CN117181581A - Internal driving type self-synchronizing vibrator and parameter determining method - Google Patents
Internal driving type self-synchronizing vibrator and parameter determining method Download PDFInfo
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Abstract
The invention belongs to the technical field of vibration devices, and discloses an internal driving type self-synchronizing vibration machine and a parameter determining method, wherein the internal driving type self-synchronizing vibration machine comprises: two vibration exciters, three plastids and springs; the three plastids are respectively two inner plastids and one outer plastid, the outer plastids are connected with the foundation through vibration isolation springs, and the inner plastids are symmetrically arranged in the plastids through two groups of main vibration springs; the axes of the two vibration exciters are respectively overlapped with the mass centers of the two internal bodies, each vibration exciter is internally provided with an eccentric rotor, the eccentric rotors are driven by an induction motor to respectively rotate around the centers of the respective rotation axes, and the rotation directions of the two vibration exciters are the same; when the two vibration exciters are installed in a large distance, the synchronous phase difference of the two vibration exciters is stabilized at 0, and the centroid track at the moment is a circular track, so that the energy-saving circular motion vibration function of the vibration exciter is realized.
Description
Technical Field
The invention relates to the technical field of vibrating devices, in particular to an internal driving type self-synchronous vibrating machine and a parameter determining method.
Background
Vibration technology has many applications in practical engineering, for example, engineering vibration crushing screening technology is used as an important technical means in industry, and penetrates into a plurality of fields of nonmetallic minerals, chemical raw materials, genetic engineering, novel medicines, advanced ceramics and the like, and the product performance of the vibration technology needs to meet different requirements of the industries. The driving device (CN 216987799U) of the traditional crushing and screening equipment is usually driven by a vibration exciter and a flexible coupling in a matched manner, and a cylinder body filled with materials to be ground and media enables the materials to be subjected to vibration impact in the periodical rotation process, so that the ball milling, crushing or screening process is completed. The defects are as follows:
1. steel, synthetic rubber, a high-power motor, a gear transmission part, a bearing, a grinding cylinder and the like are all important materials and key parts for the production and the manufacture of mechanical equipment of the crushing mill, and the flexible coupling, the eccentric shaft and the like cause the overlarge volume of the equipment, so that the quality and the investment cost of the equipment can be increased when the equipment is produced in the face of large-scale crushing grinding screening.
2. The conventional crushing and screening device has a limitation in a driving mode, and the rotating speed can be increased only by changing the type of a single motor.
3. Due to the limitation of vibration frequency and amplitude, the particles of the ground product are uneven or the screening efficiency is low, so that the engineering requirement is difficult to meet.
Therefore, it is necessary to design a vibration apparatus that is efficient, compact and energy-saving. The invention provides an internal driving type self-synchronous vibrator and a parameter determining method.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides an internal driving type self-synchronous vibrating machine and a parameter determination method.
The technical scheme of the invention is as follows: an internally driven self-synchronizing vibrator comprising: two vibration exciters, three plastids and springs; the three plastids are respectively two inner plastids 5 and one outer plastid 6; the outer body 6 is connected with the foundation through vibration isolation springs 2 which are symmetrically distributed; each inner body 5 is symmetrically arranged inside the outer body 6 through two groups of main vibrating springs 1 respectively; the vibration exciter is respectively arranged on the inner mass body 5, the axes of the two vibration exciters are respectively overlapped with the mass center of the arranged inner mass body 5, and each vibration exciter is internally provided with an eccentric rotor; the eccentric rotors are driven by induction motors to rotate around the centers of the respective rotation axes, and the rotation directions of the two vibration exciters are the same.
The working frequency of the vibration exciter is 60rad and the first natural frequency omega n1 Between them.
A method for determining parameters of an internal driving self-synchronous vibrator comprises the following steps:
step 1, establishing a dynamic model and a system motion differential equation;
setting a fixed coordinate Oxy, wherein the two vibration exciters are a first vibration exciter 3 and a second vibration exciter 4 respectively; the rotation centers of the first vibration exciter 3 and the second vibration exciter 4 are o respectively 1 And o 2 The corresponding phases of the first vibration exciter 3 and the second vibration exciter 4 are respectively expressed asAnd->The whole internal driving type self-synchronous vibrator system has three degrees of freedom, and is divided into vibration in the x direction, vibration in the y direction and swinging psi around the respective mass centers of an inner mass body and an outer mass body;
the number of x, y, ψ,for generalized coordinates, based on Lagrange equation, the differential equation of motion of the internal driving self-synchronous vibrator system is deduced as follows:
wherein x is 1 、x 2 、x 3 After the internal driving self-synchronous vibrator system is started, the centers of mass of the two internal bodies and the external body are respectively displaced in the horizontal direction away from the balance position, y 1 、y 2 、y 3 After the internal driving self-synchronous vibrator system is started, the centers of mass of the two internal mass bodies and the external mass body are displaced in the vertical direction away from the balance position;
M 1 ＝m 1 +m 01 ,M 2 ＝m 2 +m 02 ,M 3 ＝m 3 ,J 1 ＝J m1 +m 01 (r 2 +l 1 2 ),J 2 ＝J m2 +m 02 (r 2 +l 1 2 )
wherein; m is m 0i The mass of the eccentric rotor of the vibration exciter i is i=1, 2; m is m s For mass of plastid, s=1, 2,3; j is the rotational inertia of the whole system; j (J) md D=1, 2,3, the moment of inertia of the mass; j (J) i I=1, 2, which is the moment of inertia of the exciter i; l (L) 1 Is the rotation axis o of the vibration exciter i i Distance to the centre O of the exosome, i=1, 2; l (L) e The radius of gyration is the equivalent of the system; r is (r) i The eccentricity of the vibration exciter i is i=1, 2; g is gravity acceleration; f (f) p P=1, 2, which is the axis damping coefficient of the induction motor p; t (T) ep For electromagnetic output torque of induction motor p, p=1, 2; k (k) x ,k y ,k ψ The spring stiffness of the internal driving self-synchronous vibrator system in the x, y and psi directions; f (f) x ,f y ,f ψ Damping coefficients of the internal driving type self-synchronous vibrator system in x, y and psi directions;is the time first derivative; />Is the time second derivative;
step 2, analyzing displacement response of the system;
the phases of the two vibration exciters are averagedAnd the difference value 2 alpha is indicated,
in the method, in the process of the invention,and->
When the square of the viscous damping coefficient of the internal driving type self-synchronizing vibrator system is 0, the natural frequency of the system is equal in value under the damping and undamped conditions; therefore, the free vibration characteristic equation of the internal driving self-synchronous vibrator system is as follows:
wherein m=diag (M 1 ,M 2 ,M 3 ,M 1 ,M 2 ,M 3 ,J 1 ,J 2 ,J 3 )
ω n Is the natural frequency of the system; the eccentric rotor installed on two internal mass vibration exciters has the same mass, the two internal mass of the system has the same size and mass, the connected spring and damping coefficient also have the same value, and m is set 01 ＝m 02 、M 1 ＝M 2 、k 1 ＝k 2 And k ψ1 ＝k ψ2 The method comprises the steps of carrying out a first treatment on the surface of the In engineering applications in general, exosomes m 3 Vibration isolation spring rate k with foundation 3 Is far smaller than the main vibration spring stiffness k between the inner and outer plasties 1 And k 2 Thus neglecting k 3 And k ψ3 Stiffness k of vibration isolation spring 2 between outer body 6 and ground foundation 3 And k ψ3 And the natural frequency of the obtained internal driving self-synchronous vibrator system is 0:
when the internal driving self-synchronous vibrator system keeps a specific phase relation to stably run, the rotating speed of the motor is a constant value, and the angular acceleration of the eccentric rotor is not consideredThe effect of i=1, 2, solving the first 9 equations of equation (1) by transfer function method, yields the response as:
wherein,
the three responses of the same frequency for each degree of freedom of formulas (5) - (13) are superimposed to obtain:
wherein,
A 1 ＝r[F 2 sin(α+γ 2 )-F 1 sin(α-γ 1 )]
B 1 ＝r[F 1 cos(α-γ 1 )+F 2 cos(α+γ 2 )]
A 2 ＝r[F 1 sin(α+γ 1 )-F 2 sin(α-γ 2 )]
B 2 ＝r[F 2 cos(α-γ 2 )+F 1 cos(α+γ 1 )]
A 3 ＝r[F 3 sin(α+γ 3 )-F 3 sin(α-γ 3 )]
B 3 ＝r[F 3 cos(α-γ 3 )+F 3 cos(α+γ 3 )]
A 4 ＝rl 1 [-F 4 cos(α-γ 4 )+F 5 cos(α+γ 5 )]
B 4 ＝rl 1 [-F 4 sin(α-γ 4 )-F 5 sin(α+γ 5 )]
A 5 ＝rl 1 [-F 5 cos(α-γ 5 )+F 4 cos(α+γ 4 )]
B 5 ＝rl 1 [-F 5 sin(α-γ 5 )-F 4 sin(α+γ 4 )]
A 6 ＝rl 1 [-F 6 cos(α-γ 6 )+F 6 cos(α+γ 6 )]
B 6 ＝rl 1 [-F 6 sin(α-γ 6 )-F 6 sin(α+γ 6 )]
the swinging of the two inner mass bodies around the mass center of the inner driving type self-synchronous vibrator system respectively uses the mass center of the outer mass body as a swinging center, the absolute movement of the mass centers of the two inner mass bodies in the horizontal and vertical directions is the result of superposition of horizontal displacement and vertical displacement and swinging displacement, and the swinging angle of the two inner mass bodies around the mass center of the inner mass bodies is equal to the swinging angle around the mass center of the outer mass body, so that the absolute displacement response of each mass body of the inner driving type self-synchronous vibrator system is obtained;
wherein,
step 3, determining the conditions of synchronism and stability;
a synchronicity condition;
when the internal driving self-synchronous vibrator system reaches a steady state, the average angular velocity of the two vibration exciters is omega m0 For x in formulas (4) - (12) 1 ，x 2 ，x 3 ，y 1 ，y 2 ，y 3 ，ψ 1 ，ψ 2 Sum phi 3 Obtaining first and second derivatives with respect to time tSubstituting the above result into the last two expressions of the formula (1) and at +.>After the interval integrates the two vibration exciter, a balanced differential equation of the two vibration exciters is obtained:
wherein;
and->For the effective loading moment of the two induction machines, and +.>The change in 2α is smaller than the change over time t, so 2α is a slowly varying parameter, the median +.>Replacement;
rearranging (17) to obtain
(T e01 -f d1 ω m0 )+(T e02 -f d2 ω m0 )＝T Load (20)
Wherein,
T Difference ＝(T e01 -f d1 ω m0 )-(T e02 -f d2 ω m0 )
T Capture ＝2W 3 T u
T Load representing the total loading moment of the two induction motors, T Difference Is the difference of dimensionless effective electromagnetic output torque of two induction motors, T Capture The torque is captured by the frequency of the internal driving self-synchronous vibrator system;
in the formula (19), the amino acid sequence of the compound,the form of the two exciter synchronism criteria is:
the formula (20) is a dimensionless expression, is a synchronicity criterion of an internal driving type self-synchronizing vibrator system, and shows that the absolute value of the dimensionless residual electromagnetic output torque difference between two motors is smaller than the dimensionless cosine coupling coefficient of the two motors; based on the formulae (18) - (19)And omega m0 The synchronous solution for obtaining the system phase difference and the operating frequency in the synchronous state is expressed as +.>And->Furthermore, according to formula (19), the exciter phase differenceThe expression is
At this time, the synchronization capability coefficient ζ of the two exciters is defined as the ratio of the frequency capturing torque to the total load torque of the two motors, i.e
Since the two motors are identical, the motor torque relationship (T e01 -f d1 ω m0 )-(T e02 -f d2 ω m0 ) =0; at this time, the solution of the stable phase difference of the vibration exciter has two different states, namelyAnd->Therefore, the corresponding form of the synchronization capability coefficients of the two exciters is simplified as:
stability conditions;
in the vibration system of the internal drive type self-synchronous vibrator, the expression of kinetic energy T and potential energy V is as follows:
the average motion of Hamiltonian in one period is defined as I, and then the expression is expressed as
The solution of the phase difference satisfying the stability criterion in the synchronous state is called a stable phase difference solutionThe stable phase difference value corresponds to the minimum value of the Hamiltonian average motion quantity, meaning that the second derivative of I is positive in the neighborhood of the stable phase difference solution, i.e
Wherein;
the expression in the formula (28) is the stability criterion of the two vibration exciters, and H is defined as the stability capacity coefficient of the two vibration exciters; when the system is to operate synchronously and stably, when H>At the time of 0, the temperature of the liquid,otherwise, go (L)>
The two exciters are identical, and H is known from the formula (23)>0 is thenShould stabilize around zero, which is what is expected in practical engineering; and when H<At 0, the +>Then it stabilizes around pi. Specifically, H>At 0, the +>Stable at-10 deg. and 10 deg]The method comprises the steps of carrying out a first treatment on the surface of the On the contrary, the method comprises the steps of,then stabilize at [170 DEG, 190 DEG ]]。
Taking into account l 1 The values of (2) may have an effect on the synchronisation stability of the system, so different r are discussed in the analysis of the stability in synchronisation l (r l ＝l 1 /l e ) State of the system at the value of (1), where r l Is the radius of gyration of the vibration exciter 1 Equivalent radius of rotation to the system l e Ratio of r l The larger the value of (2), the larger the ratio of the phase difference between the two exciters to be stabilized at 0 deg.. According to dimensionless parameters r l And quality parameter r m And η:r m ＝m 0 /M 1 +M 2 +M 3 ,η＝m 2 /m 1 ＝1；0<r l <r lmax 。
the invention has the beneficial effects that:
(1) In engineering, the double-machine homodromous self-synchronous driving is adopted, and when two vibration exciters are installed in a large distance, the circular track motion of the machine body can be realized at more working points;
(2) The working range of the ball mill is in a sub-resonance area, so that the energy-saving effect can be realized;
(3) The conventional ball mill is mostly driven by a single machine, and the double-machine circumferential track driving is realized, so that the working efficiency of the ball mill can be greatly improved.
Drawings
Fig. 1 is a dynamic model diagram of an internal driving self-synchronous vibrator system according to the present invention.
In the figure: 1. a main vibrating spring; 2. a vibration isolation spring; 3. a first vibration exciter; 4. a second vibration exciter; 5. an endoplasm; 6. and (3) exosomes.
O 1 -a first exciter rotation center; o (O) 2 -a second exciter rotation center;-a first exciter rotational phase angle; />-a second exciter rotational phase angle; m is m 01 -the mass of the first exciter; m is m 02 -the mass of the second exciter; r—the eccentricity of the exciter i (i=1, 2); k (k) 1 /2,k 2 2-the rate of the primary vibrating spring; k (k) 3 2-the stiffness coefficient of the vibration isolation spring; l (L) 1 -the distance of the rotation center of the exciter from the center of the system;
FIG. 2 (a) is x i Amplitude-frequency response curves;
FIG. 2 (b) is y i Amplitude-frequency response curves;
FIG. 2 (c) is ψ i Amplitude-frequency response curves;
FIG. 3 is a synchronization capability factor;
FIG. 4 different r l Stability and phase difference of the corresponding values; r is (r) l Is the radius of gyration of the vibration exciter 1 Equivalent radius of rotation to the system l e Is a ratio of (2);
FIG. 4 (a) is r l =0.8 stability coefficient;
FIG. 4 (b) is r l =0.8 phase difference of the first exciter and the second exciter;
FIG. 4 (c) is r l =1.5 stability coefficients;
FIG. 4 (d) is r l =1.5 phase difference of the first exciter and the second exciter;
FIG. 4 (e) is r l =2.0 stability coefficients;
FIG. 4 (f) is r l =2.0 phase difference of the first exciter and the second exciter;
FIG. 4 (g) shows different r l A phase difference three-dimensional diagram of the corresponding first vibration exciter and the second vibration exciter;
FIG. 5 is a graph showing the phase lag relationship between the systematic plastid displacement response and the exciter; FIG. 5 (a) is r l =1.5 corresponds to the x and y direction hysteresis angles of the mass to the exciter; FIG. 5 (b) is r l =1.5 corresponds to the ψ -directional hysteresis angle of the mass to the exciter;
FIG. 6 is a simulation result diagram of the region I; fig. 6 (a) is motor rotation speed; FIG. 6 (b) shows the phase difference between the first and second vibration exciter; FIG. 6 (c) is an x-direction displacement; FIG. 6 (d) is an enlarged view of displacement in the x direction; FIG. 6 (e) is a y-direction displacement; FIG. 6 (f) is an enlarged view of y-direction displacement; fig. 6 (g) is a swing angle; fig. 6 (h) is an enlarged view of the swing angle; fig. 6 (i) is a motion profile of a plasmid.
FIG. 7 is a simulation result diagram of region II; fig. 7 (a) is motor rotation speed; FIG. 7 (b) shows the phase difference between the first and second vibration exciter; FIG. 7 (c) is an x-direction displacement; FIG. 7 (d) is an enlarged view of displacement in the x direction; FIG. 7 (e) is a y-direction displacement; FIG. 7 (f) is an enlarged view of y-direction displacement; fig. 7 (g) is a swing angle; fig. 7 (h) is an enlarged view of the swing angle; fig. 7 (i) shows the motion trace of the plastid.
FIG. 8 is a simulation result diagram of region III; fig. 8 (a) is motor rotation speed; fig. 8 (b) shows the phase difference between the first vibration exciter and the second vibration exciter; FIG. 8 (c) is an x-direction displacement; FIG. 8 (d) is an enlarged view of displacement in the x direction; FIG. 8 (e) is a y-direction displacement; FIG. 8 (f) is an enlarged view of y-direction displacement; fig. 8 (g) is a swing angle; fig. 8 (h) is an enlarged view of the swing angle; fig. 8 (i) is a motion profile of a plasmid.
Detailed Description
Example 1
To further analyze the system characteristics, numerical analysis was performed.
The above parameter determination method is combined with specific numerical analysis to qualitatively discuss theoretical results. Wherein, four driving motors of the system are three-phase squirrel-cage motors, and the common parameters are as follows: rated frequency 50Hz, rated voltage 380V, pole pair number 6-pole, rated power 0.75kW, rated rotating speed 980R/min, rotor resistance R r =3.40Ω, stator resistance R s =3.35Ω, stator mutual inductance L m Rotor inductance l=164 mH r =170 mH, stator inductance L s =170 mH, shaft damping coefficient f d1 ＝f d2 =0.05. The system main body parameters include: k (k) 1 ＝k 2 ＝6000kN/m，k 3 ＝10kN/m，k ψ1 ＝k ψ2 ＝10568kN·m/rad，k ψ3 ＝8kN·m/rad，m 1 ＝m 2 ＝500kg，m 3 ＝3000kg，J m1 ＝J m2 ＝54kg·m 2 ，J m3 ＝2000kg·m 2 ，m 03 ＝2kg，f 1 ＝f ψ1 ＝3.83kN·s/m，f ψ3 ＝11.49kN·s/m，r＝0.15m，l e ＝0.71m。
Bringing the system parameters into equation (4) yields four natural frequencies of ω for the system n1 ＝109rad/s，ω n2 ＝126rad/s，ω n1 ＝364rad/s，ω n4 =383 rad/s. Taking into account l 1 The values of (2) may have an effect on the synchronisation stability of the system, so different r are discussed in the analysis of the stability in synchronisation l (r l ＝l 1 /l e ) State of the system at the value of (1), where r l Is the radius of gyration of the vibration exciter 1 Equivalent radius of rotation to the system l e Is a ratio of (2). In other analyses than this, all are at r l ＝1.5(l 1 =1.065 m).
The amplitude-frequency characteristic of the relative motion of the two masses is considered. Combining equation (16) with system stability conditions, the amplitude-frequency response curves of the system liposomes in the x, y and ψ directions are shown in fig. 2. The whole excitation frequency is divided into 3 regions according to four natural frequencies of the system. Natural frequency omega n1 And omega n2 Omega, omega n3 And omega n4 The difference between the two excitation frequencies is small, and a tiny area between the two groups of excitation frequencies is not suitable for being used as an operating point of a system, so that the tiny area is ignored in area division. FIG. 2 (a) is a plastid m 1 、m 2 And m 3 Amplitude-frequency curve in x direction, at ω n2 The motion amplitude of the two inner bodies is increased along with the excitation frequency, the motion amplitude of the outer bodies is changed slowly, and the system has good vibration isolation effect. In addition, in region I the working plastid, i.e. endoplasmid m 1 And m 2 Is maximum throughout the excitation frequency interval. The motion amplitude of the three plastids is slowly reduced along with the rise of the excitation frequency corresponding to the region II, and the change of the motion amplitude on the region III is more gentle. In FIG. 2 (b) the excitation is reflectedThe effect of the increase in the vibration frequency on the magnitude in the y-direction. In the region I, the variation trend is similar in the x direction, and the amplitude is similar. In the region II, the two values are obviously different, and as can be seen from fig. 2 (c), the two inner masses swing by a small amplitude, and the swing center is the centroid of the outer mass, so that the influence of the swing angle on the amplitude of the y direction of the mass is more obvious. Meanwhile, an inflection point appears in the two plastid amplitudes in the region and is a minimum value point in the region II, and the reason for the appearance is that the point is a balanced point influenced by the four natural frequencies of the system together. Through this point, the amplitude in the y-direction continuously increases with the increase in excitation frequency and the influence of the pivot angle. As shown in fig. 2 (c), in the region III, the amplitude of the oscillation angle decreases with an increase in the excitation frequency, and the amplitude in the y direction gradually approaches the amplitude in the x direction.
In order to obtain larger relative motion vibration amplitude in actual engineering, a reasonable working point of the system is selected in the region I, and only two plastids can obtain larger relative amplitude, and the energy-saving effect is achieved by utilizing the resonance effect of the sub-resonance region.
Analyzing the synchronism capability of the system; the synchronization of the two vibration exciters is derived from the coupling effect of the motors, and the synchronization capability coefficient ζ can be used for describing the capability of adjusting the coupling moment between the two motors to realize synchronization. The trend of the system synchronization performance with increasing operating frequency is discussed herein based on the expression in equation (24), when r l When=1.5, the minimum value is reached again in the vicinity of the resonance point. The results show that the synchronization capability of the system is weaker near the resonance point.
Stability capability analysis in a synchronous state; since the external excitation of the vibration system is derived from the vibration exciter, the stable phase difference of the vibration exciter determines the motion form of the two bodies, so that the research on the stable phase difference of the two vibration exciters is absolutely necessary. Furthermore, according to the expressions and stability criteria in the formulas (27) to (28), the stability phase difference curves of the two exciters at different turning radii and the stability ability coefficient curves of the system are shown in fig. 4 (g). When r is l Smaller, the system has fewer available operating points, and the phase difference is more stable near 0 when gradually increasingThere are more working points available.
The phase lag relationship of the system at steady state; FIG. 5 shows the phase lag relationship between the systematic plastid displacement response and the exciter. Obtaining gamma from formulas (5) - (13) in combination with a synchronization stability criterion i (i=1, 2..6). Fig. 5 (a) and (b) are the displacement response hysteresis angles of the three masses in the x and y directions and the ψ direction, respectively. In region I of FIG. 5 (a), with ω m0 Elevated gamma of (2) 1 、γ 2 、γ 3 Slowly increases. When omega m0 Near resonance point omega n1 And omega n2 Four curves simultaneously show resonance characteristics, gamma 1 And gamma 3 At omega n1 At approximately pi/2, gamma 2 And gamma 3 Respectively at omega n1 And omega n2 Near 3 pi/2. In region II, except gamma 3 In addition, the remaining three hysteresis curves stabilize at the new equilibrium state. With omega m0 Is increased by the system reaches omega n1 And omega n2 Is a super-resonance region and an ultra-far resonance region, gamma 1 、γ 2 、γ 3 The curve area is stable. In FIG. 5 (b), region I is the resonant frequency ω n2 And thus gamma 4 Near 0 degrees gamma 6 、γ 5 Approaching pi.
In region II, when ω m0 Near omega n3 And omega n4 When gamma is 5 、γ 6 And gamma 4 An upward trend occurs, followed by omega n3 And omega n4 When gamma is 4 And gamma 5 Approaching pi/2 and 3 pi/2, respectively, a new steady state is reached in region III. Gamma ray 6 Is a vibration exciter m 01 And m 02 Hysteresis in the direction psi with the exosomes, thus m over almost the whole excitation interval 3 Is always delayed by m 01 Or m 02 Near pi because of m 3 The resonance frequency in the psi direction is much smaller than the whole excitation interval.
Example 2
In order to better describe the dynamic characteristics of two vibration exciters under the condition of frequency doubling synchronization, a Runge-Kutta program can be applied to simulate a system motion differential equation. In the synchronous barAs can be seen in fig. 4 in the stability under the part analysis, r l The larger the value of (2), the more stable the phase difference of the two vibration exciters, so that the larger r is selected when analyzing the resonance region I l Values.
Simulation results of region I;
FIG. 6 is a graph consisting of k 1 ＝11000kN/m，k ψ1 Simulation results obtained =25410 kn·m/rad. Corresponds to ω in FIG. 4 (f) m0 And 70rad/s. As can be seen from fig. 6, after the four motors are simultaneously powered, the angular accelerations of the four motors are different due to the different masses of the vibration exciter on the inner and outer bodies. After the motor starts to work, the system works in a low-frequency state, and at the moment, the load moment of the motor is smaller, the system symmetry is good, and 2 alpha is 0 degrees. The motor rotation speed is relatively stable within 5s, and at the moment, 2 alpha is stabilized near 0 degrees under the action of the system coupling torque, which is consistent with the analysis of fig. 4 (f). The synchronous rotation speed of the two motors is about 979.8r/min, after the disturbance is added for 100s, the system responds quickly, the motors can quickly recover to a stable state due to the existence of coupling moment, and the rotation speeds of the motors 1 and 2 still recover to dynamic balance due to the small amplitude swing of the endosome as shown in fig. 6 (a). In fig. 6 (b), 2α also stabilizes around the initial phase difference of 0 ° after a short fluctuation. By combining the track figure 6 (i), the system plastids do approximate circular motion before interference, the internal plastids are large in amplitude, the external plastids can offset each other due to partial exciting force and are large in mass, the internal plastids are small in amplitude motion, the system response after interference can be quickly restored to a steady state as shown in the figure 6 (c) and the figure 6 (e), and the system response after interference has good amplitude response and vibration isolation effect in regional engineering application.
Simulation results for region II;
FIG. 7 is k 1 ＝1000kN/m，k ψ1 Simulation results of 1170kn·m/rad. Corresponds to omega in each of the map areas II in section (d) of FIG. 4 m0 And approximately 240rad/s. And (3) synchronous and stable operation is realized between the motors about 5s after the motors are powered, and 2 alpha is stabilized at 0 degrees, which is consistent with the result of fig. 4 (d). Because the motor of the second vibration exciter is interfered, the curve fluctuates and is restored immediately, and the strong stability of the system is proved. Meanwhile, as shown in fig. 7 (g), the two inner masses have angular wobbles while the outer mass does not.
Simulation results for region III;
FIG. 8 is k 1 ＝100kN/m，k ψ1 Simulation results of 117kn·m/rad. Region III region II is similar.
Claims (9)
1. An internal driving type self-synchronizing vibrator, characterized in that the internal driving type self-synchronizing vibrator comprises: two vibration exciters, three plastids and springs; the three plastids are respectively two inner plastids (5) and one outer plastid (6); the exosome (6) is connected with the foundation through vibration isolation springs (2) which are symmetrically distributed; each inner body (5) is symmetrically arranged inside the outer body (6) through two groups of main vibrating springs (1); the vibration exciter is respectively arranged on the inner body (5), the axes of the two vibration exciters are respectively overlapped with the mass center of the arranged inner body (5), and each vibration exciter is internally provided with an eccentric rotor; the eccentric rotors are driven by induction motors to rotate around the centers of the respective rotation axes, and the rotation directions of the two vibration exciters are the same.
2. The internal driving self-synchronizing vibrator according to claim 1, wherein the operating frequency of the vibration exciter is located at ω n2 Is within the sub-resonance region of (c).
3. A method for determining parameters of an internal driving self-synchronous vibrator according to claim 1 or 2, comprising the steps of:
step 1, establishing a dynamic model and a system motion differential equation;
setting a fixed coordinate Oxy, wherein the two vibration exciters are a first vibration exciter (3) and a second vibration exciter (4) respectively; the rotation centers of the first vibration exciter (3) and the second vibration exciter (4) are o respectively 1 And o 2 The corresponding phases of the first vibration exciter (3) and the second vibration exciter (4) are respectively expressed asAnd->The whole internal driving type self-synchronous vibrator system has three degrees of freedom, and is divided into vibration in the x direction, vibration in the y direction and swinging psi around the respective mass centers of an inner mass body and an outer mass body;
the number of x, y, ψ,for generalized coordinates, based on Lagrange equation, the differential equation of motion of the internal driving self-synchronous vibrator system is deduced as follows:
wherein x is 1 、x 2 、x 3 After the internal driving self-synchronous vibrator system is started, the centers of mass of the two internal bodies and the external body are respectively displaced in the horizontal direction away from the balance position, y 1 、y 2 、y 3 After the internal driving self-synchronous vibrator system is started, the centers of mass of the two internal mass bodies and the external mass body are displaced in the vertical direction away from the balance position;
M 1 ＝m 1 +m 01 ,M 2 ＝m 2 +m 02 ,M 3 ＝m 3 ,J 1 ＝J m1 +m 01 (r 2 +l 1 2 ),J 2 ＝J m2 +m 02 (r 2 +l 1 2 )
wherein; m is m 0i The mass of the eccentric rotor of the vibration exciter i is i=1, 2; m is m s For mass of plastid, s=1, 2,3; j is the rotational inertia of the whole system; j (J) md Is the moment of inertia of the mass,d＝1,2,3；J i i=1, 2, which is the moment of inertia of the exciter i; l (L) 1 Is the rotation axis o of the vibration exciter i i Distance to the centre O of the exosome, i=1, 2; l (L) e The radius of gyration is the equivalent of the system; r is (r) i The eccentricity of the vibration exciter i is i=1, 2; g is gravity acceleration; f (f) p P=1, 2, which is the axis damping coefficient of the induction motor p; t (T) ep For electromagnetic output torque of induction motor p, p=1, 2; k (k) x ,k y ,k ψ The spring stiffness of the internal driving self-synchronous vibrator system in the x, y and psi directions; f (f) x ,f y ,f ψ Damping coefficients of the internal driving type self-synchronous vibrator system in x, y and psi directions;is the time first derivative; />Is the time second derivative;
step 2, analyzing displacement response of the system;
step 3, determining the conditions of synchronism and stability;
and finally determining the internal driving type self-synchronizing vibrator system meeting the requirements according to the parameters determined in each step.
4. The method for determining parameters of an internal driving self-synchronizing vibrator according to claim 3, wherein the step 2 is specifically;
the phases of the two vibration exciters are averagedAnd the difference value 2 alpha is indicated,
in the method, in the process of the invention,and->
When the square of the viscous damping coefficient of the internal driving type self-synchronizing vibrator system is 0, the natural frequency of the system is equal in value under the damping and undamped conditions; therefore, the free vibration characteristic equation of the internal driving self-synchronous vibrator system is as follows:
wherein,
M＝diag(M 1 ,M 2 ,M 3 ,M 1 ,M 2 ,M 3 ,J 1 ,J 2 ,J 3 )
ω n is the natural frequency of the system; setting m 01 ＝m 02 、M 1 ＝M 2 、k 1 ＝k 2 Andstiffness k of vibration isolation spring (2) between outer body (6) and ground foundation 3 And k ψ3 And the natural frequency of the obtained internal driving self-synchronous vibrator system is 0:
when the internal driving self-synchronous vibrator system keeps a specific phase relation to stably run, the rotating speed of the motor is a constant value, and the angular acceleration of the eccentric rotor is not consideredSolving the first 9 equations of equation (1) by transfer function method to obtain the response:
wherein,
the three responses of the same frequency for each degree of freedom of formulas (5) - (13) are superimposed to obtain:
wherein,
A 1 ＝r[F 2 sin(α+γ 2 )-F 1 sin(α-γ 1 )]
B 1 ＝r[F 1 cos(α-γ 1 )+F 2 cos(α+γ 2 )]
A 2 ＝r[F 1 sin(α+γ 1 )-F 2 sin(α-γ 2 )]
B 2 ＝r[F 2 cos(α-γ 2 )+F 1 cos(α+γ 1 )]
A 3 ＝r[F 3 sin(α+γ 3 )-F 3 sin(α-γ 3 )]
B 3 ＝r[F 3 cos(α-γ 3 )+F 3 cos(α+γ 3 )]
A 4 ＝rl 1 [-F 4 cos(α-γ 4 )+F 5 cos(α+γ 5 )]
B 4 ＝rl 1 [-F 4 sin(α-γ 4 )-F 5 sin(α+γ 5 )]
A 5 ＝rl 1 [-F 5 cos(α-γ 5 )+F 4 cos(α+γ 4 )]
B 5 ＝rl 1 [-F 5 sin(α-γ 5 )-F 4 sin(α+γ 4 )]
A 6 ＝rl 1 [-F 6 cos(α-γ 6 )+F 6 cos(α+γ 6 )]
B 6 ＝rl 1 [-F 6 sin(α-γ 6 )-F 6 sin(α+γ 6 )]
the swinging of the two inner mass bodies around the mass center of the inner driving type self-synchronous vibrator system respectively uses the mass center of the outer mass body as a swinging center, the absolute movement of the mass centers of the two inner mass bodies in the horizontal and vertical directions is the result of superposition of horizontal displacement and vertical displacement and swinging displacement, and the swinging angle of the two inner mass bodies around the mass center of the inner mass bodies is equal to the swinging angle around the mass center of the outer mass body, so that the absolute displacement response of each mass body of the inner driving type self-synchronous vibrator system is obtained;
wherein,
5. the method for determining parameters of an internal driving self-synchronizing vibrator according to claim 4, wherein the determining synchronicity condition is specifically;
when the internal driving self-synchronous vibrator system reaches a steady state, the average angular velocity of the two vibration exciters is omega m0 For x in formulas (4) - (12) 1 ，x 2 ，x 3 ，y 1 ，y 2 ，y 3 ，ψ 1 ，ψ 2 Sum phi 3 Obtaining first and second derivatives with respect to time tSubstituting the above result into the last two expressions of the formula (1) and at +.>After the interval integrates the two vibration exciter, a balanced differential equation of the two vibration exciters is obtained:
wherein;
and->For the effective loading moment of the two induction machines, and +.>The change in 2α is smaller than the change over time t, so 2α is a slowly varying parameter, the median +.>Replacement;
rearranging (17) to obtain
(T e01 -f d1 ω m0 )+(T e02 -f d2 ω m0 )＝T Load (20)
Wherein;
T Difference ＝(T e01 -f d1 ω m0 )-(T e02 -f d2 ω m0 )
T Capture ＝2W 3 T u
T Load representing the total loading moment of the two induction motors, T Difference Is the difference of dimensionless effective electromagnetic output torque of two induction motors, T Capture The torque is captured by the frequency of the internal driving self-synchronous vibrator system;
in the formula (19), the amino acid sequence of the compound,the form of the two exciter synchronism criteria is:
the formula (20) is a dimensionless expression, is a synchronicity criterion of an internal driving type self-synchronizing vibrator system, and shows that the absolute value of the dimensionless residual electromagnetic output torque difference between two motors is smaller than the dimensionless cosine coupling coefficient of the two motors; based on the formulae (18) - (19)And omega m0 The synchronous solution for obtaining the system phase difference and the operating frequency in the synchronous state is expressed as +.>And->Furthermore, according to equation (19), the expression of the exciter phase difference is
At this time, the synchronization capability coefficient ζ of the two exciters is defined as the ratio of the frequency capturing torque to the total load torque of the two motors, i.e
Since the two motors are identical, the motor torque relationship (T e01 -f d1 ω m0 )-(T e02 -f d2 ω m0 ) =0; at this time, the solution of the stable phase difference of the vibration exciter has two different states, namelyAnd->Therefore, the corresponding form of the synchronization capability coefficients of the two exciters is simplified as:
6. the method for determining parameters of an internal driving self-synchronizing vibrator according to claim 4, wherein the determined stability condition is specifically;
in the vibration system of the internal drive type self-synchronous vibrator, the expression of kinetic energy T and potential energy V is as follows:
the average motion of Hamiltonian in one period is defined as I, and then the expression is expressed as
The solution of the phase difference satisfying the stability criterion in the synchronous state is called a stable phase difference solutionThe stable phase difference value corresponds to the minimum value of the Hamiltonian average motion quantity, meaning that the second derivative of I is positive in the neighborhood of the stable phase difference solution, i.e
Wherein;
the expression in equation (28) is the stability criterion of the two exciters, and H is defined as the stability capability coefficient of the two exciters.
7. The method for determining parameters of an internal driving type self-synchronizing vibrator according to claim 6, wherein when the vibration system of the internal driving type self-synchronizing vibrator is to be operated synchronously and stably, H>At the time of 0, the temperature of the liquid,otherwise the first set of parameters is selected,
8. the method for determining parameters of an internal driving self-synchronizing vibrator according to claim 9, wherein the two vibration exciters are identical, H>At the time of 0, the temperature of the liquid,stable at-10 deg. and 10 deg]The method comprises the steps of carrying out a first treatment on the surface of the On the contrary, let(s)>Then stabilize at [170 DEG, 190 DEG ]]。
9. The method for determining parameters of an internal driving self-synchronizing vibrator according to any of the claims 3-5, characterized in that the radius of gyration i of the exciter 1 Equivalent radius of rotation to the system l e Is r ratio of l According to dimensionless parameters r l And quality parameter r m And η:
r m ＝m 0 /M 1 +M 2 +M 3 ，η＝m 2 /m 1 ＝1；0<r l <r lmax 。
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