CN107159399A - A kind of multimachine driving motor synchronizing self-balancing type vibrator and parameter determination method - Google Patents

A kind of multimachine driving motor synchronizing self-balancing type vibrator and parameter determination method Download PDF

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CN107159399A
CN107159399A CN201710437303.3A CN201710437303A CN107159399A CN 107159399 A CN107159399 A CN 107159399A CN 201710437303 A CN201710437303 A CN 201710437303A CN 107159399 A CN107159399 A CN 107159399A
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mrow
msub
mtd
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msup
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张学良
马辉
屠天奇
李朝峰
姜世杰
赵春雨
闻邦椿
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Northeastern University China
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B02CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
    • B02CCRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
    • B02C17/00Disintegrating 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
    • B02C17/10Disintegrating 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 with one or a few disintegrating members arranged in the container
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B02CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
    • B02CCRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
    • B02C17/00Disintegrating 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
    • B02C17/18Details
    • B02C17/24Driving mechanisms
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/11Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13Differential equations
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/16Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

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Abstract

The invention belongs to grinding device, a kind of multimachine drives motor synchronizing self-balancing type vibrator, the characteristics of combining ball mill and vibrating mill.Using body centre and the eccentric structure of power spindle, it regard cylinder itself as vibrator, realize dither, grinding energy is big, possess multiple cylinders simultaneously, operating efficiency is high, reach stable self-balancing run-in synchronism, itself circular motion is realized in each bias cylinder revolution, multiple eccentric cylinders realize that motor synchronizing is operated, when multiple the same eccentric cylinder circumference uniform distributions are in the barycenter periphery of vibrational system, because their phase difference is stable at Pi/n (n represents the number of eccentric cylinder) place, the exciting force for causing each eccentric cylinder to produce is cancelled out each other, cause vibration body depressed dynamic, reach that vibration body is actuated to 0 to basis with this, it can realize that each eccentric cylinder realizes high speed circular motion, it can guarantee that the vector of the vibrational excitation to basis makes a concerted effort to be zero again, so as to meet the vibration noise environmental requirement of national regulation.

Description

A kind of multimachine driving motor synchronizing self-balancing type vibrator and parameter determination method
Technical field
The invention belongs to grinding device, a kind of multimachine driving motor synchronizing self-balancing type vibrator and parameter determination side Method.
Background technology
Ball mill:Vibratory milling is in small, broken bits to wait operation to be widely used in the industries such as ore dressing, building, chemistry and pharmacy.Such as exist In mining processing industry, when valuable mineral is distributed in ore in particulate, in order to be able to which the gangue in ore is separated, and have various It is separated from each other with mineral, it is necessary to by grinde ore to 0.3~0.1 millimeter, and be milled to less than 0.05~0.07 millimeter sometimes.Ore grinding Fineness has close relationship with mineral processing index, to a certain extent, and metal recovery rate increases as mog reduces.Cause And the fineness of grinding for suitably reducing ore can improve the rate of recovery and yield of metal.The power that ore grinding is consumed accounts for ore dressing plant power More than the 30% of wastage in bulk or weight.Therefore, grinding operation holds an important position in the technological process of ore dressing.
Ore grinding is carried out in ball mill.Cylinder type ore mill has a hollow cylinder 1, and cylinder two ends are to carry end cap 2 and 3 tubular journal 4 and 5, axle journal is supported on bearing.Cylinder built with various diameters crushing medium (steel ball, rod iron and Gravel etc.).When cylinder is turned round around horizontal axis by egulation rotating speed, crushing medium of the device in cylinder and ore in centrifugal force and In the presence of frictional force, as barrel rises to certain altitude, then depart from barrel and freely fall or roll down.Ore grinds master If ablation when impulsive force when being fallen by crushing medium and motion.Ore is continuous from the tubular journal of one section of cylinder Feed, and grind tubular journal of the later product through the cylinder other end and constantly exclude, the movement of ore is using not in cylinder Break and feed the pressure of ore to realize.During wet-milling, ore is taken away by current, during dry grinding, and the air-flow that ore is taken out to outside cylinder is taken out of.
General milling machine weight is high, and crushing energy is low, and product grading is big, takes up an area greatly, complicated.
The content of the invention
The present invention overcomes the problem of prior art is present to drive motor synchronizing self-balancing there is provided multimachine under a kind of Nonresonant natural vibration Formula vibrator, using body centre and the eccentric structure of power spindle, using cylinder itself as vibrator, realizes high frequency vibrating Dynamic, grinding energy is big, while possessing multiple cylinders, operating efficiency is high, reaches stable self-balancing run-in synchronism.When synchronism stability fortune When turning, itself circular motion is realized in each bias cylinder revolution, while multiple eccentric cylinders realize that motor synchronizing is operated, so when Multiple the same eccentric cylinder circumference uniform distributions are when the barycenter periphery of vibrational system, because their phase difference is stable in Pi/n (n Represent the number of eccentric cylinder) place, so that the exciting force for causing each eccentric cylinder to produce is cancelled out each other, cause vibration body not Vibration, reaches that vibration body is actuated to 0 to basis, noise is low, meets national requirements for environmental protection with this.In a word, machine of the invention Structure and principle can realize that each eccentric cylinder realizes high speed circular motion, can guarantee that the vector of the vibrational excitation to basis is closed again Power is zero, so as to meet the vibration noise environmental requirement of national regulation.
The technical scheme is that:
A kind of multimachine drives motor synchronizing self-balancing type vibrator, including barrel, flange A, flange B, rotating shaft A, rotating shaft B, upper box, middle casing, rolling bearing units, isolation spring, lower box, hydraulic cylinder, end cap, cylinder, flexible coupling, motor, master Axle, liner plate, helical blade, screen cloth and base;Upper, middle and lower casing is fixedly connected, and base is fixed on the ground, and lower box passes through Isolation spring is supported on the hydraulic cylinder on base top, and rolling bearing units are fixed on box house, the cylinder of more than three respectively with Rolling bearing units are connected by rotating shaft with bearing fit, and cylinder circumference uniform distribution is in the eccentric shaft in mass of vibration center, cylinder Away from 4~20mm, eccentric shaft is fixedly connected with cylinder;End cap is fixedly connected with cylinder one end, and cylinder inboard wall sets liner plate, cylinder end Lid side sets gradually helical blade and screen cloth is fixedly connected with cylinder, and cylinder body outer wall sets feeding mouth;The main shaft of motor and cylinder Connected by flexible coupling;The mating connection that flexible coupling passes through axle and bearing with rolling bearing units.
Beneficial effects of the present invention are, 1) multiple cylindrical body synchronous work, yield is high;2) worked under high-frequency excitation, amplitude is big; 3) motor rotates forward crushing grinding, hydraulic cylinder jack-up during reversion, and cylinder tilts discharging, simple to operate, is easy to implement automated production; 4) using defined motor rotation direction, motor synchronizing self-balancing is realized, 0 is actuated to matrix, the vibration noise ring of national regulation is met Guaranteed request.
Brief description of the drawings
Fig. 1 is conventional bead mill schematic diagram;
Fig. 2 is structure chart;
Fig. 3 is Fig. 3 top views;
Fig. 4 is Fig. 3 left views;
Fig. 5 is n dynamics models;
Fig. 6 is the schematic diagram of 4 machine scheme 1;
Fig. 7 is the schematic diagram of 4 machine scheme 2;
Fig. 8 is the schematic diagram of 4 machine scheme 3;
Fig. 9 is 3 machine schematic diagrams;
Figure 10 is k machine schematic diagrams;
In figure:1 barrel;2 flange A;3 flange B;4 rotating shaft A;5 rotating shaft B;6 upper boxes;Casing in 7;8 rolling bearing units;9 every Shake spring;10 lower boxes;11 hydraulic cylinders;12 end caps;13 cylinders;14 screws;15 flexible couplings;16 motors;17 main shafts;18 linings Plate;19 feeding mouths;20 helical blades;21 screen clothes;22 bases.
Embodiment
A kind of multimachine drives motor synchronizing self-balancing type vibrator, including barrel 1, flange A2, flange B3, rotating shaft A4, Rotating shaft B5, upper box 6, middle casing 7, rolling bearing units 8, isolation spring 9, lower box 10, hydraulic cylinder 11, end cap 12, cylinder 13, scratch Property shaft coupling 15, motor 16, main shaft 17, liner plate 18, helical blade 20, screen cloth 21 and base 22;Upper, middle and lower casing, which is fixed, to be connected Connect, base is fixed on the ground, lower box is supported on by isolation spring on the hydraulic cylinder on base top, and rolling bearing units are fixed on Box house, the cylinder of more than three is connected with rolling bearing units by rotating shaft with bearing fit respectively, and cylinder circumference uniform distribution is in ginseng Shake mass centre, barrel diameter 200mm (can be adjustable according to Practical Project demand), eccentric shaft in cylinder away from 4~ 20mm (adjustable), eccentric shaft is fixedly connected with cylinder;End cap is fixedly connected with cylinder one end, and cylinder inboard wall sets liner plate, cylinder Body end cover side sets gradually helical blade and screen cloth is fixedly connected with cylinder, and cylinder body outer wall sets feeding mouth 19;Motor and cylinder Main shaft connected by flexible coupling;The mating connection that flexible coupling passes through axle and bearing with rolling bearing units.
This invention is to more than 3 machines can be achieved, the principle of specification by taking n machines as an example:
Step 1:Set up kinetic model and differential equation of motion:
The kinetic model of the system considered is as shown in Fig. 2 n eccentric rotor is arranged on rigid frame, and is divided Not by n Induction Motor Drive, wherein q turns clockwise and p rotate counterclockwises.The motion of rigid frame is assumed to plane fortune Dynamic, framework fixed frame, its origin is the equalization point of the barycenter of rigid frame.Plane motion coordinate is represented by x, y, around its barycenter Swing with ψ (ψ<<1) represent.Each eccentric rotor rotates around itself gyroaxis, withTable Show, βiRepresent that x-axis is horizontal direction in eccentric rotor center and system barycenter o point lines and the angle of x-axis, coordinate system xoy, is sat In mark system x ' o ' y ', x ' axles are with system translation, and the angle of x ' axles and x-axis is ψ, when device is static, and ψ is 0 degree.
Order(h=p+q) it is generalized coordinates, using Lagrange's equation, obtains system motion The differential equation is
Wherein,J0i=mir2, i=1,2 ..., h.
M is rigid frame quality;JmFor rigid frame rotary inertia, miIt is eccentric rotor i quality, l0It is eccentric rotor i revolutions Center oiWith the distance between rigid frame barycenter;kx,kyAnd kψIt is the rigidity of system correspondence direction, fx fy,fψIt is x, y, the resistance in ψ directions Buddhist nun's coefficient, fiIt is rotor i damped coefficient, leIt is the equivalent radius of gyration of the vibrational system on rigid frame barycenter, TeiIt is electricity Machine i electromagnetic torque, J0iIt is eccentric rotor i rotary inertia.It is assumed that the eccentric arm of multiple eccentric rotors is identical, i.e. r1=r2 =...=rh=r.The rotary inertia very little of motor rotor and it can ignore.WithD/dt and d is represented respectively2·/ dt2
Step 2:Derivation system realizes synchronous synchronism and stability condition
Due to the periodic vibration of vibrational system, the mean angular velocity of caused multiple eccentric rotorsMechanical periodicity. If the least common multiple in multiple eccentric rotor cycles is T0, then by T0In time, the mean angular velocity of multiple eccentric rotors Average value necessarily individual definite value, i.e.,
We set as follows:
Here,With(note respectivelyWithFunction is that time t) is on ωm0WithTransient change coefficient.
Based on formula (3), have
Here, Fi12,…,αh-1) it is α12,…,αh-1Linear function, andIt isLinear function.εiEccentric rotor i dimensionless angular speed disturbance parameter is represented in formula (4), i.e.,
We define m1It is used as standard rotor m0That is,, m1=m0, and miim0(0<ηi≤ 1, i=1,2 ..., h, η1=1) is on the premise of small vibration-damping system off-resonance, in first three formula of stable state up-to-date style (1)It is negligible.System It is in x-y- and ψ-direction response
Here,
Induction machine angular speed is in ωm0The electromagnetic torque of place's stable operation is expressed asHere Te0iWithIt is that angular speed is ω respectivelym0Induction machine effective electromagnetism output torque and angular speed stiffness coefficient.By nondimensionalization After processing, we obtain system and realize that synchronous frequency catching equation is:
Here
System realizes that synchronous synchronization conditions are:
The stability condition of system angular speed is:
a′ij>0,det(A′2)>0,det(A′3)>0,…,det(A′)>0, (8)
Here, A '=(a 'ij)h×hWith B '=(b 'ij)h×hMatrix A and B determinants are represented,
In addition, wanting the stability of guarantee system, in addition to the stability of speed, the multiple eccentric rotors of consideration system are also needed The stability of phase difference.
In formula (6),Place's linearisation u=0, and considerObtain
Here ()0RepresentWithValue.
Rearrangement formula (9), is obtained
In formula Δ α=vexp (λ t), determinant equation det (D- λ I)=0 is obtained, and use Routh- Hurwitz criterions, if the eigenvalue λ of generalized ensemble all has negative real part, the solution of phase difference is stable.Only system is more The speed of individual eccentric rotor and their phase difference are all stablized, and just can guarantee that the stability of whole vibrational system.
According to cylinder quantity, two kinds of situations can be divided into:
When four, four cylinder circumference uniform distributions have three kinds of operational schemes in the barycenter periphery of ginseng vibration body;When 3 and 5 Cylinder and during above quantity, cylinder circumference uniform distribution is in ginseng vibration body barycenter periphery, and only a kind of operational scheme.It must be stressed that It is:No matter which kind of scheme, it is necessary to circumference uniform distribution shakes the barycenter periphery of plastid in ginseng.

Claims (2)

1. a kind of multimachine drives motor synchronizing self-balancing type vibrator, it is characterised in that including barrel, flange A, flange B, turn Axle A, rotating shaft B, upper box, middle casing, rolling bearing units, isolation spring, lower box, hydraulic cylinder, end cap, cylinder, flexible coupling, Motor, main shaft, liner plate, helical blade, screen cloth and base;Upper, middle and lower casing is fixedly connected, and base is fixed on the ground, nowel Body is supported on by isolation spring on the hydraulic cylinder on base top, and rolling bearing units are fixed on box house, the cylinder of more than three It is connected respectively with rolling bearing units by rotating shaft with bearing fit, cylinder circumference uniform distribution is in the bias in mass of vibration center, cylinder Eccentric shaft is fixedly connected away from 4~20mm, eccentric shaft with cylinder;End cap is fixedly connected with cylinder one end, and cylinder inboard wall sets liner plate, Barrel body end cover side sets gradually helical blade and screen cloth is fixedly connected with cylinder, and cylinder body outer wall sets feeding mouth;Motor and cylinder Main shaft connected by flexible coupling;The mating connection that flexible coupling passes through axle and bearing with rolling bearing units.
2. a kind of multimachine described in claim 1 drives the parameter determination method of motor synchronizing self-balancing type vibrator, it is special Levy and be, comprise the following steps:
Step 1:Set up system dynamics model and differential equation of motion:
Three and multiple eccentric rotors are arranged on rigid frame, each eccentric rotor respectively by an Induction Motor Drive, its Middle q turns clockwise and p rotate counterclockwises;Rigid frame is connected by slinky spring with basis, and the motion of rigid frame is plane Motion, the barycenter of the framework with eccentric rotor is the equalization point of whole vibrational system;Plane motion horizontal direction and vertical direction Coordinate is represented that system is swung with ψ (ψ around its barycenter o by x, y respectively<<1) represent;Each eccentric rotor revolves around itself gyroaxis Turn, useP+1 ..., p+q represent, βiThe eccentric rotor centre of gyration and o point lines and the angle of x-axis are represented, Gu In x-axis horizontal direction in position fixing system xoy, coordinate system x ' o ' y ', x ' axles are with device translation, and the angle of x ' axles and x-axis is ψ, when During system quiescence, ψ is 0 degree;
X, y, ψ are made,(h=p+q) it is generalized coordinates, using Lagrange's equation, the motion for obtaining system is micro- Divide equation as follows:
Wherein,
<mrow> <mi>M</mi> <mo>=</mo> <mi>m</mi> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>h</mi> </munderover> <msub> <mi>m</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>J</mi> <mo>=</mo> <msub> <mi>J</mi> <mi>m</mi> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>h</mi> </munderover> <msub> <mi>m</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>r</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>l</mi> <mn>0</mn> </msub> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>Ml</mi> <mi>e</mi> <mn>2</mn> </msubsup> <mo>,</mo> <msub> <mi>J</mi> <mrow> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mi>i</mi> </msub> <msup> <mi>r</mi> <mn>2</mn> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>,</mo> <mi>h</mi> <mo>;</mo> </mrow>
M is rigid frame (abbreviation rigid frame) quality;JmRepresent rotary inertia of the rigid frame on its barycenter, miIt is eccentric rotor i matter Amount, l0It is eccentric rotor i centres of gyration oiThe distance between to rigid frame barycenter;kx,kyAnd kψFor the rigidity in respective coordinates direction, fx fy,fψIt is the damped coefficient in x, y, ψ direction, fiIt is rotor i damped coefficient, leIt is vibrational system on rigid frame center The equivalent radius of gyration, TeiIt is motor i electromagnetism output torque, J0iIt is eccentric rotor i rotary inertia;Multiple eccentric rotors Eccentric arm riIt is the same, i.e. r1=r2=...=rh=r;The rotary inertia of the rotor of motor is due to very little and can neglect Slightly;WithD/dt and d is represented respectively2·/dt2
Step 2:Derivation system realizes synchronous synchronization conditions and stability condition
Due to the periodic vibration of vibrational system, cause the mean angular velocity of eccentric rotorCyclically-varying;If multiple inclined The least common multiple of heart rotor cycle is T0, by T0In time, mean angular velocity average value must be a definite value, i.e.,
HereWithIt is on ω respectivelym0WithTransient change coefficient;
According to formula (3), have
Fi12,…,αh-1) it is α12,…,αh-1Linear function, andIt isIt is linear Function,
Definition standard eccentric rotor is m0,m1=m0, and miim0(0<ηi≤ 1, i=1,2 ..., h, η1=1) systems are in x- Y- and ψ-direction response is:
Here
<mrow> <msub> <mi>&amp;gamma;</mi> <mi>g</mi> </msub> <mo>=</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;xi;</mi> <mrow> <mi>n</mi> <mi>g</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>n</mi> <mi>g</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>m</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>n</mi> <mi>g</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>m</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> <mi>g</mi> <mo>=</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>&amp;psi;</mi> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>n</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msub> <mi>k</mi> <mi>x</mi> </msub> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> <mo>,</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>n</mi> <mi>y</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msub> <mi>k</mi> <mi>y</mi> </msub> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> <mo>,</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>n</mi> <mi>&amp;psi;</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msub> <mi>k</mi> <mi>&amp;psi;</mi> </msub> <mo>/</mo> <mi>J</mi> </mrow> </msqrt> <mo>,</mo> <msub> <mi>&amp;xi;</mi> <mrow> <mi>n</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>f</mi> <mi>x</mi> </msub> <mrow> <mn>2</mn> <msqrt> <mrow> <msub> <mi>k</mi> <mi>x</mi> </msub> <mi>M</mi> </mrow> </msqrt> </mrow> </mfrac> <mo>,</mo> <msub> <mi>&amp;xi;</mi> <mrow> <mi>n</mi> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>f</mi> <mi>y</mi> </msub> <mrow> <mn>2</mn> <msqrt> <mrow> <msub> <mi>k</mi> <mi>y</mi> </msub> <mi>M</mi> </mrow> </msqrt> </mrow> </mfrac> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;xi;</mi> <mrow> <mi>n</mi> <mi>&amp;psi;</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>f</mi> <mi>&amp;psi;</mi> </msub> <mrow> <mn>2</mn> <msqrt> <mrow> <msub> <mi>k</mi> <mi>&amp;psi;</mi> </msub> <mi>J</mi> </mrow> </msqrt> </mrow> </mfrac> <mo>,</mo> </mrow>
Induction machine angular speed stable operation is in ωm0When, its electromagnetism output torque is expressed asTe0iWithPoint It is not that angular speed is ωm0When induction machine output torque and angular speed stiffness coefficient;
In the induction machine differential equation of motion that formula (5) is substituted into formula (1), the frequency of system is obtained after nondimensionalization is handled Capture equation as follows:
<mrow> <mi>A</mi> <mover> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>B</mi> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mo>+</mo> <mi>u</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <msup> <mrow> <mo>{</mo> <msub> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mn>2</mn> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mi>h</mi> </msub> <mo>}</mo> </mrow> <mi>T</mi> </msup> <mo>,</mo> <mi>u</mi> <mo>=</mo> <msup> <mrow> <mo>{</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>,</mo> <msub> <mi>u</mi> <mi>h</mi> </msub> <mo>}</mo> </mrow> <mi>T</mi> </msup> <mo>,</mo> </mrow>
<mrow> <mi>A</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;rho;</mi> <mn>1</mn> </msub> </mtd> <mtd> <msubsup> <mi>&amp;chi;</mi> <mn>12</mn> <mo>&amp;prime;</mo> </msubsup> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <msubsup> <mi>&amp;chi;</mi> <mrow> <mn>1</mn> <mi>h</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&amp;chi;</mi> <mn>21</mn> <mo>&amp;prime;</mo> </msubsup> </mtd> <mtd> <msub> <mi>&amp;rho;</mi> <mn>2</mn> </msub> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <msubsup> <mi>&amp;chi;</mi> <mrow> <mn>2</mn> <mi>h</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <mo>...</mo> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mo>...</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&amp;chi;</mi> <mrow> <mi>h</mi> <mn>1</mn> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> <mtd> <msubsup> <mi>&amp;chi;</mi> <mrow> <mi>h</mi> <mn>2</mn> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <msub> <mi>&amp;rho;</mi> <mi>h</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>B</mi> <mo>=</mo> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>m</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>b</mi> <mn>11</mn> </msub> </mrow> </mtd> <mtd> <msub> <mi>&amp;chi;</mi> <mn>12</mn> </msub> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <msub> <mi>&amp;chi;</mi> <mrow> <mn>1</mn> <mi>h</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;chi;</mi> <mn>21</mn> </msub> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>m</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>b</mi> <mn>22</mn> </msub> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <msub> <mi>&amp;chi;</mi> <mrow> <mn>2</mn> <mi>h</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>...</mo> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mo>...</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;chi;</mi> <mrow> <mi>h</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;chi;</mi> <mrow> <mi>h</mi> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>m</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>b</mi> <mrow> <mi>h</mi> <mi>h</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>&amp;eta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;eta;</mi> <mi>i</mi> </msub> <msub> <mi>W</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>b</mi> <mrow> <mi>i</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mover> <mi>k</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>e</mi> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> <msup> <mi>r</mi> <mn>2</mn> </msup> <msub> <msup> <mi>&amp;omega;</mi> <mn>2</mn> </msup> <mrow> <mi>m</mi> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> <msup> <mi>r</mi> <mn>2</mn> </msup> <msub> <mi>&amp;omega;</mi> <mrow> <mi>m</mi> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>W</mi> <mrow> <mi>s</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>T</mi> <mrow> <mi>e</mi> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> <msup> <mi>r</mi> <mn>2</mn> </msup> <msub> <mi>&amp;omega;</mi> <mrow> <mi>m</mi> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;chi;</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;chi;</mi> <mrow> <mi>a</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>h</mi> <mrow> <mo>(</mo> <mi>h</mi> <mo>=</mo> <mi>p</mi> <mo>+</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>|</mo> <mfrac> <mrow> <msub> <mi>&amp;Delta;T</mi> <mrow> <mn>0</mn> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <msub> <mi>T</mi> <mi>u</mi> </msub> </mfrac> <mo>-</mo> <mrow> <mo>(</mo> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>W</mi> <mrow> <mi>s</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>&amp;eta;</mi> <mi>j</mi> <mn>2</mn> </msubsup> <msub> <mi>W</mi> <mrow> <mi>s</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mo>=</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>c</mi> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>&amp;alpha;</mi> <mo>&amp;OverBar;</mo> </mover> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>&amp;alpha;</mi> <mo>&amp;OverBar;</mo> </mover> <mn>2</mn> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mover> <mi>&amp;alpha;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>h</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mo>&amp;le;</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>c</mi> <mi>i</mi> <mi>j</mi> <mi>max</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>&amp;NotEqual;</mo> <mi>j</mi> <mo>,</mo> <mi>i</mi> <mrow> <mo>(</mo> <mi>o</mi> <mi>r</mi> <mi> </mi> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>h</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
The stability criteria that can obtain the multiple eccentric rotor angular speed disturbance parameters of system by formula (6) is:
a′ij>0,det(A′2)>0,det(A′3)>0,…,det(A′)>0, (8)
Here, A '=(a 'ij)h×hWith B '=(b 'ij)h×hRepresenting matrix A and B characteristic value,
By obtaining as follows:
In formula (6),WithLocate linearization equations u=0, and considerObtain
(·)0RepresentWithValue;
Rearrangement formula (9), is obtained
<mrow> <mi>&amp;Delta;</mi> <mover> <mi>&amp;alpha;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>D</mi> <mi>&amp;Delta;</mi> <mi>&amp;alpha;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
In formula Δ α=vexp (λ t), determinant equation det (D- λ I)=0 is solved, and uses Routh-Hurwitz criterions, such as Fruit all has negative real part on system features value λ value, then the phase difference solution of multiple eccentric rotors is stable in system.
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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109499696A (en) * 2018-12-17 2019-03-22 东北大学 A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine
CN109649964A (en) * 2018-12-17 2019-04-19 东北大学 A kind of parameter determination method of three machines driving subresonance self-synchronous vibration conveyor device
CN109701697A (en) * 2018-12-17 2019-05-03 东北大学 Four machines of one kind driving double-mass vibrating impact crusher and its parameter determination method
CN109794329A (en) * 2018-12-17 2019-05-24 东北大学 A kind of parameter determination method of four machine of double mass driving circular motion high-frequency vibration grinding machine
CN110918202A (en) * 2019-11-26 2020-03-27 东北大学秦皇岛分校 Frequency-doubling synchronous vibration grinding device based on planar multi-machine driving and parameter determination method
CN114247516A (en) * 2020-09-19 2022-03-29 丹东东方测控技术股份有限公司 Disc type fixed eccentric grinder with cross slide rail

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN2087992U (en) * 1990-07-23 1991-11-06 枚卫平 Eocentric shaft vibrator grinding mill
CN1335203A (en) * 2001-09-06 2002-02-13 胡传东 Large-amplitude centrifugal vibrating grinder
CN201701981U (en) * 2010-06-23 2011-01-12 太原钢铁(集团)有限公司 Ball mill ore discharging device
CN202061665U (en) * 2011-05-05 2011-12-07 南京云泰化工总厂 Hard rock discharging device of ball mill
CN203944433U (en) * 2014-06-03 2014-11-19 陆锁根 Complete ceramic pollution-free ultramicro grinding processing vibrations mill

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN2087992U (en) * 1990-07-23 1991-11-06 枚卫平 Eocentric shaft vibrator grinding mill
CN1335203A (en) * 2001-09-06 2002-02-13 胡传东 Large-amplitude centrifugal vibrating grinder
CN201701981U (en) * 2010-06-23 2011-01-12 太原钢铁(集团)有限公司 Ball mill ore discharging device
CN202061665U (en) * 2011-05-05 2011-12-07 南京云泰化工总厂 Hard rock discharging device of ball mill
CN203944433U (en) * 2014-06-03 2014-11-19 陆锁根 Complete ceramic pollution-free ultramicro grinding processing vibrations mill

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
张学良: "双机及多机驱动振动***同步理论的研究", 《中国优秀博硕士学位论文全文数据库(博士)工程科技Ⅱ辑》 *

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109499696A (en) * 2018-12-17 2019-03-22 东北大学 A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine
CN109649964A (en) * 2018-12-17 2019-04-19 东北大学 A kind of parameter determination method of three machines driving subresonance self-synchronous vibration conveyor device
CN109701697A (en) * 2018-12-17 2019-05-03 东北大学 Four machines of one kind driving double-mass vibrating impact crusher and its parameter determination method
CN109794329A (en) * 2018-12-17 2019-05-24 东北大学 A kind of parameter determination method of four machine of double mass driving circular motion high-frequency vibration grinding machine
CN109499696B (en) * 2018-12-17 2019-11-08 东北大学 A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine
CN109701697B (en) * 2018-12-17 2020-03-24 东北大学 Four-machine-driven double-mass vibration impact crusher and parameter determination method thereof
CN110918202A (en) * 2019-11-26 2020-03-27 东北大学秦皇岛分校 Frequency-doubling synchronous vibration grinding device based on planar multi-machine driving and parameter determination method
CN114247516A (en) * 2020-09-19 2022-03-29 丹东东方测控技术股份有限公司 Disc type fixed eccentric grinder with cross slide rail

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