CN118603616B - A state detection method for electromechanical equipment under periodic excitation based on attractor - Google Patents
A state detection method for electromechanical equipment under periodic excitation based on attractor Download PDFInfo
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Abstract
The invention relates to a method for detecting the state of electromechanical equipment under periodic excitation based on an attractor, belongs to the technical field of state detection of electromechanical equipment, and solves the problems that in the prior art, the state detection of the electromechanical equipment under periodic excitation is difficult to have both interpretability and low generality, and the detection is inaccurate. The state detection method of the invention comprises the following steps: step 1, constructing an attractor model of the electromechanical equipment under periodic excitation of a generalized variable; step 2, mapping generalized variables and physical quantities of the generalized variables in an attractor model of the electromechanical equipment under periodic excitation is constructed; step 3, mapping the physical quantity of the electromechanical equipment to be detected into a generalized variable according to the mapping in the step 2; obtaining an attractor result and a performance result of the electromechanical equipment to be detected based on the generalized variable and the attractor model of the electromechanical equipment to be detected; and 4, carrying out state identification on the electromechanical equipment to be detected based on the attractor result and the performance result of the electromechanical equipment to be detected in the step 3.
Description
Technical Field
The invention belongs to the technical field of state detection of electromechanical equipment, and particularly relates to a state detection method of electromechanical equipment under periodic excitation based on an attractor, in particular to a state detection method of a single-shaft type electrodynamic vibration isolator under periodic excitation based on the attractor.
Background
Along with the rapid development of science and technology, the requirements on the use of equipment are higher and higher, whether the equipment can be normally operated or not directly influences the use cost, the working condition efficiency and the like, the state condition of the equipment is accurately obtained, and the equipment is paid more attention to and gradually applied in recent years. The bulletin number is: chinese patent CN115758260B, CN116069964B, CN113806157B and CN 113283504B.
In electromechanical devices, periodic excitation is a very widely used type of excitation in engineering practice, under which electromechanical devices typically have periodic time-varying performance characteristics. When the state detection is performed on the periodically excited electromechanical devices, the performance parameters concerned by the electromechanical devices of different types are usually different, but the state detection is mainly performed on the electromechanical devices of the same type in the prior art, so that the universality of the technology is not strong, the migration application is difficult to be performed among the electromechanical devices of different types, and a large amount of resources and time cost for the state detection of the electromechanical devices are consumed. For this reason, many detection techniques for electromechanical devices based on data driving have been developed, and these techniques do have better versatility. In practice, however, the performance parameters of the electromechanical device are physically coupled, especially under periodic excitation, and the coupling between the performance parameters of the electromechanical device is very severe, and it is often difficult to independently extract each performance parameter for analysis. However, the lack of physical interpretability of the detection technology of the electromechanical device based on data driving leads to inaccurate processing of the coupling of the performance parameters, so that the accuracy of the detection of the state of the electromechanical device is reduced. Therefore, a state detection method with both physical interpretability and universality is proposed for the periodically excited electromechanical device, and has become an important direction in the field of state detection of the electromechanical device.
However, the existing periodic excitation electromechanical equipment state detection technology based on the attractors only constructs the attractors based on time-varying signal characteristics of equipment, so that the equipment state is estimated, and the method is consistent with the problems existing in the method based on data driving in the prior art, and still has difficulty in achieving physical interpretability and universality.
Disclosure of Invention
In view of the above problems, the invention provides a method for detecting the state of an electromechanical device under periodic excitation based on an attractor, which solves the problems that in the prior art, the state detection of the electromechanical device under periodic excitation is difficult to have both interpretability and low generality, and the detection is inaccurate.
The invention provides a state detection method of electromechanical equipment under periodic excitation based on an attractor, which specifically comprises the following steps:
step 1, constructing an attractor model of the electromechanical equipment under periodic excitation of a generalized variable;
The attractor model of the electromechanical equipment under the periodic excitation consists of generalized variables, wherein the generalized variables comprise generalized coordinates, generalized speed, generalized momentum, generalized external force, residual energy function, residual energy coefficient matrix, energy function, energy coefficient matrix, dissipation function, generalized dissipation force and dissipation coefficient matrix;
The method comprises the following specific steps:
step 1.1, constructing a common operation state model of the electromechanical equipment under periodic excitation based on Lagrangian-Maxwell equation, wherein the expression is as follows:
In the formula, Is the first of the electromechanical devicesThe number of generalized coordinates is defined by,Is the total number of degrees of freedom of the electromechanical device; Is the first of the electromechanical devices A generalized velocity; And Respectively the first of the electromechanical devicesA generalized periodic external force and a generalized dissipative force; as a lagrangian function; The time is the moment;
step 1.2, carrying out regular coordinate transformation on a common operation state model of the electromechanical equipment under periodic excitation to obtain a coordinate transformation model;
Step 1.3, constructing an attractor model based on the obtained coordinate transformation model;
step 2, mapping generalized variables and corresponding physical quantities in an attractor model of the electromechanical equipment under periodic excitation is constructed;
Step 3, mapping the physical quantity of the electromechanical equipment to be detected into a generalized variable according to the mapping in the step 2; obtaining an attractor result and a performance result of the electromechanical equipment to be detected based on the generalized variable and the attractor model of the electromechanical equipment to be detected;
And 4, carrying out state identification on the electromechanical equipment to be detected based on the attractor result and the performance result of the electromechanical equipment to be detected in the step 3.
Alternatively, the Lagrangian function of the electromechanical deviceThe expression of (2) is:
In the formula, Is an energy function of the electromechanical device; is the residual energy function of the electromechanical equipment; Is a generalized coordinate vector; Is a generalized velocity vector.
Optionally, in step 1.2, performing regular coordinate transformation on the common operation state model of the electromechanical device under periodic excitation to obtain a coordinate transformation model includes the specific steps of:
Obtaining a transformation formula of a common running state model of the electromechanical equipment under periodic excitation;
Obtaining a general solution of a transformation type simple harmonic function form of a common running state model of the electromechanical equipment under periodic excitation;
obtaining an unfolding determinant about the feature matrix based on a general solution of a transformation formula and a simple harmonic function form of a common operation state model of the electromechanical equipment under periodic excitation; obtaining feature vectors of the feature values of the feature matrix based on the expanded determinant;
Obtaining a regular coordinate transformation model based on the feature vector of the feature value;
and carrying out coordinate transformation on the common operation state model of the electromechanical equipment under periodic excitation by using a regular coordinate transformation model to obtain a coordinate transformation model.
Optionally, the attractor model constructed in step 1.3 includes a reference periodic function; the reference periodic function includes a simple harmonic excitation form and a non-simple harmonic periodic excitation form, depending on the periodic excitation type.
Compared with the prior art, the invention has at least the following beneficial effects:
(1) Based on the physical principle of the operation of the electromechanical equipment, the invention considers the common periodic excitation types of the simple harmonic excitation and the non-simple harmonic periodic excitation, establishes the performance characterization and state detection method of the electromechanical equipment under the periodic excitation based on the attractor, has better physical interpretability and higher identification accuracy on the health/fault state of the electromechanical equipment.
(2) The invention uses the attractor to characterize the performance of the electromechanical device from the angle of the degree of freedom of the electromechanical device, can effectively process the coupling influence of each performance parameter under periodic excitation, and can convert the attractor into various dynamic performances of engineering concern.
(3) The method provided by the invention has strong universality and high adaptability to multi-scene and multi-type electromechanical equipment (including pure mechanical equipment and pure electromagnetic equipment) under periodic excitation. The model has a physical analysis form, so that the process of modeling and solving the running state of the periodically excited electromechanical equipment can be avoided, and the efficiency of the detection method is remarkably improved.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention.
FIG. 1 is a schematic illustration of the process flow of the present invention.
Fig. 2 is a functional schematic diagram of an embodiment of the single-axis electrodynamic vibration isolator of the present invention.
Fig. 3 (a) - (d) are perspective views of an attractor of an embodiment of a uniaxial electrodynamic vibration isolator according to the present invention in phase space.
Fig. 4 (a) - (b) are displacement and velocity curves for an embodiment of the single axis electrodynamic vibration isolator of the present invention.
Fig. 5 is a graph showing vibration isolation efficiency of the single-axis electrodynamic vibration isolator according to the present invention as an example.
Fig. 6 (a) - (c) are measured displacement, velocity and efficiency data for a single axis electrodynamic vibration isolator of the present invention as an example.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description. It should be noted that, without conflict, the embodiments of the present invention and features in the embodiments may be combined with each other. In addition, the invention may be practiced otherwise than as specifically described and thus the scope of the invention is not limited by the specific embodiments disclosed herein.
1-6, The invention discloses a state detection method of electromechanical equipment under periodic excitation based on an attractor, which specifically comprises the following steps:
and 1, constructing an attractor model of the electromechanical equipment under periodic excitation of the generalized variable.
Step 1.1, constructing a common operation state model of the electromechanical equipment under periodic excitation based on Lagrangian-Maxwell equation, wherein the expression is as follows:
（1）
In the formula, Is the total number of degrees of freedom of the electromechanical device; Is the first of the electromechanical devices A generalized coordinate; Is that For physical timeIs the derivative of the electromechanical deviceA generalized velocity; And Respectively the first of the electromechanical devicesA generalized periodic external force (e.g., voltage, current with periodic characteristics applied to the electromechanical device) and a generalized dissipative force (e.g., damping force inside the electromechanical device); as a lagrangian function; is the time of day.
Further, lagrangian function of electromechanical deviceThe expression of (2) is:
（2）
In the formula, Is an energy function of the electromechanical device; is the residual energy function of the electromechanical equipment; in the form of a generalized coordinate vector, ，Is the first of the electromechanical devicesA generalized coordinate; In the form of a generalized velocity vector, ，Is the first of the electromechanical devicesA generalized speed.
Further, the residual energy function of the electromechanical deviceAnd energy functionThe expression of (2) is:
（3）
In the formula, An energy coefficient matrix for the electromechanical device; Is the matrix of the residual energy coefficients of the electromechanical device.
Further, an energy coefficient matrix of the electromechanical deviceSum complementary energy coefficient matrixThe expression of (2) is:
（4）
（5）
In the formula, Representing an energy coefficient matrixRow 1, column 1 elements of (a); Representing a matrix of residual energy coefficients Row 1, column 1 elements of (a); Representing an energy coefficient matrix The 1 st row, the f column element; Representing a matrix of residual energy coefficients The 1 st row, the f column element; Representing an energy coefficient matrix The f-th row 1-column element of (a); Representing a matrix of residual energy coefficients The f-th row 1-column element of (a); Representing an energy coefficient matrix The element of the f-th row and the f-th column; Representing a matrix of residual energy coefficients F of line f column elements.
Further, the first of the electromechanical devicesExternal force of each generalized periodThe expression of (2) is:
（6）
In the formula, To be applied to the electromechanical device part componentPeriodic external force at each position (for example, for a crank slider mechanism with motor drive, the periodic voltage signal input to the motor and the periodic force acting on the slider are the periodic external force at two positions of the crank slider mechanism),；For the coordinate vector diameter of the ith position of the electromechanical device part component,；Is the total number of positions of the electromechanical device portion assembly.
Further, the method comprises the steps of,Having periodicity, the expression is: In which, in the process, Is the first component of the electromechanical equipment partThe minimum positive period of the periodic external force at each position,Indicating the time t applied to the electromechanical device componentPeriodic external forces on the individual locations; Representation of The first component applied to the electromechanical device part at any timePeriodic external force at each position, further, calculateCorresponding angular frequency，。
Further, the minimum positive period of the periodic external force at different positionsCalculating periodic external force at different positions under the condition of inequalityIs the common minimum positive period of (2)，In which, in the process,Is a positive integer of prime mutually; using a common minimum positive periodAs a component applied to the electromechanical device partPeriodic external force on individual positionsIs a periodic one. Further, calculateCorresponding angular frequency，。
Further, when the electromechanical device is constituted by a linear element, in the formula (6)Is a constant value, and is a function of the constant,，，Are all of period ofAngular frequency ofIs a generalized periodic external force.
Further, whenWhen the generalized periodic external forces with different amplitudes are applied, the first step of the electromechanical equipment is performedExternal force of each generalized periodWriting:
（7）
In the formula, Is the firstExternal force of each generalized periodIs a magnitude of (a); for a period of Angular frequency ofIs used for the reference period function of (a).
Specifically, the firstExternal force of each generalized periodA broad sense of force that is not a potential force applied to the electromechanical device from the outside, such as a periodic driving force or load.
Further, the first of the electromechanical devicesIndividual generalized dissipation forcesThe expression of (2) is:
（8）
In the formula, Is a dissipative function of the system.
Further, according to the characteristics of the energy dissipation functions of the mechanical part and the electromagnetic part in the electromechanical device, the dissipation function of the electromechanical deviceThe expression of (2) is:
（9）
In the formula, For the equivalent linear dissipation factor at the ith position of the electromechanical device portion assembly,，；Is the velocity vector of the ith position of the electromechanical device portion assembly,，Is thatIs provided with a die for the mold,。
Further, according to the energy dissipation function of the electromechanical deviceIs expressed in terms of (a) to obtain a generalized dissipation forceExpansion, the expression is:
（10）。
Introducing generalized momentum vectors ，In which, in the process,Is the first of the electromechanical devicesThe amount of the generalized momentum is calculated,The expression is:
（11）。
It is clear that the generalized variables of the electromechanical device include generalized coordinates, generalized velocity, generalized momentum, generalized external force, residual energy function, residual energy coefficient matrix, energy function, energy coefficient matrix, dissipation function, generalized dissipation force and dissipation coefficient matrix.
Further, substituting the formula (2), the formula (3), the formula (7) and the formula (10) into the formula (1) and writing the formula into a matrix form to obtain a common operation state model of the electromechanical equipment under periodic excitation in the matrix form, wherein the expression is as follows:
（12）
In the formula, In the form of a generalized acceleration vector,，Is the first of the electromechanical devicesThe individual generalized accelerations of the person,；Is a generalized periodic external force amplitude vector,；Is a dissipation factor matrix.
Dissipation coefficient matrix。
And 1.2, carrying out regular coordinate transformation on the common operation state model of the electromechanical equipment under periodic excitation to obtain a coordinate transformation model.
Under the condition of not considering generalized periodic external force and generalized dissipation force, a transformation formula of a common operation state model of the electromechanical equipment under periodic excitation is obtained:
（13）
Obtaining general solution of transformation type simple harmonic function form of common operation state model of electromechanical equipment under periodic excitation The expression is:
（14）
In the formula, Representing general solutionIs a function of the magnitude vector of (a),，Is a general solution of electromechanical equipmentIs the first of (2)The magnitude of the amplitude value is calculated,；Is angular frequency; is the phase.
Substituting formula (14) into formula (13) to obtain:
（15）。
Defining a feature matrix Obtaining determinant：
（16）
In the formula,Is a feature matrixIs a determinant of (2).
Expanding the determinant (16) to obtain the highest orderAlgebraic polynomial of (2) whereby the algebraic polynomial obtains a feature matrixIs of the characteristic value of (2)，。
Based on the respective characteristic valuesObtain about the firstPersonal characteristic valueFeature vectors of (a)，，Representing feature vectorsThe first of (3)The elements.
Obtaining a canonical coordinate transformation matrix based on eigenvalue-based eigenvectorsThe expression is:
（17）
wherein, Representing the 1 st eigenvalueIs a feature vector of (1); Represent the first Personal characteristic valueIs described.
Obtaining a regular coordinate transformation matrix according to the regularities of the feature vectorsIs a regular relation to:
（18）
In the formula, Is a matrix of units which is a matrix of units,In the form of a diagonal matrix,。
Further, a generalized coordinate vector is constructedThe expression of the canonical coordinate transformation of (c) is:
（19）
In the formula, For a regular generalized coordinate,，Is the first of the electromechanical devicesThe regular generalized coordinates of the number of coordinates,。
Further, to facilitate regular variation of the generalized dissipation force in equation (12), consider an energy dissipation matrixAnd complementary energy coefficient matrixAnd an energy coefficient matrixIn the case of a proportional function, the expression is:
（20）
In the formula, AndIs constant.
Further, based on the formula (19)Carrying out regular coordinate transformation on the expression (11) to obtain a coordinate transformation model after regular coordinate transformation of the expression (12), wherein the expression is as follows:
（21）
In the formula, In the form of a regular generalized velocity vector,，Is the first of the electromechanical devicesThe number of regular generalized velocities is the number,；For a regular generalized acceleration vector,，Is the first of the electromechanical devicesThe regular generalized acceleration is calculated,；Is a regular generalized periodic external force amplitude vector,In which, in the process,Is the first of the electromechanical devicesRegular generalized periodic external force amplitude values under the regular generalized coordinates,。
And 1.3, constructing an attractor model based on the coordinate transformation model.
According to the coordinate transformation model of expression (21), the expression of the operation state model at each degree of freedom is obtained as follows:
（22）
In the formula, Is the first of the electromechanical devicesRegular generalized coordinates; Is the first of the electromechanical devices A regular generalized velocity; Is the first of the electromechanical devices Regular generalized accelerations; Represent the first A characteristic value; Is the first of the electromechanical devices Regular generalized periodic external force amplitude values under regular generalized coordinates; Representing a reference periodic function; And Is constant.
Further, according to the type of periodic excitation, the reference periodic functionIncluding simple harmonic excitation forms and non-simple harmonic periodic excitation forms.
Case a, reference periodic functionIs in the form of simple harmonic excitation and reference periodic functionThe expression of (2) is:
（23）
In the formula, As a function of the reference periodIs a frequency of an angle of (a); as a function of the reference period Is a phase of (a) of (b).
Further, the first in the formula is obtained based on a phasor methodEquilibrium state of regular generalized coordinatesThe expression is:
（24）
In the formula, Is the firstEquilibrium state of regular generalized coordinatesIs used for the amplitude of (a) and (b),；Is the firstEquilibrium state of regular generalized coordinatesIs used for the phase of the (c) signal,。
Further, the firstEquilibrium state of regular generalized coordinatesAmplitude of (a) of (b)The expression of (2) is:
（25）。
further, the first Equilibrium state of regular generalized coordinatesIs of the phase of (a)The expression of (2) is:
（26）。
Further, according to the first Equilibrium state of regular generalized coordinatesIs of the phase of (a)Obtaining a regular generalized coordinate equilibrium state vector，。
Further, based on a canonical coordinate transformation matrixFor regular generalized coordinate equilibrium state vectorPerforming regular coordinate transformation to obtain generalized coordinate equilibrium state vector of electromechanical equipment under physical coordinatesThe expression is:
（27）。
Case b, reference periodic function Non-simple harmonic periodic excitation form, reference periodic functionExpanded into a fourier series, expressed as:
（28）
In the formula, ，AndAs a result of the fourier coefficients,Is the number of items; representing a reference periodic function.
Further, the method comprises the steps of,，AndThe expression of (2) is:
（29）。
For reference periodic functions Each term developed into Fourier series is solved and added based on a phasor method to obtain the firstEquilibrium state of regular generalized coordinatesThe expression is:
（30）
In the formula, Is the firstEquilibrium state of regular generalized coordinatesIs the first of (2)The magnitude of the term(s),，；Is the firstEquilibrium state of regular generalized coordinatesIs the first of (2)The phase of the term(s),，。
Further, the firstEquilibrium state of regular generalized coordinatesIs the first of (2)Amplitude of the termThe expression of (2) is:
（31）。
further, the first Equilibrium state of regular generalized coordinatesIs the first of (2)Phase of the termThe expression of (2) is:
（32）。
Further, according to the first Equilibrium state of regular generalized coordinatesIs of the phase of (a)Obtaining a regular generalized coordinate equilibrium state vector，。
Further, based on a canonical coordinate transformation matrixFor regular generalized coordinate equilibrium state vectorPerforming regular coordinate transformation to obtain generalized coordinate equilibrium state vector of electromechanical equipment under physical coordinatesThe expression is:
（33）。
further, based on the equation (24), the regular generalized coordinates of the electromechanical device under periodic excitation in the form of a simple harmonic function are obtained Corresponding regular generalized velocityThe expression is:
（34）。
Further, based on the equation (30), a regular generalized coordinate of the electromechanical device under periodic excitation in a non-simple harmonic periodic function form is obtained Corresponding regular generalized velocityThe expression is:
（35）。
Further, the regular generalized velocity equilibrium state vector under the condition (a) and the condition (b) is obtained respectively 。
Further, according to the regular coordinate transformation, generalized momentum balance state vectors of the electromechanical equipment under the physical coordinates of the condition (a) and the condition (b) are obtainedThe expression is:
（36）。
further, combining the formulas (27) and (36), and the formulas (33) and (36) to obtain the complete form of the motion balance state of the electromechanical device under the periodic excitation in the case of the condition (a) or the condition (b) The expression is:
（37）。
In particular, the complete form of the dynamic equilibrium state of the electromechanical device under periodic excitation in case a and case b Are each represented by formula (37).
Further, the electromechanical device is in a motion balance stateBy analyzing the motion stability, the motion equilibrium state of the electromechanical equipment can be foundIs stably convergent, and is therefore also calledFor the convergence value of the generalized coordinate vector,Is called a motion equilibrium state for the convergence value of generalized momentum vectorIs an attractor for periodically exciting an electromechanical device, and accordingly, the equation (37) is referred to as an attractor model.
And 2, constructing a mapping between generalized variables and physical quantities of the generalized variables in an attractor model of the electromechanical equipment under periodic excitation.
Mapping of generalized variables and physical quantities of the generalized variables in an attractor model of the electromechanical device under periodic excitation is constructed, and the results are shown in table 1.
TABLE 1 mapping of generalized variables to physical quantities of mechanical and electromagnetic parts in electromechanical devices
It can be seen from table 1 that the proposed method only focuses on the generalized variables of the device and thus can be applied to purely mechanical and purely electromagnetic devices in addition to electromechanical devices.
Step 3, mapping the physical quantity of the electromechanical equipment to be detected into a generalized variable according to the mapping in the step 2; and obtaining an attractor result and a performance result of the electromechanical equipment to be detected based on the generalized variable and the attractor model of the electromechanical equipment to be detected.
And 3.1, calculating an attractor result of the electromechanical equipment to be detected.
Mapping the physical quantity of the electromechanical equipment to be detected into a generalized variable according to the mapping table in the step 2; and obtaining an attractor result of the electromechanical equipment to be detected based on the generalized variable of the electromechanical equipment to be detected and the attractor model thereof.
And 3.2, calculating a performance result of the electromechanical device to be detected based on the attractor result of the electromechanical device to be detected.
Calculating a performance result based on the attractor result according to the relation between the performance parameter of the electromechanical equipment to be detected and the physical quantity of the electromechanical equipment to be detected, and marking the performance result as. The performance parameter of the electromechanical device is, for example, the rotational speed, which is the angular velocity in terms of units, which is the generalized velocity in the generalized variable; the performance parameter of the electromechanical device is efficiency = (rotational speed x torque)/(voltage x current), where rotational speed and current are both generalized speeds and torque and voltage are both generalized external forces, whereby efficiency can be calculated by the attractor.
And 4, recognizing the health state of the electromechanical equipment to be detected based on the attractor result and the performance result of the electromechanical equipment to be detected in the step 3.
Comparing the performance result based on the attractor obtained in the step 3 with the actually measured performance parameter of the electromechanical equipment to be detected, and establishing the health index of the electromechanical equipment:
（38）
In the formula, Is a health index of electromechanical equipment; For the values of the measured performance parameters of the electromechanical device, ，Data amount for actually measured performance parameters; Is a performance result obtained based on the attractor.
Health indexThe closer to 0 the value of (c) indicates the healthier the electromechanical device to be tested. Health indexLess than 0, indicating that the measured data is below theoretical; health indexGreater than 0 indicates that the measured data is above theoretical. According to the health indexIs used to identify the health/fault status of the electromechanical device.
In order to illustrate the effectiveness of the method according to the present invention, the following describes the above technical solution according to a specific embodiment, and uses a certain uniaxial electrodynamic vibration isolator as an embodiment, the method according to the present invention is specifically as follows:
And 1, constructing an attractor model of the uniaxial electrodynamic vibration isolator under periodic excitation of a generalized variable.
Single-shaft electrodynamic vibration isolators are common electromechanical devices, the system consisting of two massesAndIs composed of a spring (the spring has a stiffness coefficient of) Moving-coil transducer (voltage at two ends)The output force isThe basic formula of the moving coil transducer is thatAndWherein, the method comprises the steps of, wherein,In order to be able to achieve a constant of transduction,Is a mass blockIs used for the speed of the (c) in the (c),Is a mass blockIs used for the speed of the (c) in the (c),For current flowing through the moving coil transducer), an external circuit (including a voltage ofIs connected to the power supply of the equivalent resistor R). Mass blockBearing periodic external forceWherein, the method comprises the steps of, wherein,Representing the magnitude of the periodic external force,Angular frequency, mass representing periodic external forceIs the object to be vibration isolated. The functional principle of the single-shaft electrodynamic vibration isolator can be represented based on fig. 2. As can be readily seen from FIG. 2, the single-axis electrodynamic vibration isolator belongs to an electromechanical device with two degrees of freedom under periodic excitation, i.eThe method provided by the invention is suitable for detecting the state. Selecting two masses of the mechanical partAndIs of the displacement of (a)AndIs defined as coordinates, its momentumAndThen the generalized momentum is corresponding to the suction sub model of the single-shaft electrodynamic vibration isolatorCan be obtained from formula (37), wherein,，，Is displacement ofIs used for the convergence value of (a),Is displacement ofIs used for the convergence value of (a),Is momentumIs used for the convergence value of (a),Is momentumIs a convergence value of (a).
And 2, constructing a mapping between generalized variables and physical quantities of the generalized variables in an attractor model of the single-shaft type electrodynamic vibration isolator under periodic excitation.
The generalized variable and physical quantity mapping table of the electromechanical device in table 1 according to the present invention can be known as follows: complementary energy coefficient matrixEnergy coefficient matrixDissipation factor matrixGeneralized periodic external force amplitude vectorRespectively is
（39）
In the formula,The resistor is a circuit part of the uniaxial electrodynamic vibration isolator; is the amplitude of the periodic external force; Is the angular frequency of the external force.
According to energy dissipation matricesAnd complementary energy coefficient matrixAnd an energy coefficient matrixAs can be seen from the proportional relationship between them, in the formula (20),，。
The basic parameters of a single-axis electrodynamic vibration isolator are shown in table 2.
Table 2 basic parameters of certain uniaxial electrodynamic vibration isolator
The periodic external force amplitude of the uniaxial electrodynamic vibration isolator is assumed to be。
And 3, calculating an attractor result of the single-shaft type electrodynamic vibration isolator to be detected, and further calculating a performance result.
In combination with generalized variables and attractor models, first, two characteristic values of a single-axis electrodynamic vibration isolator are easily obtained as follows，And obtaining a canonical coordinate transformationThe expression of (2) is:
（40）。
further, an attractor result of the single-axis electrodynamic vibration isolator is obtained The expression of (2) is:
（41）。
under the action of periodic external force, the phase space trajectory of the single-axis type electrodynamic vibration isolator from the initial state to the static state is as shown in fig. 3 (a) - (d), and since the single-axis type electrodynamic vibration isolator is two-degrees of freedom, the phase space dimension thereof is four-dimensional, and four-dimensional images are generally difficult to intuitively draw, for which, the embodiment of the present invention draws four stereoscopic projections thereof in three-dimensional phase space in fig. 3 (a) - (d). As can be seen from fig. 3 (a) - (d), the motion state of the single-axis electrodynamic vibration isolator gradually converged to the attractor, consistent with the results of the present invention.
In the research of the single-shaft electrodynamic vibration isolator, the result of the attractor can be obtained based on the circuit principle and the mechanical principle, which verifies the theoretical correctness of the method provided by the invention. Compared with the calculation based on the circuit principle and the mechanics principle, the method provided by the invention omits the process of constructing and solving the dynamic equation of the single-shaft electrodynamic vibration isolator, thereby having higher calculation efficiency.
In engineering practice, the displacement of two masses in a single-axis electrodynamic vibration isolator is often of concernAnd(Same as generalized displacement) and velocityAnd(The relation with generalized momentum is thatAnd) Vibration isolation efficiency) It can be seen that the results are also easily obtained on the basis of attractors, and as shown in fig. 4 (a) - (b) and fig. 5, respectively, it can be found from fig. 4 (a) - (b) that the displacement and velocity of the mass 1 and the mass 2 are also gradually converged, which is consistent with the results of the single-axis electrodynamic vibration isolator state based on attractors according to the present invention. According to fig. 5, the relationship between the vibration isolation efficiency epsilon of the single-shaft type electrodynamic vibration isolator and the angular frequency omega of the external force can be obtained, and the single-shaft type electrodynamic vibration isolator can be found to have higher vibration isolation efficiency when the angular frequency of the external force is higher. This demonstrates the ability of the attractor to extrapolate to other performance parameters of the single axis electrodynamic vibration isolator.
And 4, identifying the health state of the single-shaft type electrodynamic vibration isolator to be detected.
For two single-shaft electrodynamic vibration isolators of the same type, under the condition of the same external force, the mass block is connected with the vibration isolatorThe displacement, speed, and efficiency of the single axis electrodynamic vibration isolator were tested and the test data are shown in fig. 6 (a) - (c). The health index of the two single-shaft electrodynamic vibration isolators was calculated according to equation (38), resulting in: the displacement health index of the No. 1 single-shaft electrodynamic vibration isolator is 0.0425, the speed health index is 0.2871, and the efficiency health index is 0.0135; the displacement health index of the No. 2 single-shaft type electrodynamic vibration isolator is 0.0969, the speed health index is 0.0017, and the efficiency health index is 0.0838. The health index of the displacement, the speed and the efficiency of the No. 1 single-shaft type electrodynamic vibration isolator can be found to be closer to 0, which indicates that the health state of the No. 1 single-shaft type electrodynamic vibration isolator is better, so that the No. 2 single-shaft type electrodynamic vibration isolator needs to be concerned about whether the No. 2 single-shaft type electrodynamic vibration isolator meets the requirement or not; and for the single-shaft type electric power vibration isolator 1, the speed health index is worse, so that the speed state of the vibration isolator needs to be paid more attention to.
In summary, the invention establishes the performance characterization and state detection method of the electromechanical device based on the attractor based on the physical principle of the operation of the electromechanical device aiming at the periodic excitation of the electromechanical device, can simultaneously have physical interpretability and stronger universality, can carry out rapid migration application on the electromechanical device with multiple scenes and multiple types (including pure mechanical and pure electromagnetic devices) under the periodic excitation, and realizes the high-accuracy health/fault state identification.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.
Claims (2)
1. The method for detecting the state of the electromechanical equipment under the periodic excitation based on the attractor is characterized by comprising the following steps of:
step 1, constructing an attractor model of the electromechanical equipment under periodic excitation of a generalized variable;
The attractor model of the electromechanical equipment under the periodic excitation consists of generalized variables, wherein the generalized variables comprise generalized coordinates, generalized speed, generalized momentum, generalized external force, residual energy function, residual energy coefficient matrix, energy function, energy coefficient matrix, dissipation function, generalized dissipation force and dissipation coefficient matrix;
The method comprises the following specific steps:
step 1.1, constructing a common operation state model of the electromechanical equipment under periodic excitation based on Lagrangian-Maxwell equation, wherein the expression is as follows:
In the formula, Is the first of the electromechanical devicesThe number of generalized coordinates is defined by,Is the total number of degrees of freedom of the electromechanical device; Is the first of the electromechanical devices A generalized velocity; And Respectively the first of the electromechanical devicesA generalized periodic external force and a generalized dissipative force; as a lagrangian function; The time is the moment;
Wherein the Lagrangian function of the electromechanical device The expression of (2) is:
In the formula, Is an energy function of the electromechanical device; is the residual energy function of the electromechanical equipment; Is a generalized coordinate vector; Is a generalized velocity vector;
step 1.2, carrying out regular coordinate transformation on a common operation state model of the electromechanical equipment under periodic excitation to obtain a coordinate transformation model;
step 1.3, constructing an attractor model based on the obtained coordinate transformation model, wherein the method comprises the following specific steps of:
Obtaining an operation state model under each degree of freedom according to the coordinate transformation model;
Wherein the running state model comprises a reference periodic function;
Determining a reference periodic function according to the type of periodic excitation, wherein the reference periodic function comprises a simple harmonic excitation form and a non-simple harmonic periodic excitation form;
Obtaining a complete form of the dynamic equilibrium state of the electromechanical device under periodic excitation when the reference periodic function comprises a simple harmonic excitation form and a non-simple harmonic periodic excitation form The expression is:
wherein, Representing a generalized coordinate equilibrium vector of the electromechanical device under the physical coordinates; Representing a canonical coordinate transformation matrix; Representing a regular generalized velocity equilibrium vector; representing a matrix of residual energy coefficients; representing a regular generalized coordinate equilibrium state vector; representing a generalized momentum balance state vector of the electromechanical device under physical coordinates;
Step 2, mapping generalized variables in an attractor model of the electromechanical device under periodic excitation and corresponding physical quantities of the electromechanical device is constructed;
Step 3, mapping the physical quantity of the electromechanical equipment to be detected into a generalized variable according to the mapping in the step 2; obtaining an attractor result and a performance result of the electromechanical equipment to be detected based on the generalized variable and the attractor model of the electromechanical equipment to be detected;
And 4, carrying out state identification on the electromechanical equipment to be detected based on the attractor result and the performance result of the electromechanical equipment to be detected in the step 3.
2. The state detection method according to claim 1, wherein the specific step of performing regular coordinate transformation on the common operation state model of the electromechanical device under periodic excitation in step 1.2 to obtain a coordinate transformation model is as follows:
Obtaining a transformation formula of a common running state model of the electromechanical equipment under periodic excitation;
Obtaining a general solution of a transformation type simple harmonic function form of a common running state model of the electromechanical equipment under periodic excitation;
obtaining an unfolding determinant about the feature matrix based on a general solution of a transformation formula and a simple harmonic function form of a common operation state model of the electromechanical equipment under periodic excitation; obtaining feature vectors of the feature values of the feature matrix based on the expanded determinant;
Obtaining a regular coordinate transformation model based on the feature vector of the feature value;
and carrying out coordinate transformation on the common operation state model of the electromechanical equipment under periodic excitation by using a regular coordinate transformation model to obtain a coordinate transformation model.
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