CN109649965A - A kind of parameter determination method of four machine of subresonance double mass driving vibrosieve conveyer - Google Patents
A kind of parameter determination method of four machine of subresonance double mass driving vibrosieve conveyer Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
- B65G—TRANSPORT OR STORAGE DEVICES, e.g. CONVEYORS FOR LOADING OR TIPPING, SHOP CONVEYOR SYSTEMS OR PNEUMATIC TUBE CONVEYORS
- B65G27/00—Jigging conveyors
- B65G27/10—Applications of devices for generating or transmitting jigging movements
- B65G27/16—Applications of devices for generating or transmitting jigging movements of vibrators, i.e. devices for producing movements of high frequency and small amplitude
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
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- G06F30/17—Mechanical parametric or variational design
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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Abstract
The invention belongs to large scale equipments to sieve conveying technology field, provide a kind of parameter determination method of four machine of subresonance double mass driving vibrosieve conveyer.The vibrosieve conveyer is converted to kinetic model are as follows: be rigidly connected four vibration excitors respectively on main vibrating system, is divided to or so two groups, every group of vibration excitor is symmetrically distributed in plastid m along spring1Upper and lower two sides, symmetrical vibration excitor turn to opposite；Plastid m1Pass through spring k1With plastid m2Connection, and the side between two plastids perpendicular to telescopic spring sets up guide plate, makes system one degree of freedom in the x-direction；Vibrating isolation system plastid m2Lower section passes through spring k2On the basis of being fixed on guide plate；Using Vibration Synchronization Theory, the exciter parameters of separator conveyer are determined using the vibrational state of different resonance-types, when system is in relative to ω0Subresonance state under, stable phase potential difference between each vibration excitor is 0, can be by the work range selection of the equipment in the area, and finally realize its engineering application value.
Description
Technical field
The invention belongs to large scale equipments to sieve conveying technology field, mainly apply Vibration Synchronization Theory, utilize vibrational system
The vibrational state of different resonance-types sieve to material developing for the large scale equipment of conveying, and finally realizes its engineering
Application value.
Background technique
In vibrosieve transportation art, many equipment have been applied to engineering in practice, and this patent propose it is a kind of new
Vibrosieve conveying equipment model.Using four machine of double mass driving kinetic model as research object, using the method for average and Hamilton
The principle of least action respectively obtains four vibration excitors and finally realizes synchronous synchronism criterion, analyzes system and realizes synchronization
Coupling mechanism, define synchronism and stability force coefficient, in terms of numerical value, give width-frequency of two plastid relative motions
Curved line relation, system synchronizing capacity coefficient curve, dimensionless coupling torque maximum value and stability coefficient define system difference
Three classes phase relation under interval of resonance: the phase relation between vibration excitor, between plastid and between plastid and vibration excitor.And three classes phase
Position relationship is exactly the embodiment of the final function of mechanical equipment.Emulation aspect, demonstrates the correctness of numerical solutions.It can be according to double mass
Four machines drive Vibration Synchronization Theory to provide reason for the development of novel, long range, big conveying capacity vibrosieve conveying equipment
By guidance.
Summary of the invention
Goal of the invention: it is mentioned for drawbacks, the present invention such as short distance, miniaturization, the energy consumptions of current vibrosieve conveying equipment
The design method for having gone out four machine of subresonance double mass driving vibrating screen, theoretically discusses the synchronization conditions of the kinetic model
And the stability criteria under synchronous regime, and by the correctness of simulation analysis verifying numerical analysis, subresonance has finally been determined
Area is the reasonable operating point of system, to realize two vibration excitor Downward additions, in turn, for the vibration of novel long range, big conveying capacity
The development of conveyer provides theoretical direction.
The present invention is achieved by the following technical solutions, which is converted to kinetic model are as follows:
Main vibrating system and vibrating isolation system are referred to as including two plastids, four vibration excitors and two groups of springs, upper and lower two parts；
Be rigidly connected four vibration excitors respectively on main vibrating system, is denoted as two groups of left and right respectively, every group of vibration excitor is each along bullet
Spring is symmetrically distributed in plastid m1Upper and lower two sides, one group of symmetrical vibration excitor turn to opposite；Plastid m1Pass through one group of spring k1It will
Itself and plastid m2Connection, and the side between two plastids perpendicular to telescopic spring sets up guide plate, makes system only along x
Direction one degree of freedom；
Vibrating isolation system plastid m2Top is connected to plastid m1, lower section passes through spring k2On the basis of being fixed on guide plate；It is described
Vibration excitor and vibrational system parameter determination method, include the following steps:
Step 1, the foundation of dynamic model
Vibrosieve conveyer kinetic model is shown in Fig. 1, establishes two by origin of the mass center of plastid 1 and plastid 2 respectively
Coordinate system O1-x1、O2-x2。
In generalized coordinates system o-x, according to the kinetic energy T of system, potential energy V and energy function obtain two plastids in the x direction
Differential equation of motion it is as follows
Wherein
M1=m1+4m0, M2=m2, Joi=m0iri 2
In formula, m1--- 1 mass of plastid；
m2--- 2 mass of plastid；
m0i--- vibration excitor i mass (i=1~4)；
R --- vibration excitor eccentricity；
k1,k2--- the direction x upper spring rigidity；
f1,f2--- damped coefficient on the direction x.
Joi--- the rotary inertia (i=1~4) of vibration excitor i；
--- the phase angle (i=1~4) of vibration excitor i；
--- the angular speed (i=1~4) of vibration excitor i；
--- the angular acceleration (i=1~4) of vibration excitor i；
It enables all parameters of four in system vibration excitors be consistent, takes m01=m02=m03=m04=m0.It is assumed that four
The average phase of vibration excitor isCorresponding phase difference is respectively 2 α1, 2 α2, 2 α3, it can obtain,
Set four eccentric rotors in stable state synchronous angular velocity as ωm0, when systematic steady state operation when, can obtain displacement with
The relationship of acceleration, it is as follows,
When system is in steady-state operation, angular acceleration is almost 0, i.e.,Formula (5) is brought into (1) and (2),
Ignore f simultaneously2(because its is comparatively small), obtains:
For formula (6) and (7), due to k2<<k1, haveM1'=M1。
Following processing is done,Following plastid m can be obtained1And m2In the direction x phase
To differential equation of motion,
Wherein,
x1=x1-x2
In formula, m is induction quality.
By formula (8), two plastids can be obtained in the direction x relative motion natural frequency ω0(the also referred to as main intrinsic frequency of vibrating system)
For
The response of formula (8) is
Wherein
In engineering, for small damping vibration machine, f1=2 ξ 'xmω0, wherein ξ 'xFor equivalent relative damping factor, ξ 'x≤
0.07.By formula (10) it is found that working as z0=1 (i.e. ωm0=ω0) when, A12It is maximized at resonance point, illustrates ω0It is corresponding to be
Two direction plastid x antiphase relative motion intrinsic frequencies.By the way that formula (10) further abbreviation, available antiphase is opposite to be transported
Dynamic response amplitude λ12, it is expressed as λ12=| A12·S| (11)
Wherein
S=(η1 2+η2 2+η3 2+η4 2+2η1η2cos(2α1)+2η2η3cos(2α2)+2η3η4cos(2α3)+2η1η3cos(2α1+2
α2)+2η1η4cos(2α1+2α2+2α3)+2η2η4cos(2α2+2α3))1/2
Antiphase relative motion response amplitude λ12There is very big application value in engineering.
Step 2, system synchronicity is analyzed
Using transfer function method, formula (1) is solved with (2), enables x1=X1(s),x2=
X2(s),S=i ω substitutes into formula (1) and (2) respectively, and further abbreviation arranges to obtain x1,x2's
It responds as follows
Wherein
In formula, γ1--- the angle of lag of plastid 1 in the x direction；
γ2--- the angle of lag of plastid 2 in the x direction.
According to formula (1), can obtaining two plastids, mass matrix, stiffness matrix and characteristic equation are as follows in the x direction
In formula, M ' is mass-coupling matrix, and K ' is stiffness coupling matrix, Δ (ω2) it is characterized equation.
Enable Δ (ω2)=0, it is available
Under normal circumstances, the rigidity k of vibrating isolation system2The rigidity k of far smaller than main vibrating system1, i.e. k2<<k1, therefore will
ωInvIn k2Ignore, then has ωInv=ω0, it can be seen that ωInvCorresponding is two plastids in the antiphase relative motion of the direction x
Intrinsic frequency.Obviously, ωSaIt is two plastids in the direction x same-phase relative motion intrinsic frequency.
When four vibration excitors can operate synchronously, haveBy formula (12) to x1、x2Second order is carried out about time t
Derivation, and bring formula (3) into, it is right on 0~2 πIt is integrated, after taking mean value and arranging, obtains the equilibrium equation of four vibration excitors
It is as follows:
Wherein
In above-mentioned integral process, it should be noted that natural frequency ω1For the intrinsic frequency of plastid 2, in subsequent numerical value
It can be stressed with simulation analysis.ComparisonThe variation degree of t at any time, 2 α1, 2 α2With 2 α3Variation very
It is small, three parameters can be regarded it as slow-changing parameters, 2 α in integral process1, 2 α2With 2 α3With its Integral Mean ValueWithIt indicates.
The difference of output torque is between each vibration excitor
Formula (16)~(18) are arranged, can be obtained,
Wherein
In above-mentioned derivation,WithRespectively vibration excitor 1,2 it
Between, dimensionless coupling torque, constraint function are as follows between vibration excitor 2,3 and between vibration excitor 3,4
To sum up, in conjunction with (19), the synchronization criterion of (20) and (21), available four vibration excitors is
By formula (25), (26) and (27), it can be seen that the difference of the dimensionless residual moment of two neighboring vibration excitor it is exhausted
It is less than or equal to the maximum value of dimensionless coupling torque to value.τ further can be obtainedc41maxExpression formula it is as follows:
τc41max=-(τc12max+τc23max+τc34max) (28)
It is rightSummation, and divided by 4F1Tu, it can it is negative to obtain the four vibration excitors dimensionless that is averaged
Torque is carried, is expressed as
Four vibration excitors be averaged dimensionless loading moment constraint function it is as follows
Definition synchronizing capacity coefficient is ζij(i, j=1,2,3,4), can obtain,
Synchronizing capacity coefficient is bigger, and the synchronizing capacity of system is stronger, easier to reach synchronous.
Step 3, stability condition is derived
For four exciter system of double mass, the kinetic energy (T) and kinetic energy (V) of system are as follows,
Mean kinetic energy (E in one cycleT) and average potential energy (EV) be respectively
Wherein
The Hamilton mean effort amount (I) of system is in one cycle
Stable phase potential difference solution in two kinds of synchronous regimesCorresponding is that Hamilton averagely makees
Dosage minimum point, that is to say, that the Hesse matrix of the Hesse matrix normal Wishart distribution of I, I is expressed as H, obtains
Wherein
It enables,
In order to make the Hesse matrix normal Wishart distribution of I, i.e. H-matrix positive definite, should meet
H1>0,H2>0,H3>0 (39)
By H1, H2With H3The stabilizing power coefficient being defined as under the synchronous condition of system, formula (39) are the stability of system
The expression formula of ability, when meeting formula (39), system is stablized.
Beneficial effects of the present invention:
(1) present invention is innovated on model, selects two plastids, wherein there are four motors for peace on a plastid, is used
The driving of four machines, another plastid make vibration isolator, and similarly pass through spring phase between two plastids and between vibration isolator and ground
It connects, is innovated on model, closer to engineering practice.
(2) present invention applies Vibration Synchronization Theory, using the synchronous working of four machines driving realization system.The previous work of difference
Vibrosieve of the point selection in super remote workspace conveys class equipment, and the model that this patent proposes selects working region in subresonance
Region, in the area, system is under conditions of same-amplitude, exciting needed for the same amplitude evoked in subresonance region
Power is 1/5~1/3 under its super remote resonance condition.Thus, the driving motor function needed for the vibrational system of subresonance work status
Rate can be reduced accordingly, and then the saving of the energy may be implemented.
(3) research contents of the invention for screening conveying large-scale in engineering mechanical equipment, i.e., it is novel, over long distances, it is big
Yield large-scale vibrating sieves conveying equipment, has great directive function to the selection of its design of Structural Parameters and working region.
Detailed description of the invention
Four machine of Fig. 1 double mass drives dynamics model of vibration system
In figure: 1. vibration excitors 2,2. plastids 1,3. springs 1,4. plastids 2,5. guide plates, 6. springs 2,7. vibration excitors
4,8. vibration excitors 1,9. vibration excitors 3
Each meaning of parameters in figure:
O1-x11 coordinate system of plastid；
O2-x22 coordinate system of plastid；
-- 1 phase angle of vibration excitor；
-- 2 phase angle of vibration excitor；
-- 3 phase angle of vibration excitor；
-- 4 phase angle of vibration excitor；
-- 1 angular speed of vibration excitor；
-- 2 angular speed of vibration excitor；
-- 3 angular speed of vibration excitor；
-- 4 angular speed of vibration excitor；
m01--- 1 mass of vibration excitor；
m02--- 2 mass of vibration excitor；
m03--- 3 mass of vibration excitor；
m04--- 4 mass of vibration excitor；
m1--- 1 mass of plastid；
m2--- 2 mass of plastid；
k1--- spring 1 is in x1Direction upper spring rigidity；
k2--- spring 2 is in x2Direction upper spring rigidity.
Fig. 2 antiphase relative motion width-frequency response curve.
Fig. 3 system synchronicity power curve.
Fig. 4 system stability capacity factor；
(a) stability force coefficient H1；
(b) stability force coefficient H2；
(c) stability force coefficient H3。
Phase relation between tetra- vibration excitor of Fig. 5.
The response of Fig. 6 system and its phase relation between vibration excitor.
Fig. 7 is with respect to ω1Subresonance state (region I) simulation result；
(a) vibration excitor 1,2 stable phase potential differences；
(b) vibration excitor 2,3 stable phase potential differences；
(c) vibration excitor 3,4 stable phase potential differences；
(d) plastid 1,2 relative displacement (x1-x2)；
(e) displacement x1With x2。
Fig. 8 is with respect to ω0Subresonance state (region II) simulation result；
(a) vibration excitor 1,2 stable phase potential differences；
(b) vibration excitor 2,3 stable phase potential differences；
(c) vibration excitor 3,4 stable phase potential differences；
(d) relative displacement (x of plastid 1,21-x2)；
(e) displacement x1With x2。
Fig. 9 is with respect to ω0Super resonance state (region III) simulation result；
(a) vibration excitor 1,2 stable phase potential differences；
(b) vibration excitor 2,3 stable phase potential differences；
(c) vibration excitor 3,4 stable phase potential differences；
(d) plastid 1,2 relative displacement (x1-x2)；
(e) displacement x1With x2。
Specific embodiment
A kind of embodiment 1: four machine of subresonance double mass driving vibrosieve conveyer.Its kinetic model is shown in Fig. 1, including
1. vibration excitor 1；2. plastid 1；3. spring 1；4. plastid 2；5. guide plate；6. spring 2；7. vibration excitor 4；8. vibration excitor 2；
9. vibration excitor 3.The model is made of two plastids, four vibration excitors and two groups of springs, and four groups of vibration excitors are reversibly mounted on two-by-two
On plastid 1, it is connect with plastid 2 by spring 1, and the spring Vertical Square between two plastids sets up guide plate, makes
System only has one degree of freedom in the x-direction, meanwhile, plastid 2 is connected on ground by spring 2.Such as Fig. 1, four vibration excitors
The centre of gyration uses o respectively1, o2, o3And o4It indicates, the radius of gyration is r.Vibration excitor 1 and 4 reversed turning of vibration excitor, vibration excitor 2
With 3 reversed turning of vibration excitor.Whole system generates displacement in the x direction, and each vibration excitor is rotated around itself rotating shaft, withIt indicates.Furthermore, it is possible to be adapted to variety classes material by adjusting the angle β (0 < β < pi/2) of spring and horizontal direction
Screening, delivery requirements.
The numerical analysis of four machine of double mass driving vibrational system
Based on the driving of four machines (reversed two-by-two) double mass kinetic model, some numerical value are given to system parameter, are divided
Analysis, has verified that the correctness of theory deduction.Specific system parameter is as follows: m1=600kg, m2=1500kg, m0=10kg, r=
0.15m, k1=8000kN/m, k2=100kN/m.It is consistent to choose four motor models, three phase squirrel cage (model VB-1082-W,
The pole 380V, 50Hz, 6-, Δ-connection, 0.75kw, revolving speed 980r/min, 39kg).
In conjunction with the analysis of previous contents, it can be seen that for the driving of four machines (reversed two-by-two) double mass system, co-exist in three
The important intrinsic frequency of group, the natural frequency ω of plastid 21, antiphase relative motion natural frequency ωInvAnd relative motion is solid
There is frequencies omega0(the also referred to as main intrinsic frequency of vibrating system).As the rigidity k for ignoring vibrating isolation system2When, ωInv=ω0.It will inherently frequently
Rate ω1With ω0As the divide value of excited frequency, the frequency separation of whole system is divided into three parts, works as ωm0<ω1When, the area
Domain is opposite ω1Subresonance region, be denoted as region I；Work as ω1≤ωm0≤ω0When, which is opposite ω1Super resonance region
Domain and opposite ω0Subresonance region, be denoted as region II；Work as ωm0>ω0When, which is opposite ω0Super resonance zone, note
Make region III.
In the following, to stable state width-frequency characteristic of system, synchronism ability, system maximum coupling torque, synchronous regime stabilization
System phase relationship is numerically analyzed when property and stable state.
(a) stable state width-frequency characteristic
Fig. 2 is system's relative motion width-frequency response curve, according to the inherent characteristic of system, by plastid relative motion width-frequency
Response curve is divided into three parts.
As can be seen that in region I, excited frequency ωm0Increase by 0rad/s, the relative displacement of two plastids is 0mm.When
Excited frequency gradually increases, and moves closer to ω1, i.e. A point, frequency 73.03rad/s.System enters region II, and response amplitude is not
It is disconnected to increase, reach maximum relative magnitude at B point.Herein, another natural frequency ω of correspondence system0Two plastid relative motions
Intrinsic frequency, size 133.48rad/s.With ωm0It continues growing, system enters region III, under response amplitude starts
Drop, and there is breakpoint at C point, then, phase-shifted is returned to 0mm.It has been analyzed as a result, in different resonance zones, two
The variation tendency of plastid relative motion amplitude, can be contrasted with emulation, while can also clearly find out the opposite of double mass
Motion state.
It can be seen that region I by above-mentioned analysis and the relative amplitude of region III be substantially zeroed, and in response curve
Region II, i.e., with respect to ω1Super resonance zone and opposite ω0Subresonance region, be useful region, the system in this section of region
With larger and stable amplitude, engineering can be applied in practice.
(b) synchronism ability
Net synchronization capability force coefficient is indicated with ζ, is to measure each motor to reach synchronous index, net synchronization capability force coefficient is got over
Greatly, the synchronism ability of system is better.Since the model of four motors is consistent, the net synchronization capability force coefficient of four motors is big
Small consistent, such as Fig. 3, four curves are completely coincident.Equally, two natural frequency ωs of system1And ω0By net synchronization capability force curve
It is divided into three parts.In the I of region, the initial stage, when frequency increases, net synchronization capability force coefficient is gradually increased, then, net synchronization capability
Force coefficient is with excited frequency ωm0Increase and reduce, reach minimum at point A, be herein resonance point ω1.With exciting frequency
Rate continues growing, and net synchronization capability force curve enters region II, and in the area, net synchronization capability force coefficient first increases, after with being
For system close to another resonance point B, net synchronization capability force coefficient is reduced to minimum again, and B point is resonance point ω0.By between vibration excitor
The numerical analysis of phase difference is it is found that stable phase angle is 0 in this section.Later, net synchronization capability force curve enters region III, and same
Step performance force coefficient constantly increases with the increase of excited frequency.
Wherein, the A point and B point in net synchronization capability force curve, A point are ω1Resonance point, frequency 73.03rad/s, B point are
ω0Resonance point, frequency 133.48rad/s.When excited frequency is in A, when B point, net synchronization capability force coefficient is minimum.As it can be seen that working as
When system is in resonance point, the synchronism ability of system is minimum.
(c) system maximum coupling torque
According to the dimensionless coupling torque between four vibration excitor of formula (19)~(21), system parameter is brought into, four is obtained and swashs
Maximum coupling torque between vibration device, it is known that the maximum between vibration excitor 1,2 and vibration excitor 2,3 and vibration excitor 3,4 and vibration excitor 4,1
Coupling torque is equal.
With excited frequency ωm0Increase, either in region I, II or III, after stablizing, the nothing between four vibration excitors
Dimension maximum coupling torque is near 5.2, in addition to A and B point.Equally, such as net synchronization capability force curve, A point is ω1Resonance
Point, frequency 73.03rad/s, B point are ω0Resonance point, frequency 133.48rad/s.In A, B two o'clock, i.e., at resonance point, four
Dimensionless maximum coupling torque between vibration excitor produces decline.
(d) stability of synchronous regime
System parameter is brought into the H of formula (38)1, H2With H3In, the stability force coefficient of system is obtained, as shown in figure 4,
In the I of region, scheme (a), (b), stabilizing power curve variation tendency having the same (c), with the increase of excited frequency, surely
Qualitative capacity factor is 0.When excited frequency gradually passes through natural frequency ω1, stability force curve enters region II, stable
Performance force coefficient generates apparent increase, meanwhile, there is stable phase difference in the region.With continuing growing for frequency,
Into region III, stability force coefficient H1It is always more than 0, and H2Then there is multiple stable values, H3Then it is returned to 0.
Phase difference relationship between the result and the vibration excitor of Fig. 5 corresponds to each other, it may be said that diversity occurs in bright system
The phenomenon that, which will be described in detail in Fig. 5.By Numerical results it can be concluded that there are nonlinear system multiplicity disposition
The condition of condition has 2: one is stability coefficient of the system under synchronous condition is 0；The second is there are the steady of multiple phase differences
Fixed solution.
Due to the diversity of nonlinear system, in region I and III, stability coefficient is 0 or multiple stabilizations occurs
Value.And in region II, i.e., with respect to natural frequency ω0Subresonance region, system have stronger stability.Therefore, the region
With by strong application value.
(e) system phase relationship when stable state
The stable phase relationship of system mainly includes three classes phase relation, is the phase difference between vibration excitor, system respectively
The phase relation between phase relation and system response between response and vibration excitor.
As shown in figure 5, indicating the phase relation between four vibration excitors, 2 α12Indicate the phase difference of vibration excitor 1 and 2, similarly, 2
α23Indicate the phase difference of vibration excitor 2 and 3,2 α34Indicate the phase difference of vibration excitor 3 and 4.It can be seen from the figure that altogether according to two
Shake point ω1And ω0It is three regions by phase difference, the phase when excited frequency is in region I and region III, between four vibration excitors
There are multivalues between [- 180,180] for potential difference, that is, there are multiple stable solutions, illustrate the diversity of system.And work as excited frequency
When in region II, there is stable phase difference between four vibration excitors, be 0, i.e. 2 α12=2 α23=2 α34=0rad/s.The knot
By corresponding with the simulation result of next chapters and sections.It can be seen that the phase difference between four vibration excitors in region II be it is stable, also
It is to say in opposite ω0Subresonance area be stable.
As shown in fig. 6, the system of expression responds the phase relation between phase relation and system response between vibration excitor,
γ1Indicate 1 response lag of plastid in the angle of vibration excitor, γ2Indicate 2 response lag of plastid in the angle of vibration excitor, γ12It indicates
1 response lag of plastid is in the angle of plastid 2.Vibration excitor is lagged behind in region I, plastid 1 and plastid 2 it can be seen from the following figure
180 °, i.e., be in antiphase with vibration excitor.In region II, the angle that plastid 1 lags behind vibration excitor is gradually reduced；And plastid 2 lags
It is gradually increased again after the angle of vibration excitor first reduces.In the III of region, the lag angle of plastid 1 and vibration excitor close to 0 degree,
I.e. plastid 1 and vibration excitor are moved in same-phase；The lag angle of plastid 2 and vibration excitor is still 180 °, i.e., is in reverse phase with vibration excitor
Position movement.
Pass through γ12It can be seen that the relationship between system response, in region I, γ12In 0 attachment, illustrate plastid 1 and matter
There is no angles to lag between body 2, the state moved in same-phase.In region II, angle later between the two is gradually increased,
Move closer to 180 °.Angle lags 180 ° after region III, the two, in the state of anti-phase movement.
Above-mentioned analytic explanation ω1For the critical synchronous rotational speed of plastid 1 and the same anti-phase movement of plastid 2.When exciting frequency
Rate ωm0Less than ω1When, two plastids are moved in same-phase, and angle of lag is 0 °；Work as ω1≤ωm0≤ω0When, the response of two plastids is opened
Begin lag；Work as ωm0>ω0When, two plastids are in anti-phase movement, and angle of lag is 180 °.The simulation result of this result and next section is protected
It holds consistent.
Embodiment 2: the simulation analysis of four machine of double mass driving vibrational system
Four machine of double mass drives dynamics model of vibration system, and to the differential equation of its system, i.e. formula (1)~(3) utilize
Quadravalence Rouge-Kutta program is emulated.In specificity analysis, according to the inherent characteristic of system, its operating status is divided into
Three regions, as shown in region I, II and the III of Fig. 2~6.Similarly, in simulation analysis, three groups of parameters is taken, make system respectively
In three regions.Go out the system revolving speed of motor, phase difference and matter in stable state in corresponding region by simulation analysis
The displacement curve of body 1 and 2.
In practical engineering application, identical vibration excitor is generally taken, the parameter of four motors is identical, i.e.,
η1=η2=η3=η4=1.0.System univers parameter is selected as follows: rotor resistance Rr=3.40 Ω, stator resistance Rs
=3.35 Ω, inductor rotor Lr=170mH, stator inductance Ls=170mH, mutual inductance Lm=164mH, f1=f2=0.05.Vibration system
The other parameters of system: r=0.15m, m1=600kg, m2=1500kg, m0=10kg, fx=7.6kNs/m, ξnx=0.07.It adjusts
Whole parameter makes system be respectively at subresonance state and super resonance state.
(a) opposite ω1Subresonance state (region I) simulation result
Take k1=80000kN/m, k2=100kN/m, zx=0.45, system is in region I, i.e., relative to ω1Subresonance
State.In the following, the displacement of phase difference, plastid 1 and 2 between system in the stable state of region I the revolving speed of motor, vibration excitor carries out
Analysis.As the time increases, in preceding 20s, four vibration excitors have reached synchronous and have stablized.But after being interfered, system goes out
Non-linear various implementations are showed.
Synchronous rotational speed if the curve in Fig. 7 is four motors in steady-state operation is stablized in 980r/min~985r/min
It is drawn in range.When system is in region I steady-state operation, the revolving speed of each motor is close to exciting revolving speed 983r/min.
As Fig. 7 (a) (b) (c) indicates the stable phase potential difference curve of system in the I of region, it can be seen that undisturbed
Before, i.e., preceding 20s, 2 α of stable phase potential difference of vibration excitor 1 and vibration excitor 212=-180 °, the stable phase angle of vibration excitor 2 and vibration excitor 3
Difference is 2 α23=0 °, vibration excitor 3 and the stable phase potential difference of vibration excitor 4 are 0 °, i.e. 2 α34=0 °.It is given respectively at 20s and 35s
2 one, motor interference, it is seen then that variation occurs in system phase.The result is corresponding with the result of numerical analysis, has embodied non-
The diversity of linear system.
Fig. 7 (d) (e) indicates the displacement of plastid 1,2 and the two relative displacement curve in the I of region.Preceding 20s, plastid 1
Displacement x1Stablize in -0.4mm~0.4mm, the displacement x of plastid 22Stablize in -0.7mm~0.7mm, then the relative displacement of the two is steady
It is scheduled on -0.3mm~0.3mm.At 20s and 35s to system interference after, the displacement of plastid 1 and 2 occur variation, become
For 0mm, i.e., after given interference, system has become totally stationary from small amplitude motion.
Such as Fig. 7 (e), the displacement x of plastid 1 is clearly indicated1With the displacement x of plastid 22Between relationship, when plastid 1
Displacement when being in wave crest, the displacement of plastid 2 is also at wave crest, it is seen then that the displacement of plastid 1 and plastid 2 is in the same direction in the x direction
Movement, relative displacement are cancelled out each other.This result is consistent with Numerical results.
(b) opposite ω0Subresonance state (region II) simulation result
Take k1=8000kN/m, k2=100kN/m, zx=0.77, system is in region II, relative to natural frequency ω0's
Subresonance state.In the following, between phase difference of the system in the stable state of region II the revolving speed of motor, vibration excitor, plastid 1 and 2
Displacement is analyzed.As time increases, in preceding 20s, system has quickly reached synchronous and has stablized, and after to interference, is
System is still able to keep stablizing.
As the curve in Fig. 8 be in stable state in the short time each motor synchronous rotational speed be basically stable at 750r/min~
Data when within the scope of 800r/min are drawn.When system is in subresonance, although exciting revolving speed is 980r/min,
When systematic steady state is run, the revolving speed of each motor is respectively less than exciting revolving speed.
As Fig. 8 (a) (b) (c) indicates the stable phase potential difference curve of system in the II of region, it can be seen that steady before and after interference
Phase bit difference is constant, and system is in stable state at this time.
Such as Fig. 8 (d), the curve of displacement and the two relative displacement of plastid 1,2, preceding 20s, the displacement of plastid 1 (e) are indicated
x1Stablize in -12.5mm~12.5mm, the displacement x of plastid 22Stablize in -6.5mm~6.5mm, then the relative displacement of the two is stablized
In -19mm~19mm.At 20s and 35s to system interference after, the displacement of plastid 1 and plastid 2 is stabilized to quickly be disturbed before
State.As it can be seen that system has stronger stability.
Such as Fig. 9 (e), the displacement x of plastid 1 is clearly indicated1With the displacement x of plastid 22Between relationship, when plastid 1
Displacement when being in wave crest, the displacement of plastid 2 is in trough, it is seen then that the displacement of plastid 1 and plastid 2 is in reversed in the x direction
Movement, relative displacement are overlapped mutually.
(c) opposite ω0Super resonance state (region III) simulation result
Take k1=3000kN/m, k2=100kN/m, zxo=1.27, vibrational system is in region III, i.e., relative to intrinsic
Frequencies omega0Super resonance state.In the following, between phase difference of the system in the stable state of region III the revolving speed of motor, vibration excitor,
The displacement of plastid 1 and 2 is analyzed.As the time increases, in preceding 20s, behind system resonance area, four vibration excitors reach
It is synchronous and stable.But after being interfered, there is multifarious situation in system.
Available if the curve in Fig. 9 is the motor speed in stable state, in the operation initial stage, each motor turns
Speed quickly reaches stabilization, and for the stabilization of speed of motor 1 in 975r/min-985r/min, remaining motor is basically stable at 983r/min.
As Fig. 9 (a) (b) (c) indicates the stable phase difference of system under super resonance state, it can be seen that not by dry
Before disturbing, the stable phase potential difference of vibration excitor 1 and vibration excitor 2 is 2 α12=-180 °, the stable phase potential difference of vibration excitor 2 and vibration excitor 3 is 2
α23=0 °, vibration excitor 3 and the stable phase potential difference of vibration excitor 4 are 2 α34=180 °.I.e. when system reaches and stablizes synchronous operation,
The same-phase of vibration excitor 2 and 3,1 and 4, the antiphase of vibration excitor 1 and 2,3 and 4.It is dry to vibration excitor 2 one respectively at 20s and at 35s
After disturbing, there is gradual change in phase difference, has same situation with region I, has embodied the diversity of nonlinear system.
Such as Fig. 9 (d), the curve of displacement and the two relative displacement of plastid 1,2 (e) is indicated, pass through in incipient stage system
Cross resonance region, displacement x1With x2With higher magnitude, after about 3s, the displacement of plastid 1 and plastid 2 reaches stable.The position of plastid 1
Move x1Stablize in -2.7mm~2.7mm, the displacement x of plastid 22Stablize in -0.25mm~0.25mm, then the relative displacement of the two is steady
It is scheduled on -0.3mm~0.3mm.After interfering respectively to vibration excitor 2 at 20s and at 35s, the displacement of plastid 1 and 2 becomes 0mm,
I.e. after given interference, system has become totally stationary from small amplitude motion.
As shown in Fig. 9 (e), the displacement x for being disturbed proplastid 1 is clearly illustrated1With the displacement x of plastid 22Between pass
System, when the displacement of plastid 1 is in wave crest, the displacement of plastid 2 is then in trough, it is seen then that the displacement of plastid 1 and plastid 2 is in the side x
It is upwards in counter motion, displacement is overlapped mutually.
Embodiment 3: the sample data parameter of a vibrosieve conveyer.The present invention is not limited to this design parameter.
1 mass m of plastid1=600kg, 2 mass m of plastid2=1500kg, vibration excitor eccentric block quality m0=10kg, vibration excitor
Radius of gyration r=0.15m, the rigidity k between plastid 1,21=8000kN/m, the rigidity k between plastid 2 and ground2=
100kN/m, motor speed ω=980r/min=102.57rad/s, at this timeIt is worked at this time in intrinsic frequency
ω0Subresonance region, that is, meet stability requirement, and stable phase potential difference is 0 between each vibration excitor, plastid 1,2 is in reversed fortune
Dynamic, amplitude is maximum, in running order, realizes the purpose of remote screening conveying.It is consistent to choose four motor models, three-phase
Squirrel-cage (pole model VB-1082-W, 380V, 50Hz, 6-, Δ-connection, 0.75kw, revolving speed 980r/min, 39kg).
Claims (2)
1. a kind of parameter determination method of four machine of subresonance double mass driving vibrosieve conveyer, which is characterized in that by the vibration
Dynamic separator conveyer is converted to kinetic model are as follows: including two plastids, four vibration excitors and two groups of springs, upper and lower two parts point
It is also known as main vibrating system and vibrating isolation system；
Be rigidly connected four vibration excitors respectively on main vibrating system, is denoted as two groups of left and right respectively, every group of vibration excitor is each along spring pair
Title is distributed in plastid m1Upper and lower two sides, one group of symmetrical vibration excitor turn to opposite；Plastid m1Pass through one group of spring k1By its with
Plastid m2Connection, and the side between two plastids perpendicular to telescopic spring sets up guide plate, makes system only in the x-direction
One degree of freedom；
Vibrating isolation system plastid m2Top is connected to plastid m1, lower section passes through spring k2On the basis of being fixed on guide plate；Described swashs
The parameter determination method of vibration device and vibrational system, includes the following steps:
Step 1, the foundation of mathematical model
In vibrosieve conveyer kinetic model, two coordinate system O are established by origin of the mass center of plastid 1 and plastid 2 respectively1-
x1、O2-x2；
In generalized coordinates system, according to the kinetic energy T of system, potential energy V and energy function obtain the movement of two plastids in the x direction
The differential equation is as follows
Wherein
In formula, m1--- 1 mass of plastid；
m2--- 2 mass of plastid；
m0i--- vibration excitor i mass (i=1~4)；
R --- vibration excitor eccentricity；
k1,k2--- the direction x upper spring rigidity；
f1,f2--- damped coefficient on the direction x；
Joi--- the rotary inertia (i=1~4) of vibration excitor i；
--- the phase angle (i=1~4) of vibration excitor i；
--- the angular speed (i=1~4) of vibration excitor i；
--- the angular acceleration (i=1~4) of vibration excitor i；
All parameters of four vibration excitors in system are consistent, and take m01=m02=m03=m04=m0；Four vibration excitors it is flat
Equal phase isCorresponding phase difference is respectively 2 α1, 2 α2, 2 α3, it can obtain,
Set four eccentric rotors in stable state synchronous angular velocity as ωm0, when systematic steady state operation, two plastids are obtained in the direction x
Differential Equations of Relative Motion,
Wherein,
In formula, m is induction quality；
By formula (8), two plastids are obtained in the direction x relative motion natural frequency ω0For
The response of formula (8) is
Wherein
Obtain antiphase relative motion response amplitude λ12, it is expressed as λ12=| A12·S| (11)
Wherein
S=(η1 2+η2 2+η3 2+η4 2+2η1η2cos(2α1)+2η2η3cos(2α2)
+2η3η4cos(2α3)+2η1η3cos(2α1+2α2)+2η1η4cos(2α1+2α2+2α3)
+2η2η4cos(2α2+2α3))1/2
Step 2, derivation system synchronization conditions
Using transfer function method,
According to formula (1), can obtaining two plastids, mass matrix, stiffness matrix and characteristic equation are as follows in the x direction
In formula, M ' is mass-coupling matrix, and K ' is stiffness coupling matrix, Δ (ω2) it is characterized equation；
Enable Δ (ω2)=0, obtains
ωInvCorresponding is two plastids in the direction x antiphase relative motion intrinsic frequency, ωSaIt is two plastids in the direction x same-phase
Relative motion intrinsic frequency；
The difference of output torque is between each vibration excitor
Formula (16)~(18) are arranged, are obtained,
Wherein
WithRespectively between vibration excitor 1,2, between vibration excitor 2,3 with
And dimensionless coupling torque between vibration excitor 3,4, constraint function are as follows
In conjunction with (19), (20) and (21), the synchronization criterion for obtaining four vibration excitors are
By formula (25), (26) and (27), the absolute value of the difference for obtaining the dimensionless residual moment of two neighboring vibration excitor be less than or
Equal to the maximum value of dimensionless coupling torque；
Step 3, stability condition is derived
For four exciter system of double mass, the kinetic energy (T) and kinetic energy (V) of system are as follows,
Mean kinetic energy (E in one cycleT) and average potential energy (EV) be respectively
Wherein
The Hamilton mean effort amount (I) of system is in one cycle
Stable phase potential difference solution in two kinds of synchronous regimesCorresponding is Hamilton mean effort amount
The Hesse matrix of minimum point, the Hesse matrix normal Wishart distribution of I, I is expressed as H, obtains
Wherein
It enables,
Make the Hesse matrix normal Wishart distribution of I, meets
H1> 0, H2> 0, H3> 0 (39)
By H1, H2With H3The stabilizing power coefficient being defined as under the synchronous condition of system, formula (39) are the stability ability of system
Expression formula, when meeting formula (39), system stablize.
2. a kind of parameter determination side of four machine of subresonance double mass driving vibrosieve conveyer according to claim 1
Method, which is characterized in that during the synchronization conditions of step 2 derive, τc41maxExpression formula it is as follows:
τc41max=-(τc12max+τc23max+τc34max) (28)
It is rightSummation, and divided by 4F1Tu, obtain four vibration excitors and be averaged dimensionless loading moment, indicate
For
Four vibration excitors be averaged dimensionless loading moment constraint function it is as follows
Definition synchronizing capacity coefficient is ζij(i, j=1,2,3,4), obtains,
Synchronizing capacity coefficient is bigger, and the synchronizing capacity of system is stronger, easier to reach synchronous.
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| CN112604954A (en) * | 2020-11-27 | 2021-04-06 | 东北大学 | Double-mass four-machine frequency-doubling self-synchronous driving vibrator and parameter determination method thereof |
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| JPS60197507A (en) * | 1984-03-21 | 1985-10-07 | Rion Co Ltd | Parts supplier of vibratory type |
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