CN109499696B - A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine - Google Patents
A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine Download PDFInfo
- Publication number
- CN109499696B CN109499696B CN201811541973.0A CN201811541973A CN109499696B CN 109499696 B CN109499696 B CN 109499696B CN 201811541973 A CN201811541973 A CN 201811541973A CN 109499696 B CN109499696 B CN 109499696B
- Authority
- CN
- China
- Prior art keywords
- plastid
- follows
- vibration
- spring
- phase
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B02—CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
- B02C—CRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
- B02C17/00—Disintegrating by tumbling mills, i.e. mills having a container charged with the material to be disintegrated with or without special disintegrating members such as pebbles or balls
- B02C17/14—Mills in which the charge to be ground is turned over by movements of the container other than by rotating, e.g. by swinging, vibrating, tilting
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B02—CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
- B02C—CRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
- B02C17/00—Disintegrating by tumbling mills, i.e. mills having a container charged with the material to be disintegrated with or without special disintegrating members such as pebbles or balls
- B02C17/18—Details
- B02C17/24—Driving mechanisms
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B02—CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
- B02C—CRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
- B02C25/00—Control arrangements specially adapted for crushing or disintegrating
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- Food Science & Technology (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- Computer Hardware Design (AREA)
- General Engineering & Computer Science (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Apparatuses For Generation Of Mechanical Vibrations (AREA)
Abstract
The invention discloses a kind of parameter determination methods of multimachine driving high-frequency vibration grinding machine, which includes: 2N vibration excitor, plastid 1 and plastid 2, spring A and spring B；It is axially symmetric structure that wherein plastid 1 and plastid 2 are all central symmetry again, and plastid 1 is located at the central space of plastid 2, is connect by spring A with the inner wall of plastid 2；The axial symmetry edge of plastid 2 is connected by spring B with ground；2n vibration excitor is set in plastid 2, the rotation center of ipsilateral N number of vibration excitor is coaxial, eccentric rotor in each vibration excitor is by respective induction motor drive, it is rotated respectively around rotation axis center, rotation is all counterclockwise and revolving speed is identical, using vibration self synchronization theory, by establishing kinetic model and differential equation of motion, finding out system response, plastid relative motion, derivation synchronization conditions and stability condition.The working efficiency for improving vibrator, reduces the output of cost, and then meets the demand of large enterprise.
Description
Invention field
The invention belongs to vibration milling device technical fields, are related to a kind of parameter determination side of multimachine driving high-frequency vibration grinding machine
Method.
Background technique
Vibrating mill is using ball or stick as the Ultra-Micro Grinding Equipment of medium.Can be used for working continuously can also be used for intermittently making
Various materials are worn into thinner final products by industry.Have many advantages, such as that efficient, energy saving, saving space, product granularity are uniform, In
Ultramicro grinding occupies considerable advantage in field, is widely used.The invention belongs to the large-scale vibrating grinding machines in vibrating ball-mill.
Common large-scale vibrating grinder is identical as small vibrating grinder principle, drives using single machine, and single machine driving can produce
Raw many problems:
1. single machine drives, production capacity is low, is not able to satisfy the needs of large enterprise.
2. although the grinder of single machine driving increases single treatment amount, production efficiency, but single big vibration exciting are improved
The application of device also reduces the utilization rate of electric energy, does not meet the requirement of national energy conservation and emission reduction.
3. single vibration excitor driving, high to vibration excitor cost requirement, required cost is also high.
With constantly improve for Theory of Vibration, it is necessary to the advanced vibration principle of application designs a large-scale vibrating grinding machine,
So that it had not only been able to satisfy the needs of large enterprise but also can be reduced cost, while improving working efficiency.
Summary of the invention
The present invention is achieved through the following technical solutions:
A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine device, which includes: 2n exciting
Device (n is the integer greater than 1), plastid 1 and plastid 2, spring A and spring B；Wherein plastid 1 and plastid 2 are all that central symmetry is again
Axially symmetric structure, plastid 1 are located at the central space of plastid 2, are connect by spring A with the inner wall of plastid 2；The axial symmetry of plastid 2
Edge is connected by spring B with ground；2n vibration excitor is symmetrically set in plastid 2 along symmetrical axis direction, and ipsilateral n are swashed
Shake device rotation center it is coaxial, respectively have an eccentric rotor in each vibration excitor, eccentric rotor by respective induction motor drive,
It is rotated respectively around rotation axis center, rotation is all counterclockwise and revolving speed is identical, and self-synchronous vibration drives ball mill work
Make；The parameter determination method of two vibration excitors, includes the following steps:
Step 1, kinetic model and the system motion differential equation are established
As shown in Figure 1, establishing coordinate system as shown in the figure.2n vibration excitor is respectively around Pivot axle o1,o2Rotation；
When system remains static, rotation center is coaxial line；It is the rotation angle of multiple rotors respectively；
According to this model, the two plastids are respectively provided with 3 freedom degrees；The freedom degree of plastid 1 is by x1,y1,ψ1Indicate, plastid 2 from
By spending by x2,y2,ψ2It indicates.
According to Lagrange's equation, the differential equation of motion of system can be released
Wherein,
m0i=ηim0；Jdi=m0ir2, i=1,2；J1=Jm1；J=J1+
J2；
In formula,
M --- total system mass；
m1--- 1 mass of plastid；
m2--- 2 mass of plastid；
m0i--- vibration excitor i mass (i=1,2 ..., n)；
Joi--- the rotary inertia (i=1,2 ..., n) of vibration excitor i；
R --- vibration excitor eccentricity；
kx,ky,kψ--- the direction x, y and ψ spring rate；
fx,fy,fψ--- the direction x, y and ψ damped coefficient；
With--- d/dt and d/dt2
Step 2, the average phase responded between hypothesis eccentric rotor and the phase difference relationship for finding out vibrational system are as follows:
When vibrational system steady running, angular speed stabilizes to a constant, and expression formula is as follows:
According to the phase relation between eccentric rotor, the phase acquired between each eccentric rotor is as follows:
The response that plastid is easily acquired by transfer function method is as follows:
Wherein:
Step 3, the relative motion between two plastids
When vibrational system steady running, the displacement of plastid meets following relationship:
When stable state, since the acceleration of eccentric rotor is very small, it can ignore, in addition, f02Value be with respect to other
System parameter also seems very little, can also ignore.On the direction ψ, also due to fψ1,fψ2,fψ12Value with respect to other systems parameter
It is smaller, it is possible to assuming that fψ1≈fψ2≈fψ12.In vibrational system, general spring rigidity meets k2< < k1, kψ2< < kψ1。
In conclusion the differential equation of system can indicate as follows:
Wherein,
It enablesIt is vibrated
The Differential Equations of Relative Motion of system is as follows:
Wherein:
According to the Equation of Relative Motion with Small of system, acquiring the relative motion intrinsic frequency of vibrational system, (also known as main vibrating system is solid
Have frequency) and relative motion dynamic respond, expression formula it is as follows:
Wherein:
Step 4, synchronization conditions are derived
According to the first six differential equation in formula (1), due to mass motion differential equation left side of the equal sign portion in the x and y direction
Split-phase is same, therefore by when the first six differential equation left-hand component is write as matrix form in formula (1), can be merged into a part,
Thus their matrix form is as follows:
Wherein M is inertia coupling matrix, and K is stiffness coupling matrix, Δ (ω2) it is characterized value equation.
When eigenvalue equation being enabled to be equal to 0, i.e. Δ (ω2)=0, can be in the hope of vibrational system four on the direction x, y, ψ
Intrinsic frequency, expression formula are as follows:
In practical projects, spring rate general satisfaction k2< < k1, kψ2< < kψ1, therefore, ignore ω 'invIn k2With
And ω 'ψinvIn kψ2Afterwards, ω ' is obtainedinv≈ω0, ω 'ψinv≈ωψ0, thus it can be inferred that, ω 'invIt is two plastids in x and y
The intrinsic frequency of antiphase relative motion on direction, then ω 'saIt is then the same-phase relative motion in the x and y direction of two plastids
Intrinsic frequency.Similarly, ω 'ψinvIt is the intrinsic frequency of two plastids antiphase relative motion on the direction ψ, ω 'ψsaIt is that two plastids exist
The intrinsic frequency of same-phase relative motion on the direction ψ.
It asks single order to lead about time t the response of system in formula (5) to lead with second order, the motor being then updated in formula (1)
It is finally right on 0~2 π in balance differential equationIt quadratures and divided by 2 π, the equilibrium equation for obtaining motor is as follows:
In integral process, due to 2 αiIt varies less at steady state, is slow-changing parameters, therefore can use its Integral Mean ValueInstead of 2 αi。
Various in formula (24) is done into subtraction, obtains the difference Δ T of the output electromagnetic torque between each motor0ij, expression formula
It is as follows:
Formula (25) is converted, is obtained:
Due toMeet constraint function:
So having
Formula (28) can be described as: the difference of the dimensionless output electromagnetic torque of any two motor is less than or equal to its dimensionless coupling
The maximum value of resultant moment.
By various addition in formula (24), it is as follows to obtain the motor dimensionless load moment that is averaged:
Its constraint function is as follows:
For the synchronism of better analysis system, ζ is definedijFor the synchronism ability between motor i and j, expression formula
Are as follows:
Wherein, ζijBigger, the synchronism ability of system is stronger, and vibrational system is easier to reach synchronous.
Step 5, stability condition is derived
The kinetic energy (T) and potential energy (V) of vibrational system are as follows:
Therefore the mean kinetic energy in the vibrational system monocycle and average potential can obtain:
Wherein:
Average Hamilton actuating quantity in the monocycle of vibrational system:
Therefore the Hesse matrix H of I is as follows:
Wherein:
Stable phase potential difference solution under vibrational system synchronous regime should correspond to the minimum of average Hamilton actuating quantity, i.e. I
Hesse matrix H in the neighborhood of stable phase potential difference solution positive definite so that
H1>0,H2>0,…,H2n-1>0 (36)
Wherein:
In order to preferably analyze the stability ability of vibrational system, H is defined1i(i=1,2 ..., 2n-1) is the synchronization of system
Stability force coefficient, expression formula are as follows:
Wherein H1iBigger, the synchronism stability sexuality of vibrational system is stronger, and system is more stable.
According to formula (39) it is found that responding F in expression formula1, F2, F3, F4Value by plastid quality and rotary inertia influenced compared with
Greatly.Under normal circumstances, the rotary inertia of vibrational system is influenced by structure, and in the model, 1 mass of plastid is more concentrated,
So its rotary inertia is smaller, can be not discussed.Therefore, influence of the quality to stable state of two plastids need to be only discussed, in order to
Preferably influence of the analysis plastid quality to vibrational system stable state, it will be assumed that two plastid mass ratioes:
In order to reserve broader frequency separation in order to realizing the regulation of frequency, rlIt all should not be too large with the value of β, 0.8≤rl
≤ 1.5,0.5≤β≤0.75.
Beneficial effects of the present invention:
1) this patent drives synchronous vibration mechanism, the vibrating mill with original single vibration motor using double mass multimachine
It compares, structure is simple, low energy consumption, while more efficient.
2) this patent is driven using multimachine, and multiple vibration excitors are rotated around same rotation axis center.It is carried out on model
Innovation is applied to large-scale vibrating grinding machine closer to engineering practice more.
3) this patent application Vibration Synchronization Theory, using the synchronous working of multimachine driving realization system.The work of vibrational system
The selection section for making point should be section II, and in order to reserve broader frequency separation to realize the regulation of frequency, rl
(0.8≤r should be chosen in a certain range with the value of βl≤ 1.5,0.5≤β≤0.75).
Detailed description of the invention
Fig. 1 is that multimachine drives high-frequency vibration mill dynamics illustraton of model.
In figure: 1. plastids 1；2. plastid 2；3. spring A；4. vibration excitor；5. spring B.
Each meaning of parameters in figure:
The center of O-- whole system；
O1-- left vibration excitor rotation center；
O2-- right vibration excitor rotation center；
The phase angle vibration excitor i (i=1,2,3 ..., 2n)；
moi-- vibration excitor i mass (i=1,2,3 ..., 2n)；
R-- vibration excitor eccentricity；
m1-- 1 mass of plastid；
m2-- 2 mass of plastid；
k1-- spring A stiffness coefficient；
k2-- spring B stiffness coefficient；
l1-- two vibration excitor rotation centers are at a distance from system centre on plastid 1；
l2-- two vibration excitor rotation centers are at a distance from system centre on plastid 2；
lx1, ly1-- the radius of plastid 1；
lx2-- 2 inner wall of plastid is at a distance from system centre in x-axis；
lx3-- 2 outer wall of plastid is at a distance from system centre in x-axis；
ly2-- 2 inner wall of plastid is at a distance from system centre in y-axis；
ly3-- 2 outer wall of plastid is at a distance from system centre in y-axis；
The angle that ψ -- plastid is swung around central axis；
Fig. 2 is that the net synchronization capability of vibrational system is tried hard to；(a) β=0.5, rl=0.8；(b) β=0.5, rl=1.5；(c) β=
0.5, rl=2；(d) β=0.75, rl=0.8；(e) β=0.75, rl=1.5；(f) β=0.75, rl=2；(g) β=3, rl=
0.8；(h) β=3, rl=1.5；(i) β=3, rl=2.
Stable phase potential difference of the Fig. 3 between vibration excitor；(a) β=0.5, rl=0.8；(b) β=0.5, rl=1.5；(c) β=
0.5, rl=2；(d) β=0.75, rl=0.8；(e) β=0.75, rl=1.5；(f) β=0.75, rl=2；(g) β=3, rl=
0.8；(h) β=3, rl=1.5；(i) β=3, rl=2.
Fig. 4 is the stability ability of vibrational system；(a) β=0.5, rl=0.8；(b) β=0.5, rl=1.5；(c) β=
0.5, rl=2；(d) β=0.75, rl=0.8；(e) β=0.75, rl=1.5；(f) β=0.75, rl=2；(g) β=3, rl=
0.8；(h) β=3, rl=1.5；(i) β=3, rl=2.
Fig. 5 is the simulation result diagram in the I of region；(a) motor speed, (b) phase difference between vibration excitor 1 and 2 (c) swash
Phase difference between vibration device 2 and 3, (d) phase difference between vibration excitor 3 and 4, (e) displacement of two plastids in the x direction, (f) two
The pivot angle ψ of two plastid of displacement (g) of plastid in y-direction.
Fig. 6 is the simulation result diagram in the II of region；(a1) motor speed (true motor speed), (a2) motor speed (are repaired
Change rear motor speed), (b) phase difference between vibration excitor 1 and 2, (c) phase difference between vibration excitor 2 and 3, vibration excitor 3 (d)
And the phase difference between 4, (e) displacement of two plastids in the x direction, (f) two plastid of displacement (g) of two plastids in y-direction
Pivot angle ψ, (h) the displacement equations figure of two plastids.
Fig. 7 is the simulation result diagram in the III of region；(a) motor speed, (b) phase difference between vibration excitor 1 and 2, (c)
Phase difference between vibration excitor 2 and 3, (d) phase difference between vibration excitor 3 and 4, (e) displacement of two plastids in the x direction, (f)
The pivot angle ψ of two plastid of displacement (g) of two plastids in y-direction.
Specific embodiment
Embodiment 1:
In order to further analyze the behaviour of systems, using four machine systems as analysis object, analysis numerically is carried out to it, this
When n=2.
It is assumed that the parameter of vibrational system: k1=8000kN/m, kψ1=6400kN/rad, k2=100kN/m, kψ2=88kN/
Rad, m2=1500kG, Jm1=200kgm2,Jm2=1114.8kgm2, m0=10kG, r=0.15m, ηi=1 (i=1,2,
3,4),ξ1=0.02, ξ2=0.07, ξψ1=0.02, ξψ2=0.07.And two intrinsic frequencies thus obtained: ωψ1≈
178.9rad/s, ωψ0≈193.4rad/s.Motor type: three phase squirrel cage, 50Hz, 380V, 6 poles, 0.75kW, rated speed
980r/min.The parameter of electric machine: rotor resistance Rr=3.40 Ω, stator resistance Rs=3.35 Ω, mutual inductance Lm=164mH, inductor rotor
Lr=170mH, stator inductance Ls=170mH, damped coefficient fd1=fd2=0.05.
(a) synchronism analysis of vibrational system
As shown in Figure 2, the synchronism ability one when the uniform quality of the eccentric rotor of vibrational system, between each motor
It causes, and has ζ12=ζ23=ζ34=ζ13=ζ24=ζ14, this shows that vibrational system has broad sense dynamic symmetry characteristic.In the figure two
A main vibrating system natural frequency ω0And ωψ0The minimal point of corresponding net synchronization capability force curve, and their value is close or equal to 0, this
Illustrate that the synchronism ability of vibrational system is most weak when outer sharp frequency is close or equal to two main vibrating system intrinsic frequencies.In addition,
Consider that the value of plastid mass ratio β is constant, with rlIncrease, the peak-peak of net synchronization capability force coefficient increasing.Therefore, overall
On see, the synchronism ability of vibrational system increases with the increase of rl.Work as rlIt is constant when, with the increase of β, synchronism ability
The peak-peak of coefficient is reducing, so that the synchronism ability for being inferred to vibrational system reduces with the increase of β.
(b) stability analysis of vibrational system
In Fig. 3, according to the characteristic distributions of stable phase potential difference, it can be clearly seen that ω0It is an important cut-point, when
Sharp frequencies omega is greater than ω outside0When, there are numerous equalization points for vibrational system.Meanwhile in order to preferably divide the steady of vibrational system
Determine state region, in the figure ω1Also it is approximately used as a partitioning site, so that entire frequency separation is divided into three portions
Point, respectively correspond three kinds of vibration motion states.When outer sharp frequencies omega is less than ω1When, in vibrational system between each eccentric rotor
Phase relation and ω are greater than ω0When phase relation be consistent, all there is numerous stable phase potential difference group.In order to preferably solve
This phenomenon is released, its synchronism stability sexuality figure is given, as a result as shown in figure 4, in the figure as ω < ω1Or ω > ω0When,
H13Value be always 0, this meet nonlinear system diversity phenomenon occur condition, when the stability coefficient of system be 0 when,
There are multiple groups stable solutions for system.Work as ω > ω1, and in ω1When neighbouring, system equally exists the diversity phenomenon of nonlinear system.
As ω < ω0, and in ω0When neighbouring, there are one group of stable phase potential difference solutions for system, and have 2 α1=2 α2=2 α3=0 °.In addition, there is figure
3 can be seen that when the value of plastid mass ratio β is constant, with rlIncrease, there are the sections of one group of stable phase potential difference solution for system
Gradually reducing；If rlValue it is constant, with plastid mass ratio β increase, there are the sections of one group of stable phase potential difference solution for system
Gradually reducing.
In the II of section, there is Fig. 4 to can be seen that the stability ability of vibrational system in the area with outer sharp frequency
Increase and increases.
Analysis on synthesis obtains the vibration during actual vibration Machine Design of such similar kinetic model
The selection section of the operating point of dynamic system should be section II, and in order to reserve broader frequency separation in order to realizing the tune of frequency
Control, rlIt all should not be too large with the value of β, 0.8≤rl≤ 1.5,0.5≤β≤0.75.
Embodiment 2
In order to further analyze and verify numerical result, three groups of simulation results are given by Runge-Kutta method.Vibration
Dynamic system parameter and the parameter of electric machine have provided in embodiment 1.In the present embodiment, in order to obtain the fortune of system in different zones
Dynamic state is general by changing rigidity k1And kψ1To adjust the value of intrinsic frequency.
As shown in figure 5, rigidity k at this time1=60000kN/m, kψ1=48000kN/m, eccentric rotor quality in emulation
Than being 1, acquiring its intrinsic frequency is ω1=173.2rad/s, ω0=262.6rad/s.By Fig. 5 (a) it is found that motor it is same
Walking revolving speed is about 983r/min, i.e. ω=103rad/s, the straight line l in corresponding diagram 3 (e)1The position of (ω=37.6rad/s)
It sets.Meanwhile the interference of 2 one π/3 of motor is given in 15s.
In Fig. 5 (b) (c) (d), the stable phase angle difference between pre-eccentric rotor: 2 α is interfered1=-0.3 °, 2 α2=-
179.7 °, 2 α3=-0.3 °.Interfere the stable phase angle difference between rear eccentric rotor: 2 α1=-23 °, 2 α2=-157 °, 2 α3=-
23°.By simulation result it is found that the stable state of vibrational system is influenced by external disturbance, which meets nonlinear system
Multifarious phenomenon.In addition, the phase difference relationship between eccentric rotor always exists 2 α1+2α2=180 °, 2 α2+2α3=180 °,
The exciting force resultant force that i.e. eccentric rotor 1 and 3 generates is 0, and the exciting force resultant force that eccentric rotor 2 and 4 generates is 0, and system reaches power
Balance.The displacement curve figure shown in Fig. 5 (e) (f) is it is found that the displacement of plastid is 0 in the steady state, i.e., plastid is stationary
's.In addition, can also find that the pivot angle of two plastids is very small, can approximately think that plastid is motionless in Fig. 5 (g).
Change spring rate, k1=8000kN/m, kψ1=6400kN/m obtains the emulation in the II of region, as a result such as Fig. 6 institute
Show.And two intrinsic frequencies easily acquire: ω1=63.2rad/s, ω0=95.9rad/s.It is from Fig. 6 (a) it is found that electric in emulation
The synchronous rotational speed of machine is about 784.1r/min, i.e. ω=82.1rad/s, the straight line l in corresponding diagram 3 (e)2(ω=
Position 82.1rad/s).In simulation process, in 15s to the interference of 2 one π/3 of motor.
From Fig. 6 (b) (c) (d) as can be seen that before interference, the stable phase potential difference of system: 2 α1=0 °, 2 α2=0 °, 2 α3=
0 °, after interference, there is the fluctuation of short time in the phase difference between eccentric rotor, is then promptly restored to original state, this shows
Vibrational system is stable under the state, and motion state is not influenced by exterior interference.In Fig. 6 (e) (f), in the side x
Upwards, the amplitude of plastid 1 is about 8.1mm, and the amplitude of plastid 2 is about 9.2mm, and in y-direction, the amplitude y of plastid 1 is also about
8.1mm, the amplitude of plastid 2 are 9.2mm.In Fig. 6 (h), it can be seen that in simulations according to the displacement equations figure in emulation,
The displacement of two plastids is antiphase, amplitude superposition.Similarly, as can be seen that plastid angle of oscillation very little, can neglect in Fig. 6 (g)
Slightly.
When spring rate meets k1=3000kN/m, kψ1When=2400kN/m, the emulation of region III is obtained, result is such as
Shown in Fig. 7, in addition, can be seen that its simulation result is similar to the simulation result of region I according to image.In simulations, two connect
A natural frequency ω1=38.7rad/s, ω0=58.7rad/s.According to Fig. 7 (a) it is found that the synchronous rotational speed of two groups of emulation is about
983r/min, i.e. ω=103rad/s, the straight line l in corresponding diagram 3 (e)3The position of (ω=168.1rad/s).Simulation process
In, the interference of 2 one π/3 of motor has been given in 15s.
According to Fig. 7 (b) (c) (d), before interference, stable phase potential difference: 2 α1=-179.25 °, 2 α2=-0.75 °, 2 α3=-
179.25°；After interference, stable phase potential difference: 2 α1=159.4 °, 2 α2=20.6 °, 2 α3=159.4 °.The simulation result meets non-
The multifarious phenomenon of linear system.It can be seen that its phase difference according to the variation of phase difference and meet 2 α1+2α2=180 °, 2 α2+2
α3=180 °, exciting force caused by eccentric rotor 1 and 3 and 2 and 4 is contrary, equal in magnitude, therefore its resultant force is 0, plastid
It is similar at steady state static, displacement is as shown in Fig. 7 (e) (f).
Embodiment 3:
A kind of multimachine driving vibrating mill, is shown in Fig. 1, comprising: plastid 1, plastid 2, spring (A) 3, vibration excitor 4, spring (B)
5, plastid 2 is connected respectively to ground and plastid 1 by spring (A) 3, and multiple unbalanced rotors are mounted in plastid 2, and rotor is by feeling
Induction motor driving, the direction of rotation of vibration excitor 4 are all counterclockwise that multiple vibration excitors 4 are respectively around rotation axis center
Rotation.
Here is the sample data parameter using the wherein a high-frequency vibration grinding machine of this patent design.This patent and not only
It is limited to this design parameter.
It is assumed that the parameter of vibrational system: the rigidity k between plastid 1,21=8000kN/m, the bullet between plastid 2 and ground
Spring rigidity k2=100kN/m, 2 mass m of plastid2=1500kG, vibration excitor eccentric block quality m0=10kG, radius r=0.15m, electricity
The synchronous rotational speed of machine is about 784.1r/min, i.e. ω=82.1rad/s, can be in the hope of natural frequency ω1=63.2rad/s, ω0
=95.9rad/s.It works at this time in region II.In the x direction, the amplitude of plastid 1 is about 8.1mm, and the amplitude of plastid 2 is about
9.2mm, in y-direction, the amplitude y of plastid 1 are also about 8.1mm, and the amplitude of plastid 2 is 9.2mm.When vibrational system is in region II
Close to ω0When locating stable operation, phase difference meets 2 α1=2 α2=2 α3=0 °, so eccentric rotor generation on same plastid
Exciting force superposition, resultant direction suffered on homoplasmon is not on the contrary, the type of sports of plastid is not linear reciprocal movement at this time, and two
The displacement of plastid is antiphase.(motor type: three phase squirrel cage, 50Hz, 380V, 6 poles, 0.75kW, rated speed 980r/
min.The parameter of electric machine: rotor resistance Rr=3.40 Ω, stator resistance Rs=3.35 Ω, mutual inductance Lm=164mH, inductor rotor Lr=
170mH, stator inductance Ls=170mH, damped coefficient fd1=fd2=0.05.)
Claims (3)
1. a kind of parameter determination method of multimachine driving high-frequency vibration grinding machine device, which is characterized in that convert the vibrating mill
For kinetic model are as follows: including 2n vibration excitor, n is the integer greater than 1, plastid 1 and plastid 2, spring A and spring B；Wherein matter
Body 1 and plastid 2 all not only centered on it is symmetrical be again axially symmetric structure, plastid 1 is located at the central space of plastid 2, passes through spring A and matter
The inner wall of body 2 connects；The axial symmetry edge of plastid 2 is connected by spring B with ground；2n vibration excitor is symmetrical along symmetrical axis direction
Be set in plastid 2, the rotation center of n ipsilateral vibration excitor is coaxial, respectively there is an eccentric rotor in each vibration excitor, eccentric
Rotor is rotated by respective induction motor drive respectively around Pivot axle, and rotation is all counter clockwise direction and revolving speed phase
Together, self-synchronous vibration grinding machine works；The parameter determination method of two vibration excitors, includes the following steps:
Step 1, kinetic model and the system motion differential equation are established
Establish coordinate system: 2n vibration excitor is respectively around Pivot axle o1,o2Rotation；When system remains static, rotation
Central axis is coaxial line；It is the rotation angle of multiple eccentric rotors respectively；According to this model, the two
Plastid is respectively provided with 3 freedom degrees；The freedom degree of plastid 1 is by x1,y1,ψ1It indicates, the freedom degree of plastid 2 is by x2,y2,ψ2It indicates；
According to Lagrange's equation, the differential equation of motion of system is released
Wherein:
N=1,2 ...；M1=m1；M=M1+M2；
m0i=ηim0；Jdi=m0ir2, i=1,2；J1=Jm1；J=J1-J2；
Step 2, the response of vibrational system is found out
Average phase and phase difference relationship between eccentric rotor is as follows:
When vibrational system steady running, the angular speed of eccentric rotor stabilizes to a constant, and expression formula is as follows:
According to the phase relation between eccentric rotor, the phase acquired between each eccentric rotor is as follows:
The response that plastid is easily acquired by transfer function method is as follows:
Wherein:
c1=k1, d1=f01ωm0,
c2=kψ1, d2=fψ12ωm0,f2=fψ1ωm0
Step 3, the relative motion between two plastids
When vibrational system steady running, the displacement of plastid meets following relationship:
The differential equation of motion of system indicates as follows:
Wherein,
M′1=M1,J′1=J1,
According to the Equation of Relative Motion with Small of system, the relative motion intrinsic frequency and relative motion displacement for acquiring vibrational system are rung
It answers, expression formula is as follows:
Wherein:
Step 4, synchronization conditions are derived
Obtain the coupling matrix and characteristic equation of two plastids:
Wherein M is inertia coupling matrix, and K is stiffness coupling matrix, Δ (ω2) it is characterized value equation；
When eigenvalue equation being enabled to be equal to 0, i.e. Δ (ω2Four intrinsic frequencies of the vibrational system on the direction x, y, ψ are acquired in)=0,
Its expression formula is as follows:
ω′invIt is the intrinsic frequency of two plastids antiphase relative motion in the x and y direction, ω 'saIt is then two plastids in x and the side y
The intrinsic frequency of upward same-phase relative motion, ω 'ψinvIt is the intrinsic frequency of two plastids antiphase relative motion on the direction ψ,
ω'ψsaIt is the intrinsic frequency of two plastids same-phase relative motion on the direction ψ；
The equilibrium equation for obtaining induction conductivity is as follows:
In integral process, due to 2 αiIt varies less at steady state, is slow-changing parameters, takes its Integral Mean ValueInstead of 2
αi；
Various in formula (24) is subtracted each other, the difference Δ T of the output electromagnetic torque between each induction conductivity is obtained0ij, expression formula
It is as follows:
Due toMeet constraint function:
So having
Then
Formula (28) description are as follows: the difference of the dimensionless output electromagnetic torque of any two induction conductivity is less than or equal to its dimensionless coupling
The maximum value of resultant moment；
Step 5, stability condition is derived
The kinetic energy T and potential energy V of vibrational system are as follows:
Average Hamilton actuating quantity in the monocycle of vibrational system:
The Hesse matrix H of I is as follows:
Wherein:
The Hesse matrix H of I positive definite in the neighborhood of stable phase potential difference solution, it may be assumed that
H1> 0, H2> 0 ..., H2n-1> 0 (33)
Wherein:
Define H1i(i=1,2 ..., 2n-1) is the stability of synchronization capacity factor of system, and expression formula is as follows:
Wherein H1iBigger, the synchronism stability sexuality of vibrational system is stronger, and system is more stable.
2. a kind of parameter determination method of multimachine driving high-frequency vibration grinding machine device according to claim 1, feature exist
In it is as follows to obtain the induction conductivity dimensionless load moment that is averaged by various addition in formula (24):
Its constraint function is as follows:
Define ζijFor the synchronism ability between induction conductivity i and j, expression formula are as follows:
Wherein, ζijBigger, the synchronism ability of system is stronger, and vibrational system is easier to reach synchronous.
3. a kind of parameter determination method of multimachine driving high-frequency vibration grinding machine device according to claim 1 or 2, feature
It is, two plastid mass ratioes:
0.8≤rl≤ 1.5,0.5≤β≤0.75.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811541973.0A CN109499696B (en) | 2018-12-17 | 2018-12-17 | A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811541973.0A CN109499696B (en) | 2018-12-17 | 2018-12-17 | A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109499696A CN109499696A (en) | 2019-03-22 |
| CN109499696B true CN109499696B (en) | 2019-11-08 |
Family
ID=65752741
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811541973.0A Active CN109499696B (en) | 2018-12-17 | 2018-12-17 | A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109499696B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112620101B (en) * | 2020-11-27 | 2021-11-02 | 东北大学 | Single-mass four-machine frequency-doubling self-synchronous driving vibrator and parameter determination method thereof |
| CN113032924B (en) * | 2021-03-24 | 2023-10-20 | 东北大学 | Single-body composite synchronous driving vibrator and parameter determination method thereof |
| CN113111459B (en) * | 2021-04-12 | 2023-10-13 | 东北大学 | Dual-machine driving space motion vibration crusher and parameter determination method thereof |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101480629A (en) * | 2009-02-10 | 2009-07-15 | 南京工程学院 | Vibrating motor direct drive type double-mass monotubular vibrating grinding mill |
| CN204602326U (en) * | 2015-04-29 | 2015-09-02 | 北京远东加大科技发展有限公司 | Double-mass vibrating grinder |
| CN107159399A (en) * | 2017-06-12 | 2017-09-15 | 东北大学 | A kind of multimachine driving motor synchronizing self-balancing type vibrator and parameter determination method |
| CN108964091A (en) * | 2018-09-07 | 2018-12-07 | 云南电网有限责任公司 | A kind of probabilistic multi-machine power system hydrogovernor Parameters design of the consideration method of operation |
-
2018
- 2018-12-17 CN CN201811541973.0A patent/CN109499696B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101480629A (en) * | 2009-02-10 | 2009-07-15 | 南京工程学院 | Vibrating motor direct drive type double-mass monotubular vibrating grinding mill |
| CN204602326U (en) * | 2015-04-29 | 2015-09-02 | 北京远东加大科技发展有限公司 | Double-mass vibrating grinder |
| CN107159399A (en) * | 2017-06-12 | 2017-09-15 | 东北大学 | A kind of multimachine driving motor synchronizing self-balancing type vibrator and parameter determination method |
| CN108964091A (en) * | 2018-09-07 | 2018-12-07 | 云南电网有限责任公司 | A kind of probabilistic multi-machine power system hydrogovernor Parameters design of the consideration method of operation |
Non-Patent Citations (5)
| Title |
|---|
| 双机双质体振动系统的自同步运动;刘云山等;《中国工程机械学报》;20170415;第15卷(第2期);第95-98页 * |
| 双机驱动双质体近共振同步运动;刘云山等;《机械设计与研究》;20180420;第34卷(第2期);第62-64页 * |
| 双质体振动系统同步理论仿真与实验研究;余乐;《中国硕士学位论文全文数据库工程科技Ⅱ辑》;20170315(第3期);第40-75页 * |
| 双质体振动系统的动力学参数设计方法;贺斌等;《东北大学学报（自然科学版）》;20160115;第37卷(第1期);第127-132页 * |
| 多机及多机驱动振动系统同步理论的研究;张学良;《中国博士学位论文全文数据库工程科技Ⅱ辑》;20170315(第3期);第44-136页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109499696A (en) | 2019-03-22 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109499696B (en) | A kind of parameter determination method of multimachine driving high-frequency vibration grinding machine | |
| CN107252780B (en) | The parameter determination method of three machines driving double mass subresonance motor synchronizing probability equal thick screen | |
| CN109794329B (en) | Parameter determination method for double-mass four-machine driven circular motion high-frequency vibration mill | |
| CN101690929B (en) | Four-machine driven self-synchronizing vibrating screen and structural parameter determining method | |
| CN109499697B (en) | A kind of parameter determination method of three mill tubes high-frequency vibration grinding machine | |
| CN109499695B (en) | A kind of multimachine drives the parameter determination method of large-scale high-frequency vibration grinding machine | |
| CN105048913A (en) | Current compensation-based unbalance vibration control system for bearingless asynchronous motor | |
| CN109635453B (en) | Design parameter determining method of double-machine-driven high-frequency vibration ball mill | |
| CN109701697B (en) | Four-machine-driven double-mass vibration impact crusher and parameter determination method thereof | |
| CN107187810B (en) | A kind of structural parameter determining method of four machines driving self-synchronization vibration feeder | |
| Zhang et al. | Synchronization and stability of two pairs of reversed rotating exciters mounted on two different rigid frames | |
| CN109614725A (en) | A kind of compact vibration drying/cooling bed and its parameter determination method | |
| CN112620102B (en) | Double-machine double-frequency self-synchronous driving double-circular motion track vibrating screen and parameter determination method thereof | |
| Gordeev et al. | Conditions for stable synchronization of three and more motors mounted on one foundation | |
| CN109649965A (en) | A kind of parameter determination method of four machine of subresonance double mass driving vibrosieve conveyer | |
| Fang et al. | Self-synchronization and vibration isolation theories in anti-resonance system with dual-motor and double-frequency actuation | |
| CN109649964B (en) | Parameter determination method for three-machine-driven sub-resonance self-synchronizing vibrating conveyor device | |
| CN113032924B (en) | Single-body composite synchronous driving vibrator and parameter determination method thereof | |
| Zhang et al. | Theoretical and numerical studies on vibratory synchronization transmission of a vibrating mechanical system driven by single motor considering sliding dry friction | |
| CN105071733A (en) | Bearing-free rotor radial displacement separation control and integrated compensation method | |
| Zhang et al. | Stability characteristics of a vibrating system with double rigid frames driven by four co-rotating coupling vibrators | |
| CN110918202A (en) | Frequency-doubling synchronous vibration grinding device based on planar multi-machine driving and parameter determination method | |
| Wang et al. | Dynamic characteristics analysis of a novel vibrating screen based on electromechanical coupling simulation | |
| CN113158365B (en) | Single-machine-driven pendulum linear motion vibrator and parameter determination method thereof | |
| CN116984219A (en) | Four-machine homodromous driving self-balancing vibrating machine and parameter determination method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |