A method for determining parameters of a concrete vibration table based on self-synchronization of same-direction multi-machines

Abstract

The application provides a concrete vibration table parameter determination method based on a same-direction multi-machine self-synchronization, and specifically comprises the following steps: S1: obtaining kinetic energy, potential energy and a generalized force equation of the concrete vibration table according to a dynamic model of the concrete vibration table; S2: obtaining a motion differential equation of the concrete vibration table in combination with a Lagrange equation; S3: substituting an average phase angle, an angular velocity and an angular acceleration of an exciter into the motion differential equation of the concrete vibration table to obtain a dimensionless coupling equation of the concrete vibration table; S4: obtaining a synchronization condition in combination with the dimensionless coupling equation of the concrete vibration table and a limitation condition of an electromagnetic torque; and S5: obtaining a stability condition in combination with the dimensionless coupling equation of the concrete vibration table under the condition of meeting the synchronization condition. The method increases the vibration intensity of the multiple exciters in the concrete vibration table, thereby ensuring the vibration intensity of the concrete vibration table and improving the quality of the concrete prefabricated part.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of vibration devices, and particularly relates to a concrete vibration table parameter determination method based on self-synchronization of multiple machines in the same direction. BACKGROUND

[0002] The concrete vibration table is a vibration device for concrete vibration work. Through the vibration of the concrete vibration table, defects such as air bubbles in the concrete prefabricated component are removed, the purpose of vibration compaction and elimination of honeycomb surface is achieved, so as to improve the strength of the concrete prefabricated component and ensure the quality of the concrete component. Therefore, the parameters of the concrete vibration table are closely related to the quality of the concrete prefabricated component and affect the quality of the concrete prefabricated component.

[0003] However, in the prior art, in order to increase the vibration intensity of the concrete vibration table, the number of internal excitation devices of the concrete vibration table is often increased, but the coupling effect between multiple excitation devices is ignored, and multiple excitation devices are considered to be completely independent. Simply increasing the number of excitation devices cannot achieve complete superposition of excitation force, cannot increase the vibration intensity of the concrete vibration table, and on the contrary, the phenomenon of mutual cancellation of excitation force occurs, resulting in a decrease in the vibration intensity of the concrete vibration table. SUMMARY

[0004] The purpose of the present application is to provide a concrete vibration table parameter determination method based on self-synchronization of multiple machines in the same direction, so as to solve the technical problem that in the prior art, only the number of internal excitation devices of the concrete vibration table is increased, the coupling effect between multiple excitation devices is ignored, complete superposition of excitation force cannot be achieved, the vibration intensity of the concrete vibration table cannot be increased, and the vibration intensity of the concrete vibration table is reduced.

[0005] The present application provides a concrete vibration table parameter determination method based on self-synchronization of multiple machines in the same direction, which is performed according to the following steps:

[0006] S1: According to the dynamic model of the concrete vibration table, the kinetic energy, potential energy and generalized force equation of the concrete vibration table are obtained;

[0007] S2: The kinetic energy, potential energy and generalized force equation of the concrete vibration table are substituted into the Lagrange equation to obtain the motion differential equation of the concrete vibration table;

[0008] S3: The average phase angle, angular velocity and angular acceleration of the excitation device are substituted into the motion differential equation of the concrete vibration table, a dimensionless perturbation quantity is introduced and differentiated, and then a dimensionless coupling equation of the concrete vibration table is obtained;

[0009] S4: When multiple excitation devices are synchronously operated, the dimensionless coupling equation of the concrete vibration table and the limitation condition of the electromagnetic torque are combined to obtain a synchronization condition;

[0010] S5: In the case of meeting the synchronization condition, the dimensionless coupling equation of the concrete vibration table is combined again, and then the stability condition is obtained.

[0011] Further, in step S1, the kinetic energy equation of the concrete vibration table:

[0012]

[0013] wherein,

[0014] J i = m i r 2

[0015] In the formula, is the first-order derivative symbol with respect to time t; T is the kinetic energy of the vibration table; m is the mass of the vibration table; J P is the moment of inertia of the vibration table; is the velocity of the vibration table in the x direction; is the velocity of the vibration table in the y direction; is the angular velocity of the vibration table in the ψ direction; n is the total number of exciters; m i is the eccentric mass of the exciter i; is the translational velocity vector of the exciter i; J i is the moment of inertia of the exciter i; is the angular velocity of the exciter i; x i is the translational displacement vector of the exciter i; x is the displacement of the vibration table in the x direction; y is the displacement of the vibration table in the y direction; ψ is the displacement of the vibration table in the ψ direction; l i is the distance between the center of the vibration table and the rotation center of the exciter i; θ i is the position angle of the exciter i; is the phase angle of the exciter i; r is the eccentric radius of the exciter; T is the matrix transpose symbol;

[0016] The potential energy equation of the concrete vibration table:

[0017]

[0018] In the formula, U is the potential energy of the vibration table; k x , k y are the stiffnesses of the vibration table in the x direction and y direction, respectively; k ψ is the stiffness of the vibration table in the ψ direction;

[0019] The generalized force equation of the concrete vibration table:

[0020]

[0021] wherein,

[0022]

[0023]

[0024] In the formula, Q is the generalized force vector of the shaking table; c x c y These are the damping coefficients of the shaking table in the x and y directions; c ψ T is the damping coefficient in the ψ direction of the shaking table; ei It is the electromagnetic torque of exciter i; c i n is the damping coefficient of exciter i; n is the total number of exciters; n pi V is the number of pole pairs of exciter i; i R is the phase voltage of exciter i; ri ω is the rotor resistance of exciter i; si It is the synchronous electromagnetic angular velocity of exciter i; ω i R is the mechanical angular velocity of exciter i; si L is the stator resistance of exciter i; 1si L is the stator leakage inductance coefficient of exciter i; 1ri f is the rotor leakage inductance coefficient of exciter i; si is the power supply frequency of exciter i; T is the matrix transpose symbol.

[0025] Furthermore, in step S2, the equations for the kinetic energy, potential energy, and generalized force of the shaking table are substituted into the Lagrange equations to obtain the differential equations of motion for the concrete shaking table:

[0026]

[0027]

[0028]

[0029]

[0030] in,

[0031]

[0032] In the formula, The sign of the second derivative with respect to time t is M; the total mass of the shaking table is J; and the equivalent moment of inertia of the shaking table is J. It is the acceleration of the shaking table in the x-direction; It is the acceleration of the vibration table in the y-direction; It is the angular acceleration of the vibration table in the ψ direction; T is the angular acceleration of exciter i; Li It is the load torque of exciter i; le It is the equivalent radius of gyration of the shaking table.

[0033] Furthermore, in step S3, the angular velocity equation of the exciter is:

[0034]

[0035] in,

[0036] In the formula, t is time; Ω i or It is the average angular velocity of exciter i; It is the angular velocity fluctuation of exciter i; T0 is the average value of the angular velocity fluctuation of exciter i; T0 is the fluctuation period of the exciter's angular velocity.

[0037] By integrating and differentiating the angular velocity equation of the exciter, we can obtain the expressions for the phase angle and angular acceleration of the exciter:

[0038]

[0039] in,

[0040]

[0041] In the formula, t is time; It is the average phase angle of exciter i; It is the phase angle fluctuation of exciter i; α i It is a constant term of the phase angle of exciter i; or It is the average angular acceleration of exciter i; It is the angular acceleration fluctuation of exciter i; It is the average value of the phase angle fluctuation of exciter i; It is the average value of the angular acceleration fluctuation of exciter i;

[0042] Substituting the angular velocity equation, phase angle equation, and angular acceleration equation of the exciter into the last n terms of the motion differential equation of the concrete vibration table, the motion equation of the exciter is expressed as:

[0043]

[0044] The simplified differential equation of motion for the shaking table is:

[0045]

[0046]

[0047]

[0048] Introducing dimensionless momentum perturbation:

[0049]

[0050] In the formula, Ω1, Ω2, ..., Ω n These are the average angular velocities of exciters 1, 2, ..., n, respectively; Ω is the average angular velocity when multiple exciters achieve synchronization; and α1, α2, ..., αn are the average angular velocities of the exciters. n These are constant terms representing the phase angles of exciters 1, 2, ..., n. These are the average phase angles of exciters 1, 2, ..., n, respectively, β1, β2, ..., βn. n-1 These are the average phase differences between exciters 1 and 2, 2 and 3, ..., n-1 and n, ε1, ε2, ..., ε3, ε4, ε5, ε6, ε7, ε8, ε9, ε1, ε1, ε2, ε3, ε4, ε5, ε6, ε7, ε8, ε9, ε1, ε2, ε3, ε4, ε5 n ε is the dimensionless perturbation of the average angular velocity of exciters 1, 2, ..., n. n+1 ε n+2 、…、ε 2n-1 It is the dimensionless perturbation of the average phase difference between exciters 1 and 2, 2 and 3, ..., n-1 and n;

[0051] Differentiating and simplifying both sides of the dimensionless perturbation equation with respect to time t, the derivative of the average angular velocity of the exciter can be expressed in terms of the average angular velocity of multiple exciters when they are synchronized and the dimensionless perturbation:

[0052]

[0053] In the formula, n is the total number of exciters. Let ω be the derivative of the average angular velocity of exciters 1, 2, ..., n with respect to time t, and Ω be the average angular velocity of multiple exciters when they achieve synchronization. It is the dimensionless perturbation of the average angular velocity of exciters 1, 2, ..., n with respect to time t, ε1, ε2, ..., εn n It is the dimensionless perturbation of the average angular velocity of exciters 1, 2, ..., n. It is the dimensionless perturbation of the average phase difference between exciters 1 and 2, 2 and 3, ..., n-1 and n with respect to time t;

[0054] Dimensionless coupling equations:

[0055] Where A = diag(J1 / m1r) 2 J2 / m2r 2 … J n / m n r 2 1 1 … 1),

[0056] v = (v1 v2 … v) n 0 0 … 0) T ,

[0057] ε=(ε1 ε2 … ε n ε n+1 ε n+2 … ε 2n-1 ) T ,

[0058]

[0059]

[0060]

[0061] In the formula, ε is a vector of dimensionless perturbation. It is the derivative vector of the dimensionless perturbation, and matrix A is the dimensionless coupling equation. The coefficient matrix is ​​given by matrix B, which is the coefficient matrix of ε in the dimensionless coupling equation. v is the input vector of the dimensionless coupling equation, and n is the total number of exciters, v1, v2, ..., v n These are the first n input values ​​of the input vector v, ε1, ε2, ..., ε n ε is the dimensionless perturbation of the average angular velocity of exciters 1, 2, ..., n. n+1 ε n+2 、…、ε 2n-1 It is the dimensionless perturbation of the average phase difference between exciters 1 and 2, 2 and 3, ..., n-1 and n. It is the dimensionless perturbation of the average angular velocity of exciters 1, 2, ..., n with respect to time t. b is the dimensionless perturbation of the average phase difference between exciters 1 and 2, 2 and 3, ..., n-1 and n, with respect to time t. 11 b 22 ... b nn q are the first n diagonal elements of the coefficient matrix B. 11 q 12 , ..., q n2n-1 These are the coefficients before the dimensionless perturbation in the average load torque of vibrators 1, 2, ..., n, χ1, χ2, ..., χ3. n J1, J2, ..., Jn are constant terms in the average load torque of exciters 1, 2, ..., n. n These are the moments of inertia of exciters 1, 2, ..., n, c1, c2, ..., cn. n These are the damping coefficients of exciters 1, 2, ..., n, m1, m2, ..., mn. nΩ is the eccentric mass of exciters 1, 2, ..., n, Ω is the average angular velocity when multiple exciters achieve synchronization, and T is the eccentric mass of exciters 1, 2, ..., n. e1 T e2 ... T en It is the electromagnetic torque of exciters 1, 2, ..., n.

[0062] Furthermore, in step S4, the synchronicity condition for multiple exciters to achieve synchronous rotation is:

[0063]

[0064] In the formula, T eNi Ω is the rated electromagnetic torque of exciter i; Ω is the average angular velocity when multiple exciters achieve synchronization; χ i It is a constant term in the average load torque of exciter i.

[0065] Furthermore, in step S5, the stability condition for multiple exciters to achieve synchronous rotation is:

[0066] λ k =Re(D) k <0, k=1,2,…,2n-1

[0067] In the formula, matrix D is the system matrix; Re is the real part symbol; λ k It is the real part of the k-th eigenvalue of the system matrix D; n is the total number of exciters.

[0068] Compared to existing technologies, this invention provides a method for determining the parameters of a concrete shaking table based on multi-machine self-synchronization in the same direction. The vibration parameters of the concrete shaking table need to satisfy the following condition: the natural frequencies of the shaking table in the translational x and y directions are less than the natural frequency in the rotational ψ direction, i.e., ω x =ω y <ω ψ Simultaneously, the operating speeds of multiple exciters are selected to be lower than the natural frequencies of the vibration table in both the x and y directions, i.e., Ω < ω. x =ω y In this way, during concrete vibration table operation, the phase difference between multiple exciters will always be near 0°, and the excitation forces provided by multiple exciters will be completely superimposed, maximizing the resultant excitation force. This results in a large amplitude and high vibration intensity for the concrete vibration table. Furthermore, while ensuring ω... x =ω y <ω ψ Ω<ω x =ω yUnder certain conditions, reducing the rotation speed can decrease the amplitude of the concrete vibration table, while increasing the rotation speed can increase the amplitude of the concrete vibration table. The parameters can be adjusted and selected according to actual needs. This achieves the superposition of the excitation forces of multiple exciters, increases the vibration intensity of multiple exciters in the concrete vibration table, and thus ensures the vibration intensity of the concrete vibration table and the quality of the precast concrete components. Attached Figure Description

[0069] Figure 1 This is a flowchart illustrating the steps of the method for determining the parameters of a concrete vibrating table based on multi-machine self-synchronization in the same direction, as presented in this invention.

[0070] Figure 2 This is a three-dimensional view of the concrete vibration table of the present invention;

[0071] Figure 3 This is a schematic diagram of the dynamic model structure of the concrete vibration table of the present invention;

[0072] Figure 4 The power supply frequency f of this invention s Theoretical results for 10-50Hz: (a) Power supply frequency - rotational speed, (b) Rotational speed - phase difference between exciters 1 and 2, (c) Rotational speed - phase difference between exciters 2 and 3, (d) Rotational speed - phase difference between exciters 3 and 4, (e) Rotational speed - phase difference between exciters 4 and 5, (f) Rotational speed - phase difference between exciters 5 and 6, (g) Rotational speed - x-direction amplitude, (h) Rotational speed - y-direction amplitude, (i) Rotational speed - ψ-direction amplitude;

[0073] Figure 5 The power supply frequency of this invention is f s Simulation results for 30Hz: (a) Time-rotation speed, (b) Time-phase difference between exciters 1 and 2, (c) Time-phase difference between exciters 2 and 3, (d) Time-phase difference between exciters 3 and 4, (e) Time-phase difference between exciters 4 and 5, (f) Time-phase difference between exciters 5 and 6, (g) Time-displacement in the x-direction, (h) Time-displacement in the y-direction, (i) Time-displacement in the ψ-direction.

[0074] Figure 6 The power supply frequency of this invention is f s Simulation results for 45Hz: (a) Time-rotation speed, (b) Time-phase difference between exciters 1 and 2, (c) Time-phase difference between exciters 2 and 3, (d) Time-phase difference between exciters 3 and 4, (e) Time-phase difference between exciters 4 and 5, (f) Time-phase difference between exciters 5 and 6, (g) Time-displacement in the x-direction, (h) Time-displacement in the y-direction, (i) Time-displacement in the ψ-direction.

[0075] Figure 7 For the present invention l min / le =0.7~1.7, power supply frequency is f s Theoretical results for 30Hz; (a)l min / l e -phase difference, (b)l min / l e -x direction displacement, (c)l min / l e Displacement in the -y direction, (d)l min / l e -ψ direction displacement;

[0076] Figure 8 For the present invention l min / l e =0.7~1.7, power supply frequency is f s Theoretical results for 45Hz; (a)l min / l e -phase difference, (b)l min / l e -x direction displacement, (c)l min / l e Displacement in the -y direction, (d)l min / l e Displacement in the -ψ direction.

[0077] Explanation of reference numerals: 1. Vibrator; 2. Vibration table; 3. Spring; 4. Base;

[0078] Explanation of the meaning of the letter parameters in the attached diagram:

[0079] oxy is the absolute coordinate system; o is the center of mass of the vibration table; x and y are the displacements of the vibration table in the x and y directions, respectively, in mm; ψ is the displacement of the vibration table in the ψ direction, in rad.

[0080] o1, o2, o3, o4, o5, and o6 are the rotation centers of exciters 1, 2, 3, 4, 5, and 6, respectively.

[0081] l1, l2, l3, l4, l5, and l6 are the distances (in mm) between the center of the vibration table and the rotation centers of exciters 1, 2, 3, 4, 5, and 6, respectively.

[0082] m1, m2, m3, m4, m5, and m6 are the eccentric masses (kg) of exciters 1, 2, 3, 4, 5, and 6, respectively.

[0083] θ1, θ2, θ3, θ4, θ5, θ6 are the position angles (°) of exciters 1, 2, 3, 4, 5, and 6, respectively.

[0084] These are the phase angles (°) of exciters 1, 2, 3, 4, 5, and 6, respectively.

[0085] ω represents the angular velocities of exciters 1, 2, 3, 4, 5, and 6, in rad / s.

[0086] f s The power supply frequency (Hz) for exciters 1, 2, 3, 4, 5, and 6;

[0087] Ω is the average angular velocity of the six exciters when they are synchronized, in rad / s;

[0088] ω x ω y , , are the natural frequencies of the shaking table in the x and y directions, respectively, in rad / s;

[0089] β1, β2, β3, β4, and β5 are the average phase differences (°) between exciters 1 and 2, 2 and 3, 3 and 4, 4 and 5, and 5 and 6, respectively.

[0090] l e Let be the equivalent radius of gyration of the vibration table, in mm;

[0091] l min t is the minimum value among the distances l1, l2, l3, l4, l5, l6 between the center of the vibration table and the rotation centers of exciters 1, 2, 3, 4, 5, and 6, in mm; t is time, in seconds. Detailed Implementation

[0092] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. However, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. These embodiments are provided to provide a more thorough understanding of the present disclosure and to fully convey its scope to those skilled in the art. Unless otherwise specified, the techniques used in the embodiments are conventional means well known to those skilled in the art.

[0093] like Figure 1 As shown in the figure, this embodiment provides a method for determining the parameters of a concrete vibrating table based on multi-machine self-synchronization in the same direction. The steps of this method are as follows:

[0094] S1: Based on the dynamic model of the concrete shaking table, obtain the kinetic energy, potential energy, and generalized force equations of the concrete shaking table; specifically, in order to obtain the differential equations of motion of the concrete shaking table, it is necessary to establish the kinetic energy equation of the concrete shaking table:

[0095]

[0096] in,

[0097]

[0098] J i=m i r 2

[0099] In the formula, The sign is the first derivative with respect to time t; T is the kinetic energy of the shaking table, J; m is the mass of the shaking table, kg; J P It is the moment of inertia of the shaking table, kg·m 2 ; It is the velocity of the vibration table in the x-direction, in m / s; It is the velocity of the vibration table in the y-direction, in m / s; It is the angular velocity of the vibration table about the ψ-axis, in rad / s; m i It is the eccentric mass of exciter i, in kg; J is the translational velocity vector of exciter i; i It is the moment of inertia of exciter i, kg·m 2 ; x is the angular velocity of exciter i, in rad / s; i is the translational displacement vector of exciter i; x is the displacement of the vibration table in the x-direction, mm; y is the displacement of the vibration table in the y-direction, mm; ψ is the displacement of the vibration table in the ψ-direction, rad; l i θ is the distance between the center of the vibration table and the rotation center of the exciter i, in mm; i It is the position angle of exciter i, in °; is the phase angle of exciter i, °; r is the eccentric radius of the exciter, mm; T is the matrix transpose symbol.

[0100] To obtain the differential equations of motion for the concrete shaking table, it is necessary to establish the potential energy equation for the concrete shaking table:

[0101]

[0102] In the formula, U is the potential energy of the shaking table, J; k x k y These are the x- and y-direction stiffnesses of the shaking table, in kN / m; k ψ It is the stiffness of the shaking table in the ψ direction, in kN·m.

[0103] To obtain the differential equations of motion for the concrete shaking table, it is necessary to establish the generalized force equations for the concrete shaking table:

[0104]

[0105] in

[0106]

[0107]

[0108] In the formula, Q is the generalized force vector of the shaking table; c x c y These are the damping coefficients of the shaking table in the x and y directions, in N·s / m; c ψ T is the damping coefficient of the shaking table in the ψ direction, in N·m·s; ei It is the electromagnetic torque of exciter i, N·m; c i n is the damping coefficient of exciter i, in N·m·s; pi V is the number of pole pairs of exciter i; i R is the phase voltage of exciter i, V; ri The rotor resistance of exciter i is Ω; ω si ω is the synchronous electromagnetic angular velocity of exciter i, in rad / s; i R is the mechanical angular velocity of exciter i, in rad / s; si The stator resistance of exciter i is Ω; L 1si H;L is the stator leakage inductance coefficient of exciter i. 1ri H is the rotor leakage inductance coefficient of exciter i; f si It is the power supply frequency of exciter i, in Hz.

[0109] S2: Substitute the kinetic energy, potential energy, and generalized force equations of the concrete shaking table into the Lagrange equations to obtain the differential equations of motion for the concrete shaking table.

[0110] Specifically, in order to obtain the differential equations of motion for the concrete shaking table, the Lagrange equations need to be used:

[0111]

[0112] In the formula, T is the kinetic energy of the shaking table, J; U is the potential energy of the shaking table, J; Q i It is a generalized force relative to generalized coordinates; q i These are the generalized coordinates of the vibration table; t is the generalized velocity of the shaking table; t is time, in seconds.

[0113] Substituting the kinetic energy equation (1), potential energy equation (2), and generalized force equation (3) of the shaking table into equation (4), we obtain the differential equation of motion for the concrete shaking table:

[0114]

[0115] in,

[0116]

[0117] In the formula, The sign of the second derivative with respect to time t is M; the total mass of the shaking table is kg; and the equivalent moment of inertia of the shaking table is kg·m. 2 ; It is the acceleration of the shaking table in the x-direction, m / s². 2 ; It is the acceleration of the shaking table in the y-direction, m / s². 2 ; It is the angular acceleration of the vibration table in the ψ direction, in rad / s. 2 ; It is the angular acceleration of exciter i, in rad / s. 2 ;c i T is the damping coefficient of exciter i, in N·m·s; Li It is the load torque of the i-th exciter motor, N·m; e It is the equivalent radius of gyration of the vibration table, in mm.

[0118] S3: Substitute the average phase angle, angular velocity and angular acceleration of the exciter into the motion differential equation of the concrete vibration table, introduce the dimensionless perturbation and differentiate it, and then obtain the dimensionless coupling equation of the concrete vibration table.

[0119] Specifically, due to the violent vibration of the vibration table, the rotational speed fluctuation of the exciter is unavoidable. In order to obtain the synchronization and stability conditions for the synchronous rotation of the six exciters, it is necessary to obtain the dimensionless coupling equations concerning the average angular velocity Ω of the six exciters when they reach synchronization and the average phase differences β1, β2, ..., β5 between them. The latter six motion equations concerning the exciter in equation (5) are separated into equations concerning the average angular velocity Ω1, Ω2, ..., Ω6 of the exciter and the average phase angle. Slow motion equations and angular velocity fluctuations The equations of motion for rapid motion; the angular velocity of the exciter are expressed by the average angular velocity and the angular velocity fluctuation:

[0120] in:

[0121] In the formula, t is time, in seconds; Ω i or The average angular velocity of exciter i is rad / s; It is the angular velocity fluctuation of exciter i, in rad / s; Ti is the average value of the angular velocity fluctuation of exciter i, in rad / s; T0 is the fluctuation period of the exciter's angular velocity, in s.

[0122] Integrating and differentiating equation (6) respectively, we obtain the expressions for the phase angle and angular acceleration of the exciter:

[0123]

[0124] in,

[0125] In the formula, t is time, in seconds; It is the average phase angle of exciter i, in °; It is the phase angle fluctuation of exciter i, in °; α i It is a constant term of the phase angle of exciter i, in °; or It is the average angular acceleration of exciter i, in rad / s. 2 ; It is the angular acceleration fluctuation of exciter i, in rad / s. 2 ; It is the average value of the phase angle fluctuation of exciter i, in °; It is the average value of the angular acceleration fluctuation of exciter i, in rad / s. 2 .

[0126] Then, in order to obtain information about the average angular velocities Ω1, Ω2, ..., Ω6 of the exciter and the average phase angle Slow motion equations and angular velocity fluctuations Substituting equations (6) and (7) into the last six terms of equation (5) to obtain the equation of motion of the exciter, the equation of motion of the exciter is expressed as:

[0127]

[0128] In the formula, Ω i It is the average angular velocity of exciter i, in rad / s.

[0129] Because the angular velocity fluctuation of the exciter is much smaller than the average angular velocity of the exciter, the motion equation of the exciter shown in equation (8) can be decomposed into the relationship between the average angular velocities Ω1, Ω2, ..., Ω6 of the exciter and the average phase angle. Slow motion equations and angular velocity fluctuations Equations of fast motion:

[0130]

[0131]

[0132] In the formula, It is the average electromagnetic torque of exciter i, N·m; It is the average load torque of exciter i, in N·m.

[0133] From the expression for the load torque of the exciter in equation (5), it can be seen that the load torque of the exciter is closely related to the vibration response of the vibration table; in order to calculate the exciter's relationship with the average angular velocities Ω1, Ω2, ..., Ω6 and the average phase angle in equation (9), The average load torque is used to simplify the motion differential equation of the vibration table and obtain its vibration response; since the angular velocity fluctuation of the exciter is much smaller than the average angular velocity of the exciter, we can obtain:

[0134]

[0135] Substituting (11) into the first three terms of equation (5), we obtain the simplified differential equation of motion for the shaking table:

[0136]

[0137] To calculate the average load torque applied to the exciter due to the vibration of the concrete shaking table, the vibration response of the concrete shaking table in three directions is obtained according to equation (12):

[0138]

[0139] in:

[0140]

[0141] In the formula, γ xi γ is the phase angle of the vibration response in the x-direction under the action of exciter i on the shaking table, in °; yi γ is the phase angle of the vibration response in the y-direction under the action of exciter i on the shaking table, in °; ψi is the phase angle of the vibration response under the action of the exciter i in the ψ direction of the vibration table, in °; arctan is the arctangent function.

[0142] Substituting equation (13) into the load torque of the exciter and integrating it from 0 to T0, we obtain the relationship between the exciter's average angular velocities Ω1, Ω2, ..., Ω6 and the average phase angle. Average load torque:

[0143]

[0144] In the formula, The average load torque of exciter i is N·m; Ω j The average angular velocity of exciter j is rad / s; m j It is the eccentric mass of the vibrator j, in kg; γ is the average phase angle of the exciter j, in °; xj γ is the phase angle of the vibration response of the shaking table in the x-direction under the action of exciter j, in °; yjγ is the phase angle of the vibration response of the shaking table in the y-direction under the action of exciter j, in °; ψj It is the phase angle of the vibration response of the shaking table in the ψ direction under the action of the exciter j, in °; l j θ is the distance between the center of the vibration table and the rotation center of the exciter j, in mm; j It is the position angle of the exciter j, in °.

[0145] To obtain the expression for the average electromagnetic torque of the exciter in equation (9) with respect to the average angular velocities Ω1, Ω2, ..., Ω6, the electromagnetic torque of the exciter is expanded into a Taylor series at the average angular velocities Ω1, Ω2, ..., Ω6:

[0146]

[0147] Then, by discarding the higher-order terms (second order and above) concerning the angular velocity fluctuation of the exciter in equation (15) and integrating from 0 to T0, we can obtain the expression for the average electromagnetic torque of the exciter with respect to the average angular velocities Ω1, Ω2, ..., Ω6:

[0148]

[0149] In the formula, It is the average electromagnetic torque of exciter i, in N·m.

[0150] The average load torque and average electromagnetic torque of the exciter are obtained with respect to the average angular velocities Ω1, Ω2, ..., Ω6 and the average phase angle. Based on the expression, in order to obtain the dimensionless coupling equation for the average angular velocity Ω of the six exciters when they reach synchronization and the average phase differences β1, β2, ..., β5 between them, a dimensionless perturbation is introduced:

[0151]

[0152] In the formula, Ω1, Ω2, ..., Ω6 are the average angular velocities of exciters 1, 2, ..., 6, respectively, in rad / s; Ω is the average angular velocity of the six exciters when they reach synchronization, in rad / s; α1, α2, ..., α6 are constant terms representing the phase angles of exciters 1, 2, ..., 6, respectively, in degrees. ε1, ε2, ..., ε5 are the average phase angles of exciters 1, 2, ..., 6, in °; β1, β2, ..., β5 are the average phase differences between exciters 1 and 2, 2 and 3, ..., 5 and 6, in °; ε1, ε2, ..., ε6 are the dimensionless perturbations of the average angular velocities of exciters 1, 2, ..., 6, in °; ε7, ε8, ..., ε6 are the average phase angles of exciters 1, 2, ..., 6, in °; ε7, ε8, ..., ε9 are the average phase angles of exciters 1, 2, ..., 6, in °; ε1, β2, ..., β5 are the average phase differences between exciters 1 and 2, 2 and 3, ..., 5 and 6, in °; ε1, ε 11 It is the dimensionless perturbation of the average phase difference between exciters 1 and 2, 2 and 3, ..., 5 and 6.

[0153] Differentiating and simplifying both sides of equation (17) with respect to time t, the derivative of the average angular velocity of the exciter is expressed in terms of the average angular velocity and dimensionless perturbation of the six exciters when they are synchronized:

[0154]

[0155] In the formula, It is the derivative of the average angular velocity of exciters 1, 2, ..., 6 with respect to time t, in rad / s. 2 Ω is the average angular velocity (rad / s) when the six exciters achieve synchronization. Let ε1, ε2, ..., ε6 be the dimensionless perturbation of the average angular velocity of exciters 1, 2, ..., 6 with respect to time t, 1 / s. It is the dimensionless perturbation of the average phase difference between exciters 1 and 2, 2 and 3, ..., 5 and 6 with respect to time t, 1 / s.

[0156] To obtain the dimensionless coupling equation for the average angular velocity Ω of the six exciters when they reach synchronization and the average phase differences β1, β2, ..., β5 between them, equation (14) is expressed using the average angular velocity Ω of the six exciters when they reach synchronization, the average phase differences β1, β2, ..., β5 between them, and the dimensionless perturbation quantities ε1, ε2, ..., ε5. 11 Substituting equation (17) into equation (14) and discarding higher-order terms of the dimensionless perturbation, we obtain the average load torque with respect to the average angular velocity Ω of the six exciters when they are synchronized, the average phase differences β1, β2, ..., β5 between them, and the dimensionless perturbation ε1, ε2, ..., ε5. 11 The expression:

[0157] In the formula, Ω is the average load torque of exciter i, N·m; Ω is the average angular velocity of the six exciters when they reach synchronization, rad / s; ε k It is the k-th dimensionless perturbation; q ik The dimensionless perturbation ε is the average load torque of the exciter i. k The coefficient before, rad / s; χ i It is a constant term in the average load torque of exciter i, in rad / s.

[0158] In order to obtain the dimensionless coupling equation for the average angular velocity Ω of the six exciters when they are synchronized and the average phase differences β1, β2, ..., β5 between them, the expression (16) of the average electromagnetic torque of the exciter with respect to the average angular velocities Ω1, Ω2, ..., Ω6 is expanded into a Taylor series at Ω:

[0159]

[0160] In the formula, ε i It is the dimensionless perturbation of the average angular velocity of exciter i.

[0161] Discarding the higher-order terms of the dimensionless perturbation in equation (20), we obtain the expressions for the average electromagnetic torque with respect to the average angular velocity Ω and the dimensionless perturbation ε1, ε2, ..., ε6 when the six exciters achieve synchronization:

[0162]

[0163] The average angular velocity Ω when six exciters achieve synchronization, the average phase difference β1, β2, ..., β5 between them, and the dimensionless perturbation ε1, ε2, ..., ε5 are used to determine the relationship between the six exciters and the average angular velocity Ω when six exciters achieve synchronization. 11 The average angular velocities Ω1, Ω2, ..., Ω6 of the exciter shown in equation (17), and the derivative of equation (18) The average load torque of equation (19) The average electromagnetic torque of equation (21) Substituting into equation (9), we can obtain the relationship between the average angular velocities Ω1, Ω2, ..., Ω6 of the exciter and the average phase angle. The slow motion equations yield the average angular velocity Ω and the average phase difference β1, β2, ..., β5 between the six exciters when they reach synchronization, as well as the dimensionless perturbations ε1, ε2, ..., ε5. 11 Equations of slow motion:

[0164]

[0165] In the formula, J1, J2, ..., J6 are the moments of inertia of exciters 1, 2, ..., 6, in kg·m. 2 c1, c2, ..., c6 are the damping coefficients of exciters 1, 2, ..., 6, in N·m·s; m1, m2, ..., m6 are the eccentric masses of exciters 1, 2, ..., 6, in kg; ε1, ε2, ..., ε6 are the dimensionless perturbations of the average angular velocity of exciters 1, 2, ..., 6; ε7, ε8, ..., ε6 are the eccentric masses of exciters 1, 2, ..., 6, in kg. 11 It is the dimensionless perturbation of the average phase difference between exciters 1 and 2, 2 and 3, ..., 5 and 6. It is the dimensionless perturbation of the average angular velocity of exciters 1, 2, ..., 6 with respect to time t, 1 / s; T e1 T e2 ... T e6 It is the electromagnetic torque of exciters 1, 2, ..., 6, in N·m, q 11 q 12 , ..., q 611χ1, χ2, ..., χ6 are the coefficients before the dimensionless perturbation in the average load torque of exciters 1, 2, ..., 6, in rad / s. χ1, χ2, ..., χ6 are the constant terms in the average load torque of exciters 1, 2, ..., 6, in rad / s.

[0166] Combining equation (22) with the average angular velocity Ω of the six exciters when they reach synchronization and the average phase differences β1, β2, ..., β5 between them, as well as their dimensionless perturbations ε1, ε2, ..., ε5, ... 11 The equation of slow motion and equation (18) The relationship between ε1, ε2, ..., ε6 can ultimately yield the dimensionless coupling equations for the average angular velocity Ω and the average phase differences β1, β2, ..., β5 between the six exciters when they achieve synchronization:

[0167] Where A = diag(J1 / m1r) 2 J2 / m2r 2 … J6 / m6r 2 1 1 1 1 1),

[0168] v=(v1 v2 v3 v4 v5 v6 0 0 0 0 0) T ,

[0169] ε=(ε1 ε2 ε3 ε4 ε5 ε6 ε7 ε8 ε9 ε 10 ε 11 ) T ,

[0170]

[0171]

[0172]

[0173] In the formula, ε is a vector of dimensionless perturbation. It is the derivative vector of the dimensionless perturbation, 1 / s, and matrix A is the dimensionless coupling equation. The coefficient matrix is ​​given by matrix B, which is the coefficient matrix of ε in the dimensionless coupling equation. v is the input vector of the dimensionless coupling equation, v1, v2, ..., v6 are the first 6 input quantities of the input vector v, in rad / s, ε1, ε2, ..., ε6 are the dimensionless perturbations of the average angular velocities of exciters 1, 2, ..., 6, and ε7, ε8, ..., ε6 are the coefficient matrices of the dimensionless coupling equation. 11 It is the dimensionless perturbation of the average phase difference between exciters 1 and 2, 2 and 3, ..., 5 and 6. It is the dimensionless perturbation of the average angular velocity of exciters 1, 2, ..., 6 with respect to time t, 1 / s. It is the dimensionless perturbation of the average phase difference between exciters 1 and 2, 2 and 3, ..., 5 and 6 with respect to time t, 1 / s, b 11 b 22 ... b 66 These are the first 6 diagonal elements of the coefficient matrix B, rad / s, q 11 q 12 , ..., q 611 χ1, χ2, ..., χ6 are the coefficients before the dimensionless perturbation in the average load torque of exciters 1, 2, ..., 6, in rad / s; χ1, χ2, ..., χ6 are the constant terms in the average load torque of exciters 1, 2, ..., 6, in rad / s; J1, J2, ..., J6 are the moments of inertia of exciters 1, 2, ..., 6, in kg·m. 2 c1, c2, ..., c6 are the damping coefficients of exciters 1, 2, ..., 6, in N·m·s; m1, m2, ..., m6 are the eccentric masses of exciters 1, 2, ..., 6, in kg; r is the eccentric radius of the exciter, in mm; T e1 T e2 ... T e6 It is the electromagnetic torque of exciters 1, 2, ..., 6, in N·m.

[0174] S4: When the six vibrators are running synchronously, the synchronicity condition is obtained by combining the dimensionless coupling equation of the concrete vibration table with the electromagnetic torque constraint.

[0175] Specifically, when the six vibrators are running synchronously, the average angular velocities Ω1, Ω2, ..., Ω6 of the six vibrators are all equal to the average angular velocity Ω when the six vibrators achieve synchronization, that is...

[0176]

[0177] In the formula, χ is the average load torque of exciter i, N·m; i It is a constant term in the average load torque of exciter i, in rad / s.

[0178] From the dimensionless coupling equation (23), we know that the input vector v of the dimensionless coupling equation is also equal to 0, thus:

[0179]

[0180] In the formula, T oi c is the average output torque of exciter i, N·m; i is the damping coefficient of exciter i, in N·m·s.

[0181] As can be seen from equation (25), when the system reaches stable operation, the average load torque remains unchanged. To achieve synchronous rotation of the six exciters, the average output torque T of each exciter i must be...oi It must be equal to the average load torque Therefore, electromagnetic torque is the only adjustable parameter that satisfies the synchronization condition. However, electromagnetic torque is limited and cannot exceed the rated electromagnetic torque T for an extended period of time. eNi .

[0182] The synchronization conditions for the six exciters are:

[0183] In the formula, T ei T is the electromagnetic torque of exciter i, in N·m; eNi It is the rated electromagnetic torque of exciter i, in N·m.

[0184] S5: Under the condition of synchronicity, the dimensionless coupling equation of the concrete shaking table is combined again to obtain the stability condition.

[0185] When the six exciters rotate synchronously, the average angular velocity Ω of the six exciters when they reach synchronization can be calculated according to the synchronization condition shown in equation (26), and the average phase difference β1, β2, ..., β5 between them. Substituting these values ​​into the dimensionless coupling equation shown in equation (23), we can obtain:

[0186] To obtain the stability conditions for the synchronous operation of the six exciters, since the determinant of the coefficient matrix A is not equal to 0, equation (27) can be rewritten as:

[0187] In equations (27) and (28), D is the system matrix. The stability of the synchronous motion of the six exciters is determined by calculating the eigenvalues ​​of the system matrix D: if all eigenvalues ​​of D have negative real parts, then the synchronous motion of the six exciters is stable; otherwise, it is unstable. The stability condition for the synchronous motion of the six exciters is:

[0188] λ k =Re(D) k <0, k=1,2,…,11. (29)

[0189] In the formula, matrix D is the system matrix; Re is the real part symbol; λ k It is the real part of the k-th eigenvalue of the system matrix D.

[0190] This embodiment provides a concrete vibrating table based on co-directional multi-machine self-synchronization, such as... Figure 2As shown, the system includes six vibrators 1, a vibration table 2, springs 3, and a base 4. The base 4 is placed on the ground or foundation. Springs 3 are placed on top of the base 4, and the vibration table 2 is placed on top of the springs 3. Vibrators 1 are symmetrically placed on the sides of the vibration table 2. Each vibrator 1 consists of an eccentric rotor driven by a motor and is securely connected to the vibration table. When the concrete vibration table is working, the phase angles of the six vibrators are always approximately the same, i.e., the phase difference is 0, and the excitation forces are completely superimposed, enabling the concrete vibration table to operate efficiently.

[0191] The following are example data parameters using the concrete vibration table in this embodiment. This embodiment is not limited to these parameters.

[0192] The total mass of the concrete vibrating table is M = 600 kg; the moment of inertia of the vibrating table is J. p = 97 kg·m 2 The mass of the deflected rotor is m1 = m2 = m3 = m4 = m5 = m6 = 3 kg; l1 = 559 mm, l2 = 500 mm, l3 = 559 mm, l4 = 559 mm, l5 = 500 mm, l6 = 559 mm; the exciter position angles are θ1 = 63°, θ2 = 90°, θ3 = 117°, θ4 = 243°, θ5 = 270°, θ6 = 297°; the exciter rotation radius is r = 50 mm, and the spring stiffness is k. x =240kN / m, k y =240kN / m, k ψ =120kN·m, damping coefficient c x =c y =1500 N·s / m, c ψ =450 N·s·m. Exciter type: Three-phase asynchronous motor, 50Hz, 380V, 6-pole, 1kW, rated speed 995r / min, stator resistance 19Ω, rotor resistance 10Ω, stator leakage inductance 0.055H, rotor leakage inductance 0.055H, mutual inductance 0.944H, damping coefficient c1=c2=c3=c4=c5=c6=0.005N·m·s.

[0193] Synchronous stability analysis of the concrete vibrating table: The moment of inertia of the concrete vibrating table is J = 102.3 kg·m. 2 Equivalent radius of gyration l e =412.9mm, at this time, 1.414l e =583.9mm>l i Let i = 1, 2, ..., 6. The system's natural frequency. When the power supply frequency f s The theoretical results for the vibration system at 10–50 Hz are as follows: Figure 4 As shown. In Figure 4 In (a) to (i), when the exciter speed Ω < ωx =ω y At this time, the six vibrators rotate synchronously in the same phase, i.e., β1=β2=β3=β4=β5=0°. The excitation forces provided by the six vibrators are completely superimposed in the x and y directions, and are 0 in the ψ direction. The amplitude of the concrete vibrating table in the x and y directions gradually increases with the increase of rotational speed, while the amplitude in the ψ direction remains 0. When Ω>ω x =ω y At this point, the phase difference between the six vibrators jumps from being in phase to β1 = β4 = -26.83°, β2 = β5 = -26.30°, and β3 = -126.87°. As the vibrator speed increases, β1 and β4 slightly increase, while β2 and β5 slightly decrease. At this time, the excitation forces provided by the six vibrators completely cancel each other out in the x and y directions, but are superimposed in the ψ direction. The amplitude of the concrete vibrating table in the x and y directions remains zero, exhibiting violent oscillation, which gradually increases with increasing speed. The theoretical analysis shows that the selected operating frequency of the concrete vibrating table satisfies Ω < ω. x,y , and ω x =ω y <ω ψ At that time, the six exciters can achieve synchronous motion with zero phase difference, and the excitation force is completely superimposed in the x and y directions, resulting in a large amplitude of the vibration table.

[0194] To verify the theoretical results, two sets of simulation results are presented, with the power supply frequency f. s The frequency was 30Hz (approximately Ω = 60rad / s), the simulation time was 10s, and the simulation results were as follows. Figure 5 As shown. In Figure 5 In (a), the stable rotational speed of all six exciters is approximately 60 rad / s, indicating that the six exciters achieved stable synchronous motion. Figure 5 In (b) to (f), during the steady-state phase, the phase difference between the six exciters is 0°, which is consistent with... Figure 3 The theoretical analysis results are completely consistent. Figure 5 In Figures (g) and (h), after reaching a steady state, the concrete vibrating table exhibits relatively large amplitudes in the x and y directions, approximately 13 mm. Figure 5 In (i), the swing angle of the concrete vibrating table in the ψ direction is approximately 0 rad. In summary, when the rotational speed of the six exciters is Ω = 60 rad / s, the six exciters achieve synchronous motion in the same phase, the excitation forces are completely superimposed, the concrete vibrating table mainly vibrates in the x and y directions, there is no oscillating motion, which is completely consistent with the theoretical results, the vibration is uniform, and the concrete compaction effect is good.

[0195] When the power supply frequency f s At 45Hz (approximately Ω = 93.3 rad / s), the simulation time was 10s, and the results are as follows. Figure 6 As shown. InFigure 6 In (a), the stable rotational speed of all six exciters is approximately 93.3 rad / s, indicating that the six exciters achieved stable synchronous motion, but the speed fluctuations were relatively severe. Figure 6 In (b) to (f), during the steady-state phase, the phase differences between the six exciters are β1 = β4 = -27.45°, β2 = β5 = -25.67°, and β3 = -126.87°, respectively. Figure 3 The theoretical analysis results are completely consistent. Figure 6 In (g) and (h), after reaching a stable state, the amplitude of the concrete vibrating table in the x and y directions is 0. Figure 6 In (i), the swing angle of the concrete vibrating table in the ψ direction is approximately 0.03 rad (about 1.7°), resulting in violent oscillation. In summary, when the rotational speed of the six vibrators is Ω = 93.3 rad / s, the six vibrators achieve synchronous movement, and the excitation forces provided by the six vibrators completely cancel each other out in the x and y directions. The concrete vibrating table mainly exhibits oscillating motion, resulting in uneven vibration and poor concrete compaction.

[0196] By adjusting the distances l1, l2, l3, l4, l5, and l6 between the center of the vibration table and the rotation center of the exciter, and keeping other parameters constant, the relationship between the vibration table dimensions and the system response is analyzed. When the power supply frequency f... s =30Hz (approximately Ω = 60rad / s), l min / l e When the value is between 0.7 and 1.7, the theoretical results for the vibration system are as follows: Figure 7 As shown, where l min =min(l1, l2, l3, l4, l5, l6). Figure 7 In (a), the phase difference between the six exciters is always 0°, and the excitation force is completely superimposed in the x and y directions, and does not change with l. min / l e It changes with the changes. Correspondingly, Figure 7 In (b) to (d), the vibration table exhibits relatively large amplitudes in the x and y directions, approximately 12.5 mm, while the amplitude in the ψ direction is 0. When the power supply frequency f... s =45Hz (approximately Ω = 93.3rad / s), l min / l e When the value is between 0.7 and 1.7, the theoretical results for the vibration system are as follows: Figure 8 As shown. Figure 8 In (a), as l min / l e As the phase difference β1, β2, β4, and β5 of the six exciters gradually increases, β3 gradually increases, but always satisfies β1 = β4 and β2 = β5, and the excitation forces completely cancel each other out in the x and y directions. Correspondingly, in Figure 8In (b) to (d), the amplitude of the shaking table in the x and y directions is approximately 0 mm, while the amplitude in the ψ direction gradually decreases. From the above theoretical results, it can be concluded that l min / l e The value is not a key factor in changing the synchronization state of the six exciters; that is, the synchronization state of the six exciters is unrelated to the distance from the exciter's rotation axis to the machine's center of mass.

[0197] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for determining the parameters of a concrete vibrating table based on multi-machine self-synchronization in the same direction, characterized in that, This method is performed according to the following steps: S1: Based on the dynamic model of the concrete shaking table, obtain the kinetic energy, potential energy, and generalized force equations of the concrete shaking table. S2: Substitute the kinetic energy, potential energy, and generalized force equations of the concrete shaking table into the Lagrange equations to obtain the differential equations of motion for the concrete shaking table. S3: Substitute the average phase angle, angular velocity and angular acceleration of the exciter into the motion differential equation of the concrete vibration table, introduce the dimensionless perturbation and differentiate it, and then obtain the dimensionless coupling equation of the concrete vibration table. S4: When multiple vibrators are running synchronously, the synchronicity condition is obtained by combining the dimensionless coupling equation of the concrete vibration table with the electromagnetic torque constraint. S5: Under the condition of synchronicity, the dimensionless coupling equation of the concrete shaking table is combined again to obtain the stability condition. In step S3, a dimensionless perturbation is introduced: ； In the formula, These are exciters 1, 2, ... average angular velocity, It is the average angular velocity when multiple exciters achieve synchronization. These are exciters 1, 2, ... The constant term of the phase angle, These are exciters 1, 2, ... The average phase angle, These are exciters 1 and 2, 2 and 3, ... and The average phase difference between them These are exciters 1, 2, ... The dimensionless perturbation of the average angular velocity, These are exciters 1 and 2, 2 and 3, ... and The dimensionless perturbation of the average phase difference between them; Both sides of the dimensionless perturbation equation with respect to time By taking the derivative and simplifying, the derivative of the average angular velocity of the exciter can be expressed in terms of the average angular velocity and dimensionless perturbation when multiple exciters achieve synchronization: ； In the formula, It is the total number of vibrators. These are exciters 1, 2, ... Average angular velocity with respect to time The derivative, It is the average angular velocity when multiple exciters achieve synchronization. These are exciters 1, 2, ... The dimensionless perturbation of the average angular velocity with respect to time The derivative, These are exciters 1, 2, ... The dimensionless perturbation of the average angular velocity, These are exciters 1 and 2, 2 and 3, ... and The dimensionless perturbation of the average phase difference between them with respect to time The derivative; Dimensionless coupling equations: ； in, ， ， ， ， ， ， ； In the formula, It is a dimensionless vector of perturbation. It is the derivative vector of the dimensionless perturbation, and the matrix. In the dimensionless coupling equation The coefficient matrix, the matrix In the dimensionless coupling equation The coefficient matrix, It is the input vector of the dimensionless coupling equation. It is the total number of vibrators. It is the input vector The former One input quantity, It is exciter 1, 2, ... The dimensionless perturbation of the average angular velocity, It refers to exciters 1 and 2, 2 and 3, ... and The dimensionless perturbation of the average phase difference between them. It is exciter 1, 2, ... The dimensionless perturbation of the average angular velocity with respect to time The derivative, These are exciters 1 and 2, 2 and 3, ... and The dimensionless perturbation of the average phase difference between them with respect to time The derivative, It is a coefficient matrix The former diagonal elements, It is exciter 1, 2, ... The coefficient before the dimensionless perturbation in the average load torque. It is exciter 1, 2, ... The constant term in the average load torque, It is exciter 1, 2, ... Moment of inertia, It is exciter 1, 2, ... The damping coefficient, It is exciter 1, 2, ... eccentric mass, It is the average angular velocity when multiple exciters achieve synchronization. It is exciter 1, 2, ... electromagnetic torque, r It is the eccentric radius of the exciter.

2. The method for determining the parameters of a concrete vibrating table based on self-synchronization of multiple machines in the same direction, as described in claim 1, is characterized in that... In step S1, The kinetic energy equation of a concrete shaking table: ； in, ； ； In the formula, It's about time. t The sign of the first derivative; T It is the kinetic energy of the vibration table; m It is the mass of the vibration table; It is the moment of inertia of the vibration table; It is a vibration table velocity in the direction; It is a vibration table velocity in the direction; It is a vibration table Angular velocity in the direction; This is the total number of vibrators; It is a vibrator eccentric mass; It is a vibrator The translational velocity vector; It is a vibrator Moment of inertia; It is a vibrator angular velocity; It is a vibrator The translational displacement vector; It is a vibration table Displacement in direction; It is a vibration table Displacement in direction; It is a vibration table Displacement in direction; The center of the shaking table and the exciter The distance between the centers of rotation; It is a vibrator Position angle; It is a vibrator The phase angle; It is the eccentric radius of the exciter; It is the matrix transpose symbol; Potential energy equation for a concrete vibrating table: ； In the formula, It is the potential energy of the shaking table; These are vibration tables direction, y Directional stiffness; It is a vibration table Directional stiffness; Generalized force equations for concrete shaking tables: ； in, ， ； In the formula, It is the generalized force vector of the shaking table; It is a vibration table direction, Damping coefficient in the direction; It is a vibration table Damping coefficient in the direction; It is a vibrator Electromagnetic torque; It is a vibrator Damping coefficient; This is the total number of vibrators; It is a vibrator The extreme logarithm; It is a vibrator Phase voltage; It is a vibrator The rotor resistance; It is a vibrator Synchronous electromagnetic angular velocity; It is a vibrator The mechanical angular velocity; i It is a vibrator Stator resistance; i It is a vibrator Stator leakage inductance coefficient; It is a vibrator The rotor leakage inductance coefficient; It is a vibrator The power supply frequency; It is the matrix transpose symbol.

3. The method for determining the parameters of a concrete vibrating table based on self-synchronization of multiple machines in the same direction, as described in claim 2, is characterized in that... In step S2, Substituting the equations for the kinetic energy, potential energy, and generalized force of the shaking table into the Lagrange equations, we obtain the differential equations of motion for the concrete shaking table: ； in, ， ； In the formula, It's about time. The sign of the second derivative; It is the total mass of the vibration table; It is the equivalent moment of inertia of the vibration table; It is a vibration table Acceleration in the direction of; It is a vibration table Acceleration in the direction of; It is a vibration table Angular acceleration in the direction; It is a vibrator angular acceleration; It is a vibrator The load torque; It is the equivalent radius of gyration of the shaking table.

4. The method for determining the parameters of a concrete vibrating table based on self-synchronization of multiple machines in the same direction, as described in claim 1, is characterized in that... In step S4, The synchronicity condition for multiple vibrators to rotate synchronously is: ； In the formula, It is a vibrator The rated electromagnetic torque; It is the average angular velocity when multiple exciters achieve synchronization; It is a vibrator The constant term in the average load torque.

5. The method for determining the parameters of a concrete vibrating table based on self-synchronization of multiple machines in the same direction, as described in claim 1, is characterized in that... In step S5, The stability condition for multiple vibrators to achieve synchronous rotation is: ； In the formula, the matrix It is the system matrix; It is the real part symbol; It is a system matrix No. The real part of each eigenvalue; This is the total number of vibrators.

Images