rotates anticlockwise during operation, so that the movement direction of the outer box body is the same as that of the outer box body, the inner screen mesh moves in an elliptical manner due to a certain angle of the shearing rubber spring connecting the screen mesh and the box body, and materials automatically move leftwards in the screening process due to the movement direction, so that the arrangement positions of the material inlet and the material outlet are also determined.
The double-mass body has two natural frequencies, and the working interval of the vibrating screen is arranged between the two natural frequencies, so that the aim of sub-resonance work is fulfilled, the vibration exciter rotates for one circle, the screen mesh completes one screening movement, and the sub-resonance movement of the vibration exciter, namely the sub-resonance movement of the vibrating screen, is realized by changing the parameters of the driving motor.
Because the vibrating screen is a double-mass vibrating screen, two natural frequencies can be generated under the action of external excitation, and in order to realize the sub-resonance, the working range of the vibrating screen is selected between the high-order natural frequency and the low-order natural frequency so as to achieve the purpose of the sub-resonance. In addition, the system itself is stable due to the single drive, so the stability of the system is not considered.
To further analyze the system characteristics, numerical analysis was performed.
The system parameters are set as follows ：m1+m2+...+mn＝350kg,m＝700kg,m0＝20kg,J＝500kg·m2,kx＝ky＝550kN/m,k＝11800kN/m,kψ＝450kN/rad,fx＝fy＝6.27kN·s/m,fψ＝5.20kN·s/rad,r＝0.15m. according to the parameters and the parameter determination method, and the natural frequency of the system is omega x＝ωy = 224.89rad/s, and the motor type is three-phase squirrel cage type, 50Hz,380V,6-pole,0.75kW and rated rotation speed 980r/min.

Claims (5)

1.一种单机驱动节能型水平椭圆振动筛参数确定方法，其特征在于，该单机驱动节能型水平椭圆振动筛包括：激振器(5)、外质体(2)、内质体(3)、剪切弹簧(4)、隔振弹簧(1)；隔振弹簧(1)对称分布连接地基(6)与外质体(2)；激振器(5)包括偏心转子及感应电机，位于外质体(2)质心处；激振器(5)绕自身旋转轴线中心旋转，产生激振力，驱动水平椭圆振动筛系统产生振动强度，驱动内质体(3)实现椭圆运动；内质体包括多个质体，每个质体均通过多个剪切弹簧(4)连接于外质体(2)内基座上；所有剪切弹簧(4)倾斜角度相同；相邻质体间等距；1. A method for determining parameters of a single-machine driven energy-saving horizontal elliptical vibrating screen, characterized in that the single-machine driven energy-saving horizontal elliptical vibrating screen comprises: an exciter (5), an outer mass body (2), an inner mass body (3), a shear spring (4), and a vibration isolation spring (1); the vibration isolation spring (1) is symmetrically distributed and connected to a foundation (6) and the outer mass body (2); the exciter (5) comprises an eccentric rotor and an induction motor, and is located at the mass center of the outer mass body (2); the exciter (5) rotates around the center of its own rotation axis to generate an exciting force, drive the horizontal elliptical vibrating screen system to generate vibration intensity, and drive the inner mass body (3) to achieve elliptical motion; the inner mass body comprises a plurality of masses, each of which is connected to the inner base of the outer mass body (2) through a plurality of shear springs (4); all the shear springs (4) have the same inclination angle; and adjacent masses are equidistant. 所述外质体(2)为振动筛机体，内质体(3)为筛网；剪切弹簧(4)分布在质体两端；振动筛机体的进料口和出料口以振动筛机体质心原点对称分布；The outer mass (2) is a vibrating screen body, and the inner mass (3) is a screen mesh; the shear springs (4) are distributed at both ends of the mass; the feed port and the discharge port of the vibrating screen body are symmetrically distributed with respect to the center of mass of the vibrating screen body; 所述的参数确定方法，包括如下步骤：The parameter determination method comprises the following steps: 步骤1，建立动力学模型和系统运动微分方程；Step 1, establish the dynamic model and system motion differential equation; 设定固定坐标Oxy，激振器(5)的旋转中心为O，其对应相位表示为整个水平椭圆振动筛系统有三个自由度，分为x方向的振动，y方向的振动及绕质心的摆动ψ；Set the fixed coordinate Oxy, the rotation center of the exciter (5) is O, and its corresponding phase is expressed as The entire horizontal elliptical vibrating screen system has three degrees of freedom, which are divided into vibration in the x direction, vibration in the y direction and swing around the center of mass ψ; 选定x，y，ψ，为广义坐标，基于Lagrange方程，水平椭圆振动筛系统的运动微分方程推导如下：Select x, y, ψ, For generalized coordinates, based on the Lagrange equation, the motion differential equation of the horizontal elliptical vibrating screen system is derived as follows: 其中；in; M1＝m1+m2+m3+…+mn，M2＝m0+mv，M＝M1+M2 M 1 =m 1 +m 2 +m 3 +…+m n , M 2 =m 0 +m v , M = M 1 +M 2 β＝0°-90° β＝0°-90° lx＝l1·cosβ,ly＝l2·cosβl x ＝l 1 ·cosβ,l y ＝l 2 ·cosβ 式中，M为水平椭圆振动筛系统总质量；mv为外质体质量；m0为激振器的偏心转子质量；mi为筛网的质量，i＝1,2,3…n；J为整个水平椭圆振动筛系统的转动惯量；J0为激振器的转动惯量；Jm为内质体、外质体及激振器感应电机的转动惯量；le为水平椭圆振动筛系统当量回转半径；r为激振器的偏心距；f0为感应电机的轴阻尼系数；T0为感应电机的电磁输出转矩；kx，kψ分别为水平椭圆振动筛系统在x和ψ方向上的弹簧刚度；k，ky分别为内质体和外质体在y方向的弹簧刚度；fx，fψ分别为水平椭圆振动筛系统在x和ψ方向上的阻尼系数；f1y,f2y分别为内质体、外质体在y方向的阻尼系数；l1为隔振弹簧(1)与外质体连接点到振动筛质心的直线距离；l2为隔振弹簧(1)与外质体连接点到振动筛质心的水平距离；β为剪切弹簧倾斜角度；为一阶时间导数；为二阶时间导数；Wherein, M is the total mass of the horizontal elliptical vibrating screen system; m v is the mass of the outer mass; m 0 is the mass of the eccentric rotor of the exciter; mi is the mass of the screen, i = 1, 2, 3…n; J is the moment of inertia of the entire horizontal elliptical vibrating screen system; J 0 is the moment of inertia of the exciter; J m is the moment of inertia of the inner mass, outer mass and the exciter induction motor; l e is the equivalent radius of gyration of the horizontal elliptical vibrating screen system; r is the eccentricity of the exciter; f 0 is the shaft damping coefficient of the induction motor; T 0 is the electromagnetic output torque of the induction motor; k x , k ψ are the spring stiffness of the horizontal elliptical vibrating screen system in the x and ψ directions respectively; k, ky are the spring stiffness of the inner mass and outer mass in the y direction respectively; f x , f ψ are the damping coefficients of the horizontal elliptical vibrating screen system in the x and ψ directions respectively; f 1y , f 2y are the damping coefficients of the inner mass and outer mass in the y direction respectively; l 1 is the straight-line distance from the connection point between the vibration isolation spring (1) and the outer mass to the mass center of the vibrating screen; l 2 is the horizontal distance from the connection point between the vibration isolation spring (1) and the outer mass to the mass center of the vibrating screen; β is the inclination angle of the shear spring; is the first-order time derivative; is the second-order time derivative; 步骤2，计算水平椭圆振动筛系统固有频率、稳态响应及轨迹方程；Step 2, calculating the natural frequency, steady-state response and trajectory equation of the horizontal elliptical vibrating screen system; 步骤3，计算水平椭圆振动筛系统高阶固有频率、低阶固有频率。Step 3: Calculate the high-order natural frequency and low-order natural frequency of the horizontal elliptical vibrating screen system. 2.根据权利要求1所述的单机驱动节能型水平椭圆振动筛参数确定方法，其特征在于，当剪切弹簧(4)倾角为0-90度时，此时激振器(5)逆时针旋转，进料口位于振动筛机体右上方，出料口位于振动筛机体左下方；当剪切弹簧倾角为90-180度时，此时激振器(5)顺时针旋转，进料口位于振动筛机体左上方，出料口位于振动筛机体右下方。2. The method for determining parameters of a single-machine driven energy-saving horizontal elliptical vibrating screen according to claim 1 is characterized in that, when the inclination angle of the shear spring (4) is 0-90 degrees, the vibrator (5) rotates counterclockwise, the feed port is located at the upper right side of the vibrating screen body, and the discharge port is located at the lower left side of the vibrating screen body; when the inclination angle of the shear spring is 90-180 degrees, the vibrator (5) rotates clockwise, the feed port is located at the upper left side of the vibrating screen body, and the discharge port is located at the lower right side of the vibrating screen body. 3.根据权利要求1所述的单机驱动节能型水平椭圆振动筛参数确定方法，其特征在于，所述水平椭圆振动筛系统固有频率、稳态响应及轨迹方程计算如下；3. The method for determining parameters of a single-machine driven energy-saving horizontal elliptical vibrating screen according to claim 1 is characterized in that the natural frequency, steady-state response and trajectory equation of the horizontal elliptical vibrating screen system are calculated as follows; 在稳态下，方程(2)中不考虑kx和ky均小于k，不考虑外质体的阻尼常数f2y；In steady state, equation (2) does not take into account k x and ky are both smaller than k, and the damping constant f 2y of the external mass is not considered; 综上所述，式(1)、式(2)简化为In summary, formula (1) and formula (2) are simplified to 式中In the formula M1′＝M1，忽略ky，故M 1 ′＝M 1 , Ignore k y , so M2′＝M2 M 2 ′＝M 2 整理(6)(7)式，得：Arranging equations (6) and (7), we get: 式中，Where, y3＝y1-y2 y 3 =y 1 -y 2 其中，M3为水平椭圆振动筛系统的诱导质量，y3为y1、y2的相对位移；Where, M 3 is the induced mass of the horizontal elliptical vibrating screen system, y 3 is the relative displacement of y 1 and y 2 ; 根据式(8)推出水平椭圆振动筛系统的固有频率ωn；According to formula (8), the natural frequency ω n of the horizontal elliptical vibrating screen system is derived; 式中，Where, 由上式可知，当ωm0/ωn＝1时，此时水平椭圆振动筛系统共振，此时y12具有极大值，即此时振幅为From the above formula, we can know that when ω m0 /ω n = 1, the horizontal elliptical vibrating screen system resonates, and y 12 has a maximum value, that is, the amplitude is 则水平椭圆振动筛系统在x、y和ψ方向上的绝对运动响应通过传递函数法推导如下：The absolute motion response of the horizontal elliptical vibrating screen system in the x, y and ψ directions is derived as follows by the transfer function method: 当εaεcj+εbεd＞0时，When ε a ε cj +ε b ε d >0, 当εaεcj+εbεd＜0时，When ε a ε cj +ε b ε d <0, 由上可知，内质体在x方向的最大位移为在y方向上的最大位移为 From the above, we can see that the maximum displacement of the endoplasmic body in the x direction is The maximum displacement in the y direction is 4.根据权利要求3所述的单机驱动节能型水平椭圆振动筛参数确定方法，其特征在于，所述内质体的椭圆轨迹方程为：4. The method for determining parameters of a single-machine driven energy-saving horizontal elliptical vibrating screen according to claim 3, wherein the elliptical trajectory equation of the endoplasmic body is: 式中，Where, 式中，x1，y1，ψ1分别为内质体在x，y，ψ方向上的绝对运动响应。Where x 1 , y 1 , and ψ 1 are the absolute motion responses of the endoplasmic body in the x, y, and ψ directions, respectively. 5.根据权利要求3所述的单机驱动节能型水平椭圆振动筛参数确定方法，其特征在于，所述计算水平椭圆振动筛系统高阶固有频率、低阶固有频率具体为：5. The method for determining parameters of a single-machine driven energy-saving horizontal elliptical vibrating screen according to claim 3, wherein the high-order natural frequency and the low-order natural frequency of the horizontal elliptical vibrating screen system are calculated as follows: 由式(1)和式(2)得到水平椭圆振动筛系统的特征值方程和两个对应的高阶固有频率、低阶固有频率分别表示为(k-ω2M1)(k+ky-ω2M2)-k2＝0 (14)From equations (1) and (2), the characteristic value equation of the horizontal elliptical vibrating screen system and the two corresponding high-order natural frequencies and low-order natural frequencies are expressed as (k-ω 2 M 1 )(k+ ky -ω 2 M 2 )-k 2 = 0 (14) 解得The solution is 式中In the formula b＝M1(ky+k)+M2k， b＝M 1 ( ky +k)+M 2 k, c＝[M1(k+ky)]2+(M2k)2+2M1M2k(k-ky)c＝[M 1 (k+k y )] 2 +(M 2 k) 2 +2M 1 M 2 k(kk y ) 忽略参数k1y后，得到ω1＝ω0；由上式可知水平椭圆振动筛系统的两个频率，且ω2＜ω1＝ω0；调整电机的运转频率使其小于水平椭圆振动筛系统的固有频率ω0实现振动筛的亚共振工作。After ignoring the parameter k 1y , we get ω 1 = ω 0 ; from the above formula, we can know the two frequencies of the horizontal elliptical vibrating screen system, and ω 2 < ω 1 = ω 0 ; adjusting the operating frequency of the motor to be less than the natural frequency ω 0 of the horizontal elliptical vibrating screen system to achieve sub-resonance operation of the vibrating screen.
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