Internal drive self-synchronous vibration machine and parameter determination method

Abstract

The application belongs to the technical field of vibration devices, and discloses an internal drive type self-synchronous vibration machine and a parameter determination method. The internal drive type self-synchronous vibration machine motor comprises two vibration exciters, three masses and springs. The three masses are two internal masses and one external mass. The external mass is connected with the foundation through a vibration isolation spring. The internal masses are symmetrically installed in the internal masses by two groups of main vibration springs. The shaft centers of the two vibration exciters coincide with the centers of mass of the two internal masses, and each vibration exciter has an eccentric rotor. The eccentric rotors are driven by induction motors, rotate around the respective rotation axis centers, and the rotation directions of the two vibration exciters are the same. When the two vibration exciters are installed at a large distance, the phase difference of the two vibration exciters is stabilized at 0, and the center of mass trajectory is a circular trajectory, so that the energy-saving circular motion vibration function is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vibration devices, in particular to an internal drive type self-synchronous vibration machine and a parameter determination method. BACKGROUND

[0002] Vibration technology has many uses in practical engineering, for example, engineering vibration crushing and screening technology as an important technical means in industry, penetrates into non-metallic minerals, chemical raw materials, genetic engineering, new drugs and advanced ceramics and many other fields, and the performance of its products must meet the different needs of these industries. The driving device of the traditional crushing and screening equipment (CN216987799U) is usually a combination of an exciter and a flexible coupling transmission, and the cylinder containing the material to be ground and the medium is subjected to vibration impact during periodic rotation to complete the ball milling, crushing or screening process. The disadvantages are as follows:

[0003] 1. Steel, synthetic rubber, high-power motor, gear transmission parts, bearings and grinding cylinders are important materials and key components for the production and manufacture of grinding machinery equipment, and the flexible coupling and eccentric shaft etc. lead to an oversized equipment, which will increase the weight and investment cost of the equipment when facing large-scale crushing and grinding screening production.

[0004] 2. The traditional crushing and screening equipment has limitations in driving mode, which can only increase the speed by changing the type of single motor.

[0005] 3. Due to the limitation of vibration frequency and amplitude, the grinding product particles are not uniform or the screening efficiency is not high, which is difficult to meet the engineering requirements.

[0006] Therefore, it is necessary to design a high-efficiency, compact and energy-saving vibration equipment. The present application provides an internal drive type self-synchronous vibration machine and a parameter determination method. SUMMARY

[0007] In order to solve the problems in the prior art, the present application provides an internal drive type self-synchronous vibration machine and a parameter determination method.

[0008] The technical scheme of the present application is as follows: an internal drive type self-synchronous vibration machine, comprising: two exciters, three masses and springs; the three masses are two internal masses 5 and one external mass 6; the external mass 6 is connected with the foundation through symmetrically distributed vibration isolation springs 2; each internal mass 5 is symmetrically installed inside the external mass 6 through two groups of main vibration springs 1; an exciter is installed on each internal mass 5, the shaft centers of the two exciters coincide with the mass centers of the installed internal masses 5 respectively, and each exciter has an eccentric rotor; the eccentric rotors are driven by induction motors and rotate around their respective rotation axis centers, and the two exciters rotate in the same direction.

[0009] The working frequency of the exciter is between 60 rad and the first natural frequency ω n1

[0010] A parameter determination method of an end-driven self-synchronous vibration machine, comprising the following steps:

[0011] Step 1, establishing a dynamic model and a system motion differential equation;

[0012] A fixed coordinate Oxy is set, and two exciters are a first exciter 3 and a second exciter 4; the rotation centers of the first exciter 3 and the second exciter 4 are o1 and o2 respectively, and the corresponding phases of the first exciter 3 and the second exciter 4 are and The entire end-driven self-synchronous vibration machine system has three degrees of freedom, which are vibration in the x direction, vibration in the y direction, and swing ψ around the respective centers of mass of the endoplasm and ectoplasm;

[0013] x, y, ψ, are selected as generalized coordinates, and the motion differential equation of the end-driven self-synchronous vibration machine system is derived based on the Lagrange equation as follows:

[0014]

[0015] wherein x1, x2, x3 are respectively horizontal direction displacements of the respective centers of mass of the two endoplasm and ectoplasm from their equilibrium positions after the start of the end-driven self-synchronous vibration machine system, y1, y2, y3 are respectively vertical direction displacements of the respective centers of mass of the two endoplasm and ectoplasm from their equilibrium positions after the start of the end-driven self-synchronous vibration machine system;

[0016] M1=m1+m 01 ,M2=m2+m 02 ,M3=m3,J1=J m1 +m 01 (r 2 +l1 2 ),J2=J m2 +m 02 (r 2 +l1 2 )

[0017] J3=J m3 ,k ψ1 =(l1 2 +r m R)k1,k ψ2 =(l1 2 +r m R)k2,

[0018] f​ψ13 = (l1 2 + r m R)f1,f ψ23 = (l1 2 + r m R)f2

[0019] where m 0i is the eccentric rotor mass of the exciter i, i = 1, 2; m s is the mass of the mass body s, s = 1, 2, 3; J is the moment of inertia of the whole system; J md is the moment of inertia of the mass body d, d = 1, 2, 3; J i is the moment of inertia of the exciter i, i = 1, 2; li is the distance from the rotation axis o i of the exciter i to the center O of the mass body; i = 1, 2; li e is the equivalent rotation radius of the system; ri i is the eccentricity of the exciter i, i = 1, 2; g is the acceleration of gravity; f p is the shaft damping coefficient of the induction motor p, p = 1, 2; Tp ep is the electromagnetic output torque of the induction motor p, p = 1, 2; kp x , kp y , kp ψ is the spring stiffness of the internally driven self-synchronous vibration machine system in the x, y and ψ directions; fx x , fy y , fy ψ is the damping coefficient of the internally driven self-synchronous vibration machine system in the x, y and ψ directions; is the first order derivative with respect to time; is the second order derivative with respect to time;

[0020] Step 2, displacement response analysis of the system;

[0021] The phases of the two exciters are expressed as their average value and the difference value 2a,

[0022]

[0023] where, and

[0024] When the square of the viscous damping coefficient of the internally driven self-synchronous vibration machine system is 0, the natural frequency of the system under the conditions of damping and no damping is equal in value; therefore, the free vibration characteristic equation of the internally driven self-synchronous vibration machine system is:

[0025]

[0026] Where M = diag(M1,M2,M3,M1,M2,M3,J1,J2,J3)

[0027]

[0028] ω n The system's natural frequency; the eccentric rotors installed on the two internal mass exciters have the same mass, the two internal masses of the system are exactly the same size and mass, and the connected springs and damping coefficients also use the same values, set m. 01 =m 02 M1 = M2, k1 = k2 and k ψ1 =k ψ2 In general engineering applications, the vibration isolation spring stiffness k3 between the external mass m3 and the foundation is much smaller than the main vibration spring stiffness k1 and k2 between the internal and external masses. Therefore, k3 and k2 are ignored. ψ3 The stiffness k3 and k of the vibration isolation spring 2 between the exomass 6 and the foundation ψ3 The natural frequency of the internally driven self-synchronizing vibratory machine system is 0, thus the natural frequency is:

[0029]

[0030] Once the motors in the internally driven self-synchronizing vibratory machine system maintain a stable operation with a specific phase relationship, the motor speed becomes a constant value, and the angular acceleration of the eccentric rotor is not considered. The effect of this is addressed by solving the first nine equations of equation (1) using the transfer function method, yielding the response as follows:

[0031]

[0032]

[0033] in,

[0034]

[0035] By superimposing the three responses of the same frequency for each degree of freedom in formulas (5)-(13), we obtain:

[0036]

[0037] in,

[0038]

[0039] A1=r[F2 sin(α+γ2)-F1 sin(α-γ1)]

[0040] B1 = r[F1 cos(a - γ1) + F2 cos(a + γ2)]

[0041] A2 = r[F1 sin(a + γ1) - F2 sin(a - γ2)]

[0042] B2 = r[F2 cos(a - γ2) + F1 cos(a + γ1)]

[0043] A3 = r[F3 sin(a + γ3) - F3 sin(a - γ3)]

[0044] B3 = r[F3 cos(a - γ3) + F3 cos(a + γ3)]

[0045] A4 = rI1[-F4 cos(a - γ4) + F5 cos(a + γ5)]

[0046] B4 = rI1[-F4 sin(a - γ4) - F5 sin(a + γ5)]

[0047] A5 = rI1[-F5 cos(a - γ5) + F4 cos(a + γ4)]

[0048] B5 = rI1[-F5 sin(a - γ5) - F4 sin(a + γ4)]

[0049] A6 = rI1[-F6 cos(a - γ6) + F6 cos(a + γ6)]

[0050] B6 = rI1[-F6 sin(a - γ6) - F6 sin(a + γ6)]

[0051] The absolute motion of the two inner bodies in the horizontal and vertical directions of the inner-driven self-synchronous vibration machine system is the result of superimposing the horizontal and vertical displacements and the swing displacement, and the swing angle of the two inner bodies around their own centers of mass is equal to the swing angle around the center of mass of the outer body, so that the absolute displacement response of each mass of the inner-driven self-synchronous vibration machine system is;

[0052]

[0053] wherein,

[0054]

[0055] Step 3, determine the synchronization and stability conditions;

[0056] synchronization condition;

[0057] When the self-synchronous vibration system reaches steady state, the average angular velocity of the two exciters is ω m0 The first and second order derivatives of x1, x2, x3, y1, y2, y3, ψ1, ψ2 and ψ3 with respect to time t in equations (4)-(12) are Substitute the above results into the last two expressions of equation (1), and in After integrating the interval, the equilibrium differential equations of the two exciters are obtained:

[0058]

[0059] where

[0060]

[0061] and are the effective loading torques of the two induction motors, and in the above integration process, Compared with the change of t, the change of 2α is smaller, so 2α is a slowly varying parameter, and its integral mean value is substituted;

[0062] Rearrange equation (17) to obtain

[0063] (T e01 -f d1 ω m0 )+(T e02 -f d2 ω m0 )=T Load (20)

[0064]

[0065] where,

[0066]

[0067] T Difference =(T e01 -f d1 ω m0 )-(T e02 -f d2 ω m0 )

[0068] T Capture =2W3T u

[0069] T Load represents the total loading torque of the two induction motors, and T Difference is the difference between the dimensionless effective electromagnetic output torques of the two induction motors, and T Captureis the frequency capture torque of the self-synchronous vibration system;

[0070] In equation (19), Therefore, the form of the synchronization criterion of the two excitators is

[0071]

[0072] Equation (20) is a dimensionless expression, which is the synchronization criterion of the self-synchronous vibration system, indicating that the absolute value of the dimensionless difference between the electromagnetic output torques of the two motors is less than their dimensionless cosine coupling coefficient; based on the nonlinear functions of and ω m0 , the synchronization solutions of the phase difference and the operating frequency of the system in the synchronization state are respectively expressed as and In addition, according to equation (19), the expression of the phase difference of the exciter is

[0073]

[0074] At this time, the synchronization ability coefficient ζ of the two excitators is defined as the ratio of the frequency capture torque to the total load torque of the two motors, that is,

[0075]

[0076] Since the two motors are the same, the relationship between the motor torques is (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 exciter has two different states, that is, and Therefore, the corresponding form of the synchronization ability coefficient of the two excitators is simplified as

[0077]

[0078] Stability condition;

[0079] In the self-synchronous vibration system of the self-synchronous vibration motor, the expressions of the kinetic energy T and the potential energy V are:

[0080]

[0081]

[0082] The Hamiltonian average action quantity I in a period is defined as I, and its expression is expressed as

[0083]

[0084] The solution of the phase difference satisfying the stability criterion in the synchronous state is called stable phase difference solution The stable phase difference value corresponds to the minimum value of the Hamiltonian average action, which means that the second derivative of I is positive definite in the neighborhood of the stable phase difference solution, that is,

[0085]

[0086] In the formula, ;

[0087]

[0088] The expression in formula (28) is the stability criterion of the two exciters, and H is defined as the stability coefficient of the two exciters; when the system is to be synchronously stable, when H>0, Otherwise,

[0089] The two exciters are the same, and according to formula (23), when H>0, It should be stably around zero, which is exactly what is expected in actual engineering; and when H<0, It is stably around π. Specifically, when H>0, It is stably in [-10°, 10°]; otherwise, It is stably in [170°, 190°].

[0090] Considering that the value of l1 may affect the synchronous stability of the system, the state of the system under different values of r l (r l =l1 / l e ) is discussed in the stability analysis in the synchronous state, wherein r l is the ratio of the exciter rotation radius l1 to the equivalent rotation radius l e of the system, and the greater the value of r l , the greater the proportion of the two exciters stably at 0°. According to the relationship between the dimensionless parameter r l , the mass parameter r m , and η: r m =m0 / M1+M2+M3,η=m2 / m1=1;0<r l <r lmax .

[0091] Advantages of the present application:

[0092] (1) In engineering, when two exciters are installed at a large distance, the circular trajectory motion of the machine body can be achieved at more working points by using double-machine self-synchronous driving in the same direction;

[0093] (2) the working range of the ball mill is in the sub-resonance zone, and energy saving can be realized;

[0094] (3) the conventional ball mill is driven by a single machine, while the ball mill is driven by double machines in a circumferential track, and the working efficiency of the ball mill is greatly improved. BRIEF DESCRIPTION OF DRAWINGS

[0095] Figure 1 It is a dynamic model diagram of the inner driving self-synchronous vibration machine system.

[0096] In the figure: 1. main vibration spring; 2. vibration isolation spring; 3. first exciter; 4. second exciter; 5. inner mass; 6. outer mass.

[0097] O1 - first exciter rotation center; O2 - second exciter rotation center; - first exciter rotation phase angle; - second exciter rotation phase angle; m 01 - first exciter mass; m 02 - second exciter mass; r - exciter i (i = 1, 2) eccentricity; k1 / 2, k2 / 2 - main vibration spring stiffness coefficient; k3 / 2 - vibration isolation spring stiffness coefficient; l1 - distance between exciter rotation center and system center;

[0098] Fig. 2 (a) is the x i amplitude amplitude-frequency response curve;

[0099] Fig. 2 (b) is the y i amplitude amplitude-frequency response curve;

[0100] Fig. 2 (c) is the ψ i amplitude amplitude-frequency response curve;

[0101] Figure 3 It is a synchronization ability coefficient;

[0102] Fig. 4 is the stability and phase difference corresponding to different r l values; r l is the ratio of the exciter rotation radius l1 to the equivalent rotation radius l e of the system;

[0103] Fig. 4 (a) is the stability coefficient when r l = 0.8;

[0104] Fig. 4 (b) is the phase difference of the first exciter and the second exciter when r l = 0.8;

[0105] Fig. 4 (c) is the stability coefficient when r l = 1.5;

[0106] Fig. 4(d) is a graph of r l = 1.5 phase difference between the first exciter and the second exciter;

[0107] Fig. 4(e) is a graph of r l = 2.0 stability coefficient;

[0108] Fig. 4(f) is a graph of r l = 2.0 phase difference between the first exciter and the second exciter;

[0109] Fig. 4(g) is a graph of different r l corresponding phase difference between the first exciter and the second exciter;

[0110] Figs. 5(a) and 5(b) are graphs of system mass displacement response and exciter interphase lag; Fig. 5(a) is a graph of r l = 1.5 corresponding mass lag angle in the x and y directions of the exciter; Fig. 5(b) is a graph of r l = 1.5 corresponding mass lag angle in the ψ direction of the exciter;

[0111] Figs. 6(a), 6(b), 6(c), 6(d), 6(e), 6(f), 6(g), 6(h), and 6(i) are simulation result graphs of region I; Fig. 6(a) is motor speed; Fig. 6(b) is phase difference between the first exciter and the second exciter; Fig. 6(c) is x direction displacement; Fig. 6(d) is an enlarged view of the x direction displacement; Fig. 6(e) is y direction displacement; Fig. 6(f) is an enlarged view of the y direction displacement; Fig. 6(g) is swing angle; Fig. 6(h) is an enlarged view of the swing angle; and Fig. 6(i) is mass motion trajectory.

[0112] Figs. 7(a), 7(b), 7(c), 7(d), 7(e), 7(f), 7(g), 7(h), and 7(i) are simulation result graphs of region II; Fig. 7(a) is motor speed; Fig. 7(b) is phase difference between the first exciter and the second exciter; Fig. 7(c) is x direction displacement; Fig. 7(d) is an enlarged view of the x direction displacement; Fig. 7(e) is y direction displacement; Fig. 7(f) is an enlarged view of the y direction displacement; Fig. 7(g) is swing angle; Fig. 7(h) is an enlarged view of the swing angle; and Fig. 7(i) is mass motion trajectory.

[0113] Fig. 8(a), Fig. 8(b), Fig. 8(c), Fig. 8(d), Fig. 8(e), Fig. 8(f), Fig. 8(g), Fig. 8(h), Fig. 8(i) are simulation results of region III; Fig. 8(a) is the motor speed; Fig. 8(b) is the phase difference of the first exciter and the second exciter; Fig. 8(c) is the x direction displacement; Fig. 8(d) is the enlarged view of the x direction displacement; Fig. 8(e) is the y direction displacement; Fig. 8(f) is the enlarged view of the y direction displacement; Fig. 8(g) is the swing angle; Fig. 8(h) is the enlarged view of the swing angle; Fig. 8(i) is the motion trajectory of the mass. DETAILED DESCRIPTION

[0114] Example 1

[0115] In order to further analyze the system characteristics, numerical analysis is carried out.

[0116] The above parameter determination method is combined with specific numerical analysis to qualitatively discuss the theoretical results. Among them, the four driving motors of the system are all selected as three-phase squirrel cage motors, and their common parameters are: rated frequency 50Hz, rated voltage 380V, pole number 6-pole, rated power 0.75kW, rated speed 980r / min, rotor resistance R r =3.40Ω, stator resistance R s =3.35Ω, stator mutual inductance L m =164mH, rotor inductance L r =170mH, stator inductance L s =170mH, shaft damping coefficient f d1 =f d2 =0.05. The main parameters of the system include: k1=k2=6000kN / m, k3=10kN / m, k ψ1 =k ψ2 =10568kN·m / rad, k ψ3 =8kN·m / rad, m1=m2=500kg, m3=3000kg, J m1 =J m2 =54kg·m 2 , J m3 =2000kg·m 2 , m 03 =2kg, f1=f ψ1 =3.83kN·s / m, f ψ3 =11.49kN·s / m, r=0.15m, l e =0.71m.

[0117] The four natural frequencies of the system are obtained by bringing the system parameters into formula (4) ω n1 =109rad / s, ω n2 =126rad / s, ωn1 = 364 rad / s, ω n4 = 383 rad / s. Considering the influence of the value of l1 on the synchronization stability of the system, the stability analysis in the synchronization state is discussed for different values of r l (r l = l1 / l e ), where r l is the ratio of the exciter revolution radius l1 to the equivalent revolution radius l e of the system. In other analyses, the value of r l = 1.5 (l1= 1.065 m) is discussed.

[0118] The amplitude-frequency characteristics of the relative motion of the two masses are considered. The amplitude-frequency response curves of the masses in the x, y and ψ directions are shown in Fig. 2, which are obtained by combining formula (16) with the stability condition of the system. According to the four natural frequencies of the system, the entire excitation frequency is divided into three regions. The difference between ω n1 and ω n2 and between ω n3 and ω n4 is very small, and the small region between the two groups of excitation frequencies is not suitable as a working point of the system, so it is ignored in the region division. Fig. 2(a) is the amplitude-frequency curve of the masses m1, m2 and m3 in the x direction. In the sub-resonance region of ω n2 , the motion amplitude of the two inner masses increases with the increase of the excitation frequency, while the motion amplitude of the outer mass changes slowly, and the system has good vibration isolation effect. In addition, the motion amplitudes of the working masses m1 and m2 in region I are the largest in the entire excitation frequency range. Corresponding to region II, the motion amplitudes of the three masses decrease slowly with the increase of the excitation frequency, and the change in region III is more gentle. Fig. 2(b) reflects the influence of the increase of the excitation frequency on the y direction amplitude. In region I, the change trend is similar to that in the x direction, and the amplitude is approximately the same. In region II, the values of the two are obviously different. As can be seen from Fig. 2(c), the two inner masses have a small swing, and the swing center is the mass center of the outer mass, so the swing angle has a more obvious influence on the y direction amplitude. At the same time, the two inner masses have a turning point in this region, which is the minimum point in region II. The reason is that this point is a balanced point influenced by the four natural frequencies of the system. After passing through this point, the y direction amplitude continues to increase with the increase of the excitation frequency and the influence of the swing angle. As shown in Fig. 2(c), in region III, the swing angle amplitude decreases with the increase of the excitation frequency, and the y direction amplitude decreases accordingly, gradually approaching the x direction amplitude.

[0119] In order to get larger relative motion amplitude, the system should be chosen in region I, only in this way, the two masses can get larger relative amplitude and the resonance effect in sub-resonance region can be used to save energy.

[0120] The analysis of the synchronization ability of the system; the synchronization of the two exciters is due to the coupling effect of the motors, so the synchronization ability coefficient ζ can be used to describe the ability of adjusting the coupling torque between the two motors to achieve synchronization. Based on the expression in equation (24), the trend of the system synchronization performance with the increase of the operating frequency is discussed here, when r l = 1.5, it reaches the minimum value again near the resonance point. The results show that the synchronization ability of the system is weak near the resonance point.

[0121] The analysis of the stability ability of the system in the synchronization state; since the external excitation of the vibration system comes from the exciters, the stable phase difference of the exciters determines the motion form of the two masses, so it is absolutely necessary to study the stable phase difference of the two exciters. In addition, according to the expressions in equations (27)-(28) and the stability criterion, the stable phase difference curves of the two exciters and the stability ability coefficient curves of the system under different rotation radii are shown in Fig. 4(g). When r l is small, the available working points of the system are less, and when it gradually increases, the phase difference is more stable near 0, and there are more available working points.

[0122] The phase lag relationship of the system in the steady state; Fig. 5 is the phase lag relationship between the displacement response of the system mass and the exciter. The phase lag curves of γ i (i = 1, 2...6) are obtained by combining equations (5)-(13) with the synchronization stability criterion. Figs. 5(a) and (b) are the displacement response lag angles of the three masses in the x and y directions and the ψ direction, respectively. In Fig. 5(a) region I, γ1, γ2, γ3 slowly increase with the increase of ω m0 . When ω m0 approaches the resonance points ω n1 and ω n2 , the four curves simultaneously show resonance characteristics, γ1 and γ3 approach π / 2 at ω n1 , and γ2 and γ3 approach 3π / 2 at ω n1 and ω n2 , respectively. In region II, except for γ3, the remaining three lag curves are stable in the new equilibrium state. With the increase of ω m0 , the system reaches the over-resonance region and the super far-resonance region of ω n1 and ω n2 , and the γ1, γ2, γ3 curve regions are stable. In Fig. 5(b), region I is the sub-resonance region of the resonance frequency ω n2 , so γ4 approaches 0°, and γ6, γ5 approach π.

[0123] In region II, when ω m0 approaches ω n3 and ω n4 , γ5, γ6and γ4appear a rising trend, then after passing through ω n3 and ω n4 , γ4and γ5approach π / 2and 3π / 2respectively, reaching a new steady state in region III. γ6is the phase lag of the exciter m 01 and m 02 to the outer body in ψ direction, so the swing of m3is always lagging behind m 01 or m 02 through almost the entire excitation interval, because the resonance frequency of m3in ψ direction is much smaller than the entire excitation interval.

[0124] Example 2

[0125] To better describe the dynamic characteristics of the two exciters under the condition of frequency multiplication synchronization, Runge-Kutta program can be applied to simulate the system motion differential equation. In the stability analysis under the condition of synchronization, it can be seen from Fig. 4 that the larger the value of r l is, the more easily the phase difference of the two exciters is stabilized, so a larger value of r l is selected when analyzing the resonance region I.

[0126] Simulation results of region I;

[0127] Fig. 6 is a simulation result obtained by k1=11000kN / m, k ψ1 =25410kN·m / rad. Corresponding to ω m0≈70 rad / s. From Fig. 6, it can be seen that the angular accelerations of the four motors are different due to the different masses of the inner and outer bodies. When the motors start to work, the system works in a low frequency state, and the load torque of the motors is small and the system is symmetrical, so 2a is 0°. The rotational speeds of the two motors are relatively stable within 5 s, and the 2a is stable near 0° under the coupling torque of the system, which is consistent with the analysis of Fig. 4(f). The synchronous rotational speeds of the two motors are about 979.8 r / min. After the disturbance is added at 100 s, the system responds quickly, and the motors quickly return to the stable state due to the coupling torque, as shown in Fig. 6(a). Due to the small amplitude oscillation of the inner body, the rotational speeds of the motors 1 and 2 still return to the dynamic equilibrium. In Fig. 6(b), 2a also stabilizes near the initial phase difference of 0° after a short fluctuation. According to the trajectory in Fig. 6(i), before the disturbance, the masses of the system move in a nearly circular motion. The inner body has a large amplitude, and the outer body has a small amplitude due to the partial excitation force that can be offset and the large mass. From Figs. 6(c) and 6(e), it can be seen that the system responds quickly to the stable state after the disturbance, which has good amplitude response and vibration isolation effect in engineering applications.

[0128] Simulation results of region II;

[0129] Fig. 7 is a simulation result of k1=1000 kN / m, k ψ1 =1170 kN·m / rad. The corresponding ω m0 ≈240 rad / s. After the motors are powered for about 5 s, the motors are synchronized and stably operated, and 2a is stable at 0°, which is consistent with the results of Fig. 4(d). Due to the disturbance applied to the second exciter motor, the curve fluctuates and then recovers, which proves the strong stability of the system. At the same time, as shown in Fig. 7(g), the two inner bodies have angular oscillation, and the outer body does not.

[0130] Simulation results of region III;

[0131] Fig. 8 is a simulation result of k1=100 kN / m, k ψ1 =117 kN·m / rad. Region III is similar to region II.

Claims

1. A method of determining parameters of an internally driven self-synchronous vibration machine, characterized in that, The inner-driving self-synchronous vibration machine comprises two vibration exciters, three masses and springs; the three masses are two inner masses (5) and one outer mass (6); the outer mass (6) is connected with the foundation through symmetrically distributed vibration isolation springs (2); each inner mass (5) is symmetrically installed inside the outer mass (6) through two groups of main vibration springs (1); one vibration exciter is installed on each inner mass (5), the shaft centers of the two vibration exciters coincide with the mass centers of the installed inner masses (5) respectively, and each vibration exciter has one eccentric rotor; the eccentric rotors are driven by induction motors and rotate around their respective rotation axis centers in the same direction; The method comprises the following steps: Step 1, establishing a dynamic model and system motion differential equation; A fixed coordinate Oxy is set, and the two exciters are a first exciter (3) and a second exciter (4); the rotation centers of the first exciter (3) and the second exciter (4) are o1 and o2 respectively, and the corresponding phases of the first exciter (3) and the second exciter (4) are respectively and The entire endogenous self-synchronous vibration machine system has three degrees of freedom, which are vibration in the x direction, vibration in the y direction, and swing ψ around the respective mass centers of the endoplasm and the ectoplasm; Select x, y, ψ, The motion differential equation of the self-synchronous vibration machine system is derived as follows based on the Lagrange equation: Wherein, x1, x2, x3 are respectively the horizontal direction displacements of the mass centers of the two inner masses and the outer mass from their equilibrium positions after the inner-driving self-synchronous vibration machine system is started, and y1, y2, y3 are respectively the vertical direction displacements of the mass centers of the two inner masses and the outer mass from their equilibrium positions after the inner-driving self-synchronous vibration machine system is started; M1 = m1 + m 01 M2 = m2 + m 02 M3 = m3 + J1 = J m1 + m 01 (r 2 + l1 2 ) J2 = J m2 + m 02 (r 2 + l1 2 ) where; m 0i is the eccentric rotor mass of the exciter i, i = 1, 2; m s is the mass of the mass body, s = 1, 2, 3; J is the moment of inertia of the entire system; J md is the moment of inertia of the mass body, d = 1, 2, 3; J i is the moment of inertia of the exciter i, i = 1, 2; li is the distance from the rotation axis o i of the exciter i to the center O of the outer mass body, i = 1, 2; li e is the equivalent radius of gyration of the system; r i is the eccentricity of the exciter i, i = 1, 2; g is the acceleration of gravity; f p is the shaft damping coefficient of the induction motor p, p = 1, 2; T ep is the electromagnetic output torque of the induction motor p, p = 1, 2; k x , k y , k ψ is the spring stiffness of the internally driven self-synchronous vibration machine system in the x, y and ψ directions; f x , f y , f ψ is the damping coefficient of the internally driven self-synchronous vibration machine system in the x, y and ψ directions; is the first order derivative with respect to time; is the second order derivative with respect to time; Step 2, displacement response analysis of the system; Step 3, determining the synchronization and stability conditions; According to the parameters determined in each step, the inner-driving self-synchronous vibration machine system meeting the requirements is finally determined.

2. The internally driven self-synchronous vibration machine parameter determination method according to claim 1, characterized by, The step 2 is specifically as follows: The phases of the two exciters are represented by their average value and the difference 2a. In the formulae, and When the square of the viscous damping coefficient of the inner-driving self-synchronous vibration machine system is 0, the natural frequency of the system under the conditions of with damping and without damping is equal in value; therefore, the free vibration characteristic equation of the inner-driving self-synchronous vibration machine system is as follows: Wherein, M = diag (M1, M2, M3, M1, M2, M3, J1, J2, J3) ω n ω0is the natural frequency of the system; set m 01 = m 02 , M1= M2, k1= k2and the stiffness k3of the isolation spring (2) between the exoskeleton (6) and the ground foundation and is 0, the natural frequency of the self-synchronous vibration machine system driven by the inner drive is: When the inner-driven self-synchronous vibration machine system maintains a certain phase relationship between the motors and operates stably, the rotating speed of the motor is a constant value, and the angular acceleration of the eccentric rotor is not considered The response is obtained by solving the first nine equations of formula (1) in the transfer function method, and the response is: Wherein, After superimposing the three responses of each degree of freedom and frequency of the formula (5)-(13), the following formula is obtained: Wherein, A1 = r[F2 sin(α+γ2)-F1 sin(α-γ1)] B1 = r[F1 cos(α-γ1)+F2 cos(α+γ2)] A2 = r[F1 sin(α+γ1)-F2 sin(α-γ2)] B2 = r[F2 cos(α-γ2)+F1 cos(α+γ1)] A3 = r[F3 sin(α+γ3)-F3 sin(α-γ3)] B3 = r[F3 cos(α-γ3)+F3 cos(α+γ3)] A4 = rI1[-F4cos(α-γ4)+F5 cos(α+γ5)] B4 = rI1[-F4 sin(α-γ4)-F5 sin(α+γ5)] A5 = rI1[-F5 cos(α-γ5)+F4cos(α+γ4)] B5 = rI1[-F5 sin(α-γ5)-F4sin(α+γ4)] A6 = rI1[-F6cos(α-γ6)+F6 cos(α+γ6)] B6 = rI1[-F6sin(α-γ6)-F6 sin(α+γ6)] The absolute motion of the two inner mass centers in the horizontal and vertical directions is the result of superimposing the horizontal and vertical displacements and the swing displacement, and the swing angle of the two inner mass centers around their own mass centers is equal to the swing angle around the mass center of the outer mass, so the absolute displacement response of each mass of the self-synchronous vibration machine system is obtained as follows: wherein, 3. The internally driven self-synchronous vibration machine parameter determination method according to claim 2, characterized by, The operating frequency of the exciter is in the sub-resonance region of ω n2 .

4. The internally driven self-synchronous vibration machine parameter determination method according to claim 2, characterized by, The determination of the synchronization condition is specifically as follows: When the internally driven self-synchronous vibration machine system reaches a steady state, the average angular velocity of the two exciters is ω m0 Taking the first and second derivatives of x1, x2, x3, y1, y2, y3, ψ1, ψ2, and ψ3 with respect to time t in equations (4)-(12) gives Substituting the above results into the last two expressions of equation (1) and integrating over the interval After integrating over the interval, the equilibrium differential equations for the two excitators are obtained: In the formula, and are the effective load torques of the two induction machines, during the integration of which the variation of 2a is much smaller than the variation of t, so that the integral of 2a is replaced by its mean value The formula (17) is rearranged 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 = 2W3T u T Load T is the total load torque of the two induction machines Difference T is the difference between the dimensionless effective electromagnetic output torques of the two induction machines Capture T is the frequency capture torque of the internally driven self-synchronous vibratory machine system In formula (19), Therefore, the form of the synchronization criterion of the two excitators is: Equation (20) is a dimensionless expression, which is a synchronism criterion for the internally driven self-synchronous vibration machine system, indicating that the absolute value of the dimensionless residual electromagnetic output torque difference between the two motors is less than their dimensionless cosine coupling coefficients; based on the non-linear functions of equations (18)-(19) about and ω m0 The synchronous solutions of the system phase difference and operating frequency in the synchronous state are respectively expressed as and In addition, according to equation (19), the expression of the exciter phase difference is At this time, the synchronization ability coefficient ζ of the two exciters is defined as the ratio of the frequency capture torque to the total load torque of the two motors, that is 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 exciter has two different states, i.e. and Therefore, the corresponding form of the synchronization ability coefficient of the two exciters is simplified as:

5. The internally driven self-synchronous vibration machine parameter determination method according to claim 2, wherein, The determination of the stability condition is specifically as follows: In the self-synchronous vibration machine vibration system, the expressions of kinetic energy T and potential energy V are as follows: The average action amount of Hamilton in a period is defined as I, and the expression is as follows The solution of the phase difference that satisfies the stability criterion in the synchronous state is called the stable phase difference solution The stable phase difference value corresponds to the minimum value of the Hamiltonian mean action, which means that the second derivative of I is positive definite in the neighborhood of the stable phase difference solution, i.e. In the formula, The expression in the formula (28) is the stability criterion of the two exciters, and H is defined as the stability ability coefficient of the two exciters.

6. The internally driven self-synchronous vibration machine parameter determination method according to claim 5, wherein, When the internal drive self-synchronous vibration machine vibration system is to be synchronized and stably operated, H > 0, Otherwise, 7. The internally driven self-synchronous vibration machine parameter determination method according to claim 6, characterized by, The two exciters are identical, H > 0, Stable in [-10°, 10°]; otherwise, Stable in [170°, 190°].

8. The internally driven self-synchronous vibration machine parameter determination method according to any one of claims 1 or 3 or 4, characterized by, The ratio of the revolution radius l1 of the exciter to the equivalent revolution radius l of the system is r e The ratio of the revolution radius l1 of the exciter to the equivalent revolution radius l of the system is r l According to the relationship between the dimensionless parameter r l and the mass parameter r m and η, the relationship is: r m = m0 / M1+M2+M3, η = m2 / m1 = 1; 0 < r l < r lmax .

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