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CN118673727B - Performance degradation evaluation method of steady excitation electromechanical equipment based on attractors - Google Patents

Performance degradation evaluation method of steady excitation electromechanical equipment based on attractors Download PDF

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CN118673727B
CN118673727B CN202411060781.3A CN202411060781A CN118673727B CN 118673727 B CN118673727 B CN 118673727B CN 202411060781 A CN202411060781 A CN 202411060781A CN 118673727 B CN118673727 B CN 118673727B
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陈文彬
李晓阳
康锐
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Beihang University
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Abstract

The invention relates to a performance degradation evaluation method of steady-state excitation electromechanical equipment based on an attractor, belongs to the technical field of performance degradation evaluation of electromechanical equipment, and solves the problems that in the performance degradation evaluation of the steady-state excitation electromechanical equipment in the prior art, the coupling effect of multiple microcosmic degradation mechanisms is difficult to consider, and a performance degradation model with strong universality and clear physical mechanism is difficult to build, so that a high-accuracy performance degradation evaluation result of the steady-state excitation electromechanical equipment is provided. The method comprises the following steps: step 1, constructing an attractor model of the electromechanical equipment under the constant excitation of a generalized variable; step 2, constructing a mapping between generalized variables and corresponding physical quantities in an attractor model of the electromechanical device under constant excitation; step 3, constructing a degradation model of the electromechanical equipment under the steady excitation based on the attractors; step 4, obtaining generalized variables of the electromechanical equipment to be detected according to the mapping; and evaluating the service life result of the electromechanical equipment based on the generalized variable and the attractor degradation model.

Description

Performance degradation evaluation method of steady excitation electromechanical equipment based on attractors
Technical Field
The invention belongs to the technical field of degradation evaluation of electromechanical equipment, and particularly relates to a performance degradation evaluation method of steady excitation electromechanical equipment based on an attractor, in particular to a performance degradation evaluation method of a three-phase brushless direct current motor under steady excitation based on the attractor.
Background
As manufacturing technology advances, the design and use of mechanical devices becomes more and more complex, the degree of sophistication thereof increases gradually, and the gradual degradation of the performance of mechanical devices, and even the individual components that make up the mechanical devices, during long-term operation and use, will directly affect the overall performance of the mechanical devices. There are a great deal of equipment performance degradation studies, such as bulletin nos: chinese patent CN109992895B, CN116029164B and CN 113627088B.
With the wide application of electromechanical devices in industrial production and daily life, the problem of performance degradation of electromechanical devices is becoming more important. In general, performance degradation of an electromechanical device is derived from coupling action of multiple degradation mechanisms of the device at a microscopic level, and is reflected in degradation of macroscopic performance of the electromechanical device, which may cause problems of reduced operation efficiency, increased failure rate, and the like. Therefore, how to accurately evaluate the performance degradation of the electromechanical device under consideration of the coupling of multiple microcosmic mechanisms is an important problem to be solved.
In electromechanical devices, steady state excitation is a type of excitation typical of engineering practice, under which electromechanical devices typically have steady state performance characteristics. In the prior art, in performance degradation evaluation aiming at stable excitation electromechanical equipment, two main methods exist: the method is concerned with specific key components of the electromechanical equipment to conduct degradation mode and mechanism research, the method can go deep to the microscopic level of the electromechanical equipment, the interpretation of the microscopic degradation mechanism is realized from the physical mechanism, but the method is difficult to rise to the macroscopic performance level of the electromechanical equipment, the coupling influence mechanism of the multiple microscopic degradation mechanisms on the macroscopic performance degradation of the electromechanical equipment is given, the specificity of the method is very strong, and the method does not have the universality which can be suitable for various electromechanical equipment; the other type is to construct a performance degradation model directly according to input and output to carry out performance degradation evaluation based on a data driving principle, and the method has strong universality due to the application of a data driving method, but is difficult to give out how a multi-microcosmic degradation mechanism is coupled from a physical layer to influence macroscopic performance degradation of the electromechanical device. The above problems make it difficult for the prior art to consider the coupling effect of multiple microscopic degradation mechanisms when evaluating the performance degradation of a stationary electromechanical device, and to give a performance degradation evaluation result with high accuracy, which has strong versatility and a clear physical mechanism.
Disclosure of Invention
In view of the above problems, the invention provides a performance degradation evaluation method of steady-state excitation electromechanical equipment based on an attractor, which solves the problems that in the performance degradation evaluation of the steady-state excitation electromechanical equipment, the coupling effect of multiple microcosmic degradation mechanisms is difficult to consider and a performance degradation model with strong universality and clear physical mechanism is difficult to build in the prior art, and further provides a performance degradation evaluation result with high accuracy of the steady-state excitation electromechanical equipment.
The invention provides a performance degradation evaluation method of steady excitation electromechanical equipment based on an attractor, which is characterized by comprising the following steps of:
Step 1, constructing an attractor model of the electromechanical equipment under the constant excitation of a generalized variable;
The attractor model of the electromechanical equipment under the constant 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;
According to the relation between the energy function of the electromechanical device and the generalized coordinate vector, setting an attractor model of the electromechanical device under constant excitation as three conditions;
Step 2, constructing mapping of generalized variables in an attractor model of the electromechanical device under constant excitation and corresponding physical quantities of the electromechanical device;
Step 3, constructing a degradation model of the electromechanical device under steady excitation based on the attractors according to the mapping in the step 2;
step 3.1, constructing a microscopic parameter degradation model of the electromechanical equipment;
step 3.2, constructing an attractor degradation model of the steady excitation electromechanical device based on the attractor model and the microscopic parameter degradation model;
Step4, mapping the physical quantity of the electromechanical equipment to be detected into a generalized variable according to the mapping relation in the step 2; and evaluating the service life result of the electromechanical device based on the generalized variable of the electromechanical device to be detected and the attractor degradation model for steady excitation of the electromechanical device.
Optionally, the specific steps of constructing the micro-parameter degradation model of the electromechanical device in step 3.1 are as follows:
Analyzing microscopic degradation mechanisms which lead to performance degradation of the electromechanical device, and mapping the microscopic degradation mechanisms to generalized variables of the electromechanical device;
And constructing a microscopic parameter degradation model aiming at parameters which cause the performance degradation of the electromechanical equipment.
Alternatively, microscopic degradation mechanisms of performance degradation of an electromechanical device are mapped onto generalized variables of the electromechanical device as degradation of residual energy coefficients, and dissipation coefficients.
Optionally, the expression of the microscopic parameter degradation model is:
In the formula, For the time of degradationGeneralized variables that degrade at the timeIs a degradation amount of (1); Generalized variables for degradation to occur Is a degradation initial value of (1); To characterize generalized variables where degradation can occur Indication function of degradation direction, performance over degradation timeThe number of the components is increased by +1, otherwise, taking-1; Generalized variables for degradation to occur Performance degradation rate of (2); Generalized variables for degradation to occur Degraded time scale function.
Alternatively, a generalized variable may occur that is degradedRate of performance degradation of (2)The expression of (2) is:
In the formula, Representing degradation rate parameters without consideration of external stress effects; Is the first Generalized variables whose individual effects degradeDegraded external stress; Representing external stress A degree of influence parameter on the degradation rate; u is a generalized variable affecting degradation The number of degraded external stress types; Is the external stress Is a function of the normalization of (a).
Alternatively, according to generalized variables where degradation may occurRate of performance degradation of (2)And the firstGeneralized variables whose individual effects degradeDegraded external stressRelationship between external stressIs a normalized function of (2)The expression of (2) is:
In the formula, AndExternal stresses of the electromechanical devices, respectivelyUpper and lower limits of (2).
Optionally, the functional state of the electromechanical device is also evaluated based on an attractor degradation model that steady excites the electromechanical device.
Compared with the prior art, the invention has at least the following beneficial effects:
(1) The method of the invention provides three generalized variables (comprising residual energy coefficient, energy coefficient and dissipation coefficient) which are micro-common degradation reasons for causing the degradation of the macroscopic performance of the electromechanical equipment, and builds a micro-parameter common degradation model of the generalized variables from the degradation mechanism.
(2) The method combines the microscopic parameter commonality degradation model of the generalized variable with the attractor model thereof aiming at three types of steady excitation electromechanical equipment, builds the performance degradation model of the steady excitation electromechanical equipment based on the attractor, can realize the coupling of multiple microscopic degradation mechanisms, and characterizes the physical mechanism from microscopic parameter degradation to macroscopic performance degradation.
(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 steady excitation. The model has a physical analysis form, can avoid the process of modeling and solving the running state of the steady excitation electromechanical equipment, and remarkably improves the efficiency of performance degradation evaluation.
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 flowchart of the performance degradation evaluation method of the present invention.
Fig. 2 is a functional schematic diagram of a three-phase brushless dc motor according to an embodiment of the present invention.
Fig. 3 (a) - (d) show the degradation tracks of the attractors at different input voltages and different load torques for the three-phase brushless dc motor of the present invention.
Fig. 4 (a) - (b) are life evaluation results of the three-phase brushless dc motor of the present invention as examples.
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.
1-4, The invention provides a performance degradation evaluation method of a steady excitation electromechanical device based on an attractor, which specifically comprises the following steps:
and 1, constructing an attractor model of the electromechanical equipment under the constant excitation of the generalized variable.
Step 1.1, constructing a common operation state model of the electromechanical equipment under constant excitation based on a Hamiltonian regular 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 the first of the electromechanical devices Generalized coordinatesFor physical timeIs the derivative of the (C) represents the first of the electromechanical deviceA generalized velocity; Is the first of the electromechanical devices A generalized momentum; Is the first of the electromechanical devices The generalized momentumFor physical timeIs representative of the generalized inertial force; And Respectively the first of the electromechanical devicesA generalized external force (e.g., voltage, current applied to the electromechanical device) and a generalized dissipative force (e.g., damping force inside the electromechanical device); is the hamiltonian amount of the electromechanical device.
Further, a generalized coordinate vector is obtained，，Is the first of the electromechanical devicesA generalized coordinate; generalized velocity vector，，Is the first of the electromechanical devicesA generalized velocity; generalized momentum vector，，Is the first of the electromechanical devicesAnd a generalized momentum.
Further, hamiltonian of the electromechanical deviceThe expression of (2) is:
（2）
In the formula, Is an energy function of the electromechanical device; As a function of the residual energy of the electromechanical device.
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 devicesGeneralized external forceThe expression of (2) is:
（6）
In the formula, Representing the first component applied to the electromechanical device partThe steady external force at one location (e.g. the constant input torque and constant load torque of a gear reducer are the steady external forces at two locations of the gear reducer),；Is the coordinate vector diameter of the ith position of the electromechanical equipment part component; n represents the total number of positions of the electromechanical device portion components.
Thereby, a generalized external force vector is obtained，。
Specifically, the firstGeneralized external forceA broad sense of force that is not a potential force applied to the electromechanical device from the outside, such as the driving force or load of the system.
Further, the first of the electromechanical devicesIndividual generalized dissipation forcesThe expression of (2) is:
（7）
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:
（8）
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 a mold of (a).
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:
（9）。
thereby, a dissipation factor matrix is obtained 。
The dissipation factor matrix is expressed as:
。
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.
The common running state model of the steady excitation electromechanical device can be applied to mechanical devices and electromagnetic devices under steady excitation. Based on a common operation state model for exciting the electromechanical equipment at steady state, the operation state of the electromechanical equipment can be realized through generalized coordinate vectorsAnd generalized momentum vectorDescription in which the generalized coordinate vectorAnd generalized momentum vectorThe space formed by the stretching is the phase space.
And 1.2, constructing an attractor model based on the common running state model.
Electromechanical devices typically have multiple degrees of freedom, and for multiple degrees of freedom, the electromechanical device is dependent on the energy function of the electromechanical deviceAnd generalized coordinate vectorThe relation between the two is that the common operation state model of the electromechanical equipment under the steady excitation is set as the following three conditions:
case a, when the energy function of the electromechanical device And generalized coordinate vectorWhen the generalized coordinates of part of the energy coefficient matrix are irrelevant and the generalized coordinates of the rest of the energy coefficient matrix are relevantIs semi-positive, in which case the electromechanical device has an energy functionI.e.。
Further, the energy function is recordedThe generalized coordinate vector is irrelevant，，Is the first of the electromechanical devicesFunction of energy and energyAn unrelated generalized coordinate; and energy functionThe related generalized coordinate vector is，，Is the first of the electromechanical devicesFunction of energy and energyIn relation to the generalized coordinates of the object,。
Case b, when the energy function of the electromechanical deviceAnd generalized coordinate vectorWhen all generalized coordinates in the system are irrelevant, the energy coefficient matrixZero matrix, in which case the electromechanical device does not have an energy functionI.e.。
Case c, when the energy function of the electromechanical deviceAnd generalized coordinate vectorWhen all generalized coordinates are related, the energy coefficient matrixIs positive, the energy function of the electromechanical device isI.e.。
Further, for the case a, the common operation state model of the electromechanical device under the steady excitation is converted into a matrix form, and the expression is:
（10）
wherein, Representing a generalized momentum vector; representing generalized momentum vectors For physical timeI.e. the generalized inertial force vector.
Further, the motion equilibrium state of the matrix-form common operation state model of the electromechanical device under the steady excitation under the condition a is obtainedWherein, the method comprises the steps of, wherein,Represents the equilibrium state of the generalized coordinate vector,，Representing the equilibrium state of the generalized momentum vector,. The expression of the motion equilibrium state of the matrix-form common operation state model of the electromechanical device under constant excitation is as follows:
（11）
In the formula, Representation and energy functionIndependent generalized coordinate vectorA corresponding equilibrium state; Representation and energy function Related generalized coordinate vectorsA corresponding equilibrium state; Representation and energy function Independent generalized coordinate vectorConjugated generalized momentum vectorA corresponding equilibrium state; Representation and energy function Related generalized coordinate vectorsConjugated generalized momentum vectorA corresponding equilibrium state; Representation of Removing the lastLine and lastThe sub-matrix of the columns is a matrix,Representation ofRemoving the lastLine and lastA sub-matrix of columns, wherein,Representing a dissipation factor matrix; Representing an energy coefficient matrix Front of (2)Line and frontThe sub-matrix of the columns is a matrix,Wherein, the method comprises the steps of, wherein,Representing an energy coefficient matrixIs the first of (2)Line and thElements of a column; Representation and energy function Independent generalized coordinate vectorThe corresponding generalized external force vector is used for generating a corresponding external force vector,；Representation and energy functionRelated generalized coordinate vectorsThe corresponding generalized external force vector is used for generating a corresponding external force vector,。
Further, the method comprises the steps of,AndAre all real symmetric positive definite matrixes.
In case a, the electromechanical device is in a dynamic equilibrium stateBy analyzing the motion stability, the electromechanical device can be found to be in a motion equilibrium stateNearby, and energy functionsIndependent generalized coordinate vectorIs not contracted in the direction of (5) and is fixed in speedMotion, and energy function of (2)Related generalized coordinate vectorsAnd generalized momentum vectorIs contracted in all directions. Only consider the convergent and non-zero variables in the generalized coordinates and the generalized momentum to obtain the motion equilibrium stateIs stably convergent, and is therefore also calledAs a function of energyRelated generalized coordinate vectorsIs called as the convergence value ofAs a function of energyIndependent generalized coordinate vectorConjugated generalized momentum vectorIs called the dynamic equilibrium stateIn case a, the attractor of the electromechanical device is constantly excited, and the corresponding calculation formula, namely formula (11), becomes an attractor model.
Further, for case b, by letting formula (11)Obtaining an attractor model of the steady excitation electromechanical device in case b, namely: convergence value of generalized momentum vectorThe expression is:
（12）。
further, for case c, by letting formula (11) The attractor model of the steady excitation electromechanical device in case c can be obtained, namely: convergence value of generalized coordinate vectorThe expression is:
（13）。
and 2, constructing a mapping between generalized variables and physical quantities of the generalized variables in an attractor model of the electromechanical equipment under constant excitation.
Mapping of generalized variables and physical quantities of the generalized variables in an attractor model of the electromechanical device under constant 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.
And 3, constructing a degradation model of the electromechanical equipment under the steady excitation based on the attractors.
And 3.1, constructing a microscopic parameter degradation model of the electromechanical equipment.
First, microscopic degradation mechanisms that lead to degradation of the performance of the electromechanical device are analyzed, and parameters that lead to degradation of the performance of the electromechanical device are obtained by mapping the microscopic degradation mechanisms onto generalized variables of the electromechanical device.
Further, microscopic degradation mechanisms of performance degradation of an electromechanical device are mapped onto generalized variables of the electromechanical device as degradation of residual energy coefficients, and dissipation coefficients (i.e., parameters that lead to performance degradation of the electromechanical device).
Illustratively, in electromechanical devices, the aged deformation of the dimensions of the mechanical component and the demagnetization of the magnetic material belong to a degradation of the residual energy coefficient; spring aging causes an increase in the stiffness coefficient and capacitance aging causes a decrease in the capacity, which is a degradation of the energy coefficient; the aging increase of mechanical friction damping and the aging increase of electrical resistance are degradation of the dissipation factor.
Then, a microscopic parameter degradation model is constructed aiming at parameters which lead to the performance degradation of the electromechanical equipment, and the expression is as follows:
（14）
In the formula, Is a generalized variable that can degrade; for the time of degradation Generalized variables that degrade at the timeIs a degradation amount of (1); Generalized variables for degradation to occur Is a degradation initial value of (1); To characterize generalized variables where degradation can occur Indication function of degradation direction, performance over degradation timeThe number of the components is increased by +1, otherwise, taking-1; Generalized variables for degradation to occur Performance degradation rate of (2); Generalized variables for degradation to occur Degraded time scale function.
Further, generalized variables where degradation can occurRate of performance degradation of (2)The expression of (2) is:
（15）
In the formula, Representing degradation rate parameters without consideration of external stress effects; Is the first Generalized variables whose individual effects degradeDegraded external stress; Representing external stress A degree of influence parameter on the degradation rate; u is a generalized variable affecting degradation The number of degraded external stress types; Is the external stress Is a function of the normalization of (a).
Further, according to generalized variables where degradation occursRate of performance degradation of (2)And the firstGeneralized variables whose individual effects degradeDegraded external stressRelationship between external stressIs a normalized function of (2)The expression of (2) is:
（16）
In the formula, AndExternal stresses of the electromechanical devices, respectivelyUpper and lower limits of (2).
Alternatively, in actual engineering applications or scientific research, it may be determined according to specific requirementsAndSuch as upper and lower limits for operating stress levels, upper and lower limits for design limits, or determinations based on product specifications, etc.
Alternatively, the generalized variableDegraded time scale functionThe expression of (2) is: Wherein, the method comprises the steps of, wherein, Is a nonlinear time scale parameter.
And 3.2, constructing an attractor degradation model of the constant excitation electromechanical device based on the attractor model in the step 1 and the microscopic parameter degradation model in the step 3.1.
Substituting a parameter degradation equation (14) of a generalized variable in which degradation occurs into an attractor model of the steady-state excitation electromechanical device for the case a, the case b and the case c of the electromechanical device described in the step 1, and respectively constructing the attractor degradation model of the steady-state excitation electromechanical device based on the attractors.
For case a, a degradation model of a steady-state excitation electromechanical device based on attractorsThe expression of (2) is:
（17）
In the formula, For the time of degradationTime and energy functionsRelated generalized coordinate vectorsDegradation of convergence value of (2); for the time of degradation Time and energy functionsIndependent generalized coordinate vectorConjugated generalized momentum vectorDegradation of convergence value of (2); for the time of degradation Energy coefficient matrix at the timeFront of (2)Line and frontA sub-matrix of columns; for the time of degradation Time removeLast in (3)Line and lastA sub-matrix of columns; for the time of degradation The residual energy coefficient matrix; for the time of degradation A matrix of dissipation coefficients at that time; Representation and energy function Independent generalized coordinate vectorThe corresponding generalized external force vector is used for generating a corresponding external force vector,；Representation and energy functionRelated generalized coordinate vectorsThe corresponding generalized external force vector is used for generating a corresponding external force vector,。
Further, the method comprises the steps of,Wherein, the method comprises the steps of, wherein,For the time of degradationEnergy coefficient matrix at the timeFront of (2)Line and frontColumn sub-matrix ofLine and thElements of a column;， for the time of degradation Matrix of residual energy coefficients at the timeIs the first of (2)Line and thElements of a column;， for the time of degradation The amount of degradation of the equivalent linear dissipation factor at the ith position of the electromechanical device portion assembly.
Representing an energy coefficient matrixFront of (2)Line and frontThe sub-matrix of the columns is a matrix,Wherein, the method comprises the steps of, wherein,Representing an energy coefficient matrixIs the first of (2)Line and thElements of a column;
Further, energy coefficient matrix Is the first of (2)Line and thElements of columnsIs a degradation model of (2)The expression of (2) is:
（18）
In the formula, For the time of degradationTime energy coefficient matrixIs the first of (2)Line and thElements of columnsIs a degradation amount of (1); as a matrix of energy coefficients Is the first of (2)Line and thElements of columnsIs a degradation initial value of (1); to characterize the energy coefficient matrix Is the first of (2)Line and thElements of columnsAn indicator function of degradation direction, an energy coefficient matrixIs the first of (2)Line and thElements of columnsOver time of degradationThe number of the components is increased by +1, otherwise, taking-1; as a matrix of energy coefficients Is the first of (2)Line and thElements of columnsPerformance degradation rate of (2); as a matrix of energy coefficients Is the first of (2)Line and thElements of columnsDegraded time scale function.
Further, the complementary energy coefficient matrixIs the first of (2)Line and thElements of columnsIs a degradation model of (2)The expression of (2) is
（19）
In the formula,For the time of degradationTime complementary energy coefficient matrixIs the first of (2)Line and thElements of columnsIs a degradation amount of (1); Is a complementary energy coefficient matrix Is the first of (2)Line and thElements of columnsIs a degradation initial value of (1); To characterize the complementary energy coefficient matrix Is the first of (2)Line and thElements of columnsIndicative function of degradation direction, matrix of residual energy coefficientsIs the first of (2)Line and thElements of columnsOver time of degradationThe number of the components is increased by +1, otherwise, taking-1; Is a complementary energy coefficient matrix Is the first of (2)Line and thElements of columnsPerformance degradation rate of (2); Is a complementary energy coefficient matrix Is the first of (2)Line and thElements of columnsDegraded time scale function.
Further, the equivalent linear dissipation coefficient at the ith position of the electromechanical device portion assemblyIs a degradation model of (2)The expression of (2) is:
（20）
In the formula, For the time of degradationEquivalent linear dissipation coefficient at ith position of opportunity electrical device section assemblyIs a degradation amount of (1); equivalent linear dissipation coefficient for the ith position of the electromechanical device portion assembly Is a degradation initial value of (1); To characterize the equivalent linear dissipation coefficient of the ith position of the electromechanical device portion assembly An equivalent linear dissipation coefficient of the ith position of the electromechanical device portion componentOver time of degradationThe number of the components is increased by +1, otherwise, taking-1; equivalent linear dissipation coefficient for the ith position of the electromechanical device portion assembly Performance degradation rate of (2); equivalent linear dissipation coefficient for the ith position of the electromechanical device portion assembly Degraded time scale function.
For case b, a degradation model of a steady-state excitation electromechanical device based on attractorsThe expression of (2) is:
（21）
wherein, Representing degradation timeThe residual energy coefficient matrix; Representing degradation time A matrix of dissipation coefficients at that time; representing a generalized external force vector.
Illustratively, when the electromechanical device is single degree of freedom, i.eWhen the method is used, the method is obtained according to the step 1: the complementary energy coefficient matrix is; Dissipation factor matrix ofRecordingIs the generalized equivalent linear dissipation coefficient of the single degree-of-freedom electromechanical device,; Generalized external force vector。
Can obtain a degradation model of the steady excitation electromechanical equipment based on the attractorThe expression of (2) is:
（22）
In the formula, Is thatIs a degradation initial value of (1); Is that An indication function of the direction of degradation,Over time of degradationThe number of the components is increased by +1, otherwise, taking-1; Is that Performance degradation rate of (2); Is that A degraded time scale function; Is that Is a degradation initial value of (1); Is that An indication function of the direction of degradation,Over time of degradationThe number of the components is increased by +1, otherwise, taking-1; Is that Performance degradation rate of (2); Is that Degraded time scale function.
For case c, a degradation model of a steady-state excitation electromechanical device based on attractorsThe expression of (2) is:
（23）
wherein, Representing degradation timeAn energy coefficient matrix at the time; representing a generalized external force vector.
Illustratively, when the electromechanical device is single degree of freedom, i.eWhen the method is used, the method is obtained according to the step 1: the energy coefficient matrix is; Generalized external force vector. Can obtain a degradation model of the steady excitation electromechanical equipment based on the attractorThe expression of (2) is:
（24）
In the formula, Is thatIs a degradation initial value of (1); Is that An indication function of the direction of degradation,Over time of degradationThe number of the components is increased by +1, otherwise, taking-1; Is that Performance degradation rate of (2); Is that Degraded time scale function.
Step 4, mapping the physical quantity of the electromechanical equipment to be detected into a generalized variable according to the mapping relation in the step 2; and evaluating the service life result and the functional state of the electromechanical device based on the generalized variable of the electromechanical device to be detected and the attractor degradation model for steady excitation of the electromechanical device.
Specifically, from an attractor degradation model of a steady-state excitation electromechanical device, including the formula (17) in case a, the formula (21) in case a, and the formula (23) in case c, an arbitrary degradation time can be obtainedThe attractor results of the electromechanical device can be used to evaluate the functional status of the electromechanical device.
Further, acquiring an attractor threshold; by combining with the attractor threshold of the electromechanical device, the life result of the electromechanical device is obtained, and the expression is:
（25）
In the formula, For the lifetime of the electromechanical device,Is thatIs a function of the inverse of (a),An attractor degradation model representing a steady-state excitation electromechanical device; Representing the attractor threshold.
Illustratively, when the regularly excited electromechanical device is a single degree of freedom system in case c, the lifetime expression of the electromechanical device is:
（26）。
in order to illustrate the effectiveness of the method according to the present invention, the above technical solution of the present invention is described in detail by a specific embodiment, and the method according to the present invention is applied by using a three-phase brushless dc motor with a model of D60BLD75-24A-30S as an embodiment, specifically as follows:
And 1, constructing an attractor model of the three-phase brushless direct current motor under the constant excitation of the generalized variable.
Three-phase brushless dc motors are common electromechanical devices whose functional principle can be represented on the basis of fig. 2. As can be seen from fig. 2, the three-phase brushless dc motor belongs to an electromechanical device with two degrees of freedom under constant excitation, i.eThe method provided by the invention is suitable for detecting the state. Selecting charge of a motor circuit portionAnd the rotation angle of the mechanical part output shaftAs generalized coordinates, the corresponding generalized momentums are magnetic fluxesAnd angular momentum. Through basic analysis of the three-phase brushless direct current motor, the motor has no electric field energy in a circuit part, and only has the change of magnetic field energy on equivalent inductance; the gravity does not work in the mechanical part, and the gravitational potential energy of the system is not considered, so thatAndIn which, in the process,Is the number of generalized coordinates independent of the energy function (i.e. gravitational potential energy),Is the number of generalized coordinates related to the energy function (i.e., gravitational potential energy). Based on the analysis, the attractor model of the three-phase brushless DC motor can be knownCan be directly calculated by the formula (12), wherein,Is magnetic fluxIs used for the convergence value of (a),Is angular 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 three-phase brushless direct current motor under constant 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: energy coefficient matrix; Complementary energy coefficient matrixDissipation factor matrixAnd generalized force vector without potential forceThe expressions of (2) are respectively:
（27）
In the formula, Representing the equivalent inductance; Representing the equivalent resistance; representing an equivalent linear friction damping coefficient; Representing a direct current voltage; representing load torque; In order for the moment of inertia to be of interest, Is a constant of the moment of force,Is a back electromotive force constant;
Further, the method comprises the steps of, ：
（28）
In the formula,Represents friction torque; The rotational speed is indicated by the fact that, 。
Further, by combining the generalized variable and the attractor model, the attractor result of the three-phase brushless DC motor can be calculatedThe expression of (2) is:
（29）。
for a three-phase brushless DC motor of model D60BLD75-24A-30S, the basic parameters thereof can be determined according to the usage specifications thereof as shown in Table 2.
Table 2 basic parameters of three-phase brushless dc motor
Suppose the input voltage of a D60BLD75-24A-30S three-phase brushless DC motorLoad torque。
And 3, constructing a degradation model of the three-phase brushless direct current motor under the steady excitation based on the attractors.
And 3.1, constructing a microscopic parameter degradation model of the three-phase brushless direct current motor.
First, a microscopic degradation mechanism which leads to degradation of the performance of the three-phase brushless direct current motor is analyzed, and the following results are obtained: on one hand, torque can squeeze the lubricant, the rotating speed reflects the motion state of the lubricant, and when the torque or the rotating speed is increased, the aging rate of the lubricant is increased; on the other hand, increasing the torque and rotational speed also accelerates wear of the mechanical parts of the motor, resulting in increased impurities in the lubricant. All of the above phenomena cause a decrease in the lubrication state, and the frictional resistance becomes large. The microscopic degradation mechanism of the three-phase brushless direct current motor reflects the equivalent linear friction damping coefficientIs subject to degradation, equivalent linear friction damping coefficientBelongs to dissipation coefficients in generalized variables of three-phase brushless direct current motors.
Further, constructing equivalent linear friction damping coefficientIs expressed as:
（30）
In the formula, Is the initial value of equivalent linear friction damping coefficient degradation; taking +1 as an indication function of the degradation direction of the equivalent linear friction damping coefficient; Indicating degradation rate parameters without considering the influence of external stress, AndRespectively indicate the rotation speedAnd load torqueA degree of influence parameter on the degradation rate; And Respectively the rotation speedsAnd load torqueIs a normalization function of (2); Is a nonlinear time scale parameter.
Further, the rotational speedIs a normalized function of (2)The expression of (2) is:
（31）
In the formula, AndRotational speeds of three-phase brushless DC motors, respectivelyUpper and lower limits of (2).
Further, the load torqueIs a normalized function of (2)The expression of (2) is:
（32）
In the formula, AndLoad torque of three-phase brushless DC motorUpper and lower limits of (2).
Equivalent linear friction damping coefficientThe values of the parameters in the degradation model (30) are shown in Table 3.
Table 3 parameter settings of the friction damping coefficient degradation equation for a three-phase brushless dc motor
And 3.2, constructing an attractor degradation model of the steady excitation three-phase brushless direct current motor.
Bringing equation (30) into an attractor equation (29) for exciting the three-phase brushless direct current motor in a constant manner to obtain a degradation equation of the three-phase brushless direct current motor, wherein the expression is as follows:
（33）。
and 4, evaluating the functional state and service life of the three-phase brushless direct current motor based on an attractor degradation model of the steady excitation three-phase brushless direct current motor.
Assuming that the input voltage range of the three-phase brushless DC motor is 6-24V and the load torque range is 0.05-0.3 N.m, according to an attractor degradation model (33) for exciting the three-phase brushless DC motor at steady state, degradation tracks of attractors under different voltages and load torques can be obtained, and further the functional state of the three-phase brushless DC motor can be evaluated. FIGS. 3 (a) - (d) show two dimensions of a three-phase brushless DC motor attractor for 24V input voltages, different load torques, and 0.3N m load torque, different input voltages, magnetic flux convergence valuesAnd angular momentum convergence valueIs a degradation trace of (a). As can be seen from FIGS. 3 (a) - (d), the magnetic flux convergence value increases with the degradation timeIncreasing and angular momentum convergence valueReduced, and the higher the voltage and the greater the load torque, the flux convergence valueAnd angular momentum convergence valueThe faster the degradation rate of (c).
Further, consider that the performance threshold of the three-phase brushless DC motor includes a rotational speed thresholdAnd a current thresholdWherein the rotational speed thresholdSet to 90% of the initial time rotation speed, current threshold valueIs arranged as. When the rotation speed is lower than the rotation speed threshold valueWhen the three-phase brushless direct current motor cannot output a specified rotating speed; when the current exceeds the current thresholdWhen the three-phase brushless direct current motor is used, the three-phase brushless direct current motor is considered to be easy to generate high-current breakdown failure. According to the relation between the rotating speed and current of the three-phase brushless DC motor and the generalized variable thereof, the angular momentum threshold value is easy to calculateAnd magnetic flux threshold。
Further, the life of the three-phase brushless dc motor in both failures can be calculated according to equation (25), as shown in fig. 4 (a) - (b). As can be seen from fig. 4 (a) - (b), the life results calculated by the two failures are different, and then, according to the competition failure relationship, the minimum value of the two life results is the life result of the three-phase brushless dc motor.
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 (7)

1.一种基于吸引子的定常激励机电设备的性能退化评价方法，其特征在于，具体包括以下步骤：1. A performance degradation evaluation method for a steady-state excitation electromechanical device based on an attractor, characterized in that it specifically comprises the following steps: 步骤1、构建关于广义变量的定常激励下机电设备的吸引子模型，具体步骤为：Step 1: Construct an attractor model of electromechanical equipment under steady excitation of generalized variables. The specific steps are as follows: 步骤1.1、基于哈密顿正则方程构建定常激励下机电设备的共性运行状态模型；Step 1.1, construct a common operating state model of electromechanical equipment under steady excitation based on Hamiltonian canonical equations; 步骤1.2、基于共性运行状态模型构建吸引子模型；Step 1.2, construct an attractor model based on the common operating state model; 其中，定常激励下机电设备的吸引子模型由广义变量组成，广义变量包括广义坐标、广义速度、广义动量、广义外力、余能函数、余能系数矩阵、能量函数、能量系数矩阵、耗散函数、广义耗散力和耗散系数矩阵；Among them, the attractor model of electromechanical equipment under steady excitation is composed of generalized variables, which include generalized coordinates, generalized velocity, generalized momentum, generalized external force, complementary energy function, complementary energy coefficient matrix, energy function, energy coefficient matrix, dissipation function, generalized dissipation force and dissipation coefficient matrix; 根据机电设备的能量函数与广义坐标向量之间的关系，将定常激励下机电设备的吸引子模型设置为三种情况，三种情况为：According to the relationship between the energy function of the electromechanical equipment and the generalized coordinate vector, the attractor model of the electromechanical equipment under steady excitation is set to three cases, which are: 情况a，当机电设备的能量函数与广义坐标向量中部分广义坐标无关、其余广义坐标有关时，能量系数矩阵为半正定，此时机电设备具有能量函数，即；Case a, when the energy function of the electromechanical device With the generalized coordinate vector When some of the generalized coordinates are independent and the rest are related, the energy coefficient matrix is semi-positive definite, then the electromechanical device has an energy function ,Right now ; 情况b，当机电设备的能量函数与广义坐标向量中所有广义坐标均无关时，能量系数矩阵为零矩阵，此时机电设备不具有能量函数，即；Case b, when the energy function of the electromechanical device With the generalized coordinate vector When all generalized coordinates in are independent, the energy coefficient matrix is a zero matrix, and the electromechanical device does not have an energy function ,Right now ; 情况c，当机电设备的能量函数与广义坐标向量中所有广义坐标均有关时，能量系数矩阵为正定，此时机电设备的能量函数，即；Case c, when the energy function of the electromechanical device With the generalized coordinate vector When all generalized coordinates in are related, the energy coefficient matrix is positive definite, then the energy function of the electromechanical equipment ,Right now ; 对于情况a，将定常激励下机电设备的共性运行状态模型转化为矩阵形式，表达式为：For case a, the common operating state model of electromechanical equipment under steady excitation is converted into a matrix form, and the expression is: （10） (10) 其中，表示广义动量向量；表示广义动量向量对物理时间的导数，即广义惯性力向量；in, represents the generalized momentum vector; represents the generalized momentum vector For physical time The derivative of , that is, the generalized inertial force vector; 获取情况a下的定常激励下机电设备的矩阵形式的共性运行状态模型的运动平衡态，其中，表示广义坐标向量的平衡态，，表示广义动量向量的平衡态，；Obtain the kinematic equilibrium state of the common operating state model of the electromechanical equipment in matrix form under steady excitation in case a ,in, represents the equilibrium state of the generalized coordinate vector, , represents the equilibrium state of the generalized momentum vector, ; 其中，定常激励下机电设备的矩阵形式的共性运行状态模型的运动平衡态的表达式为：Among them, the expression of the motion equilibrium state of the matrix form common operation state model of electromechanical equipment under steady excitation is: （11） (11) 式中，表示与能量函数无关的广义坐标向量对应的平衡态；表示与能量函数有关的广义坐标向量对应的平衡态；表示与能量函数无关的广义坐标向量共轭的广义动量向量对应的平衡态；表示与能量函数有关的广义坐标向量共轭的广义动量向量对应的平衡态；表示移除最后行和最后列的子矩阵，表示移除最后行和最后列的子矩阵，其中，表示耗散系数矩阵；表示能量系数矩阵的前行和前列的子矩阵，，其中，表示能量系数矩阵的第行和第列的元素；表示与能量函数无关的广义坐标向量对应的广义外力向量，；表示与能量函数有关的广义坐标向量对应的广义外力向量，；In the formula, Representation and Energy Function Independent generalized coordinate vectors The corresponding equilibrium state; Representation and Energy Function The generalized coordinate vector The corresponding equilibrium state; Representation and Energy Function Independent generalized coordinate vectors Conjugate generalized momentum vector The corresponding equilibrium state; Representation and Energy Function The generalized coordinate vector Conjugate generalized momentum vector The corresponding equilibrium state; express Remove last Row and last The submatrix of columns, express Remove last Row and last A submatrix of columns, where represents the dissipation coefficient matrix; Represents the energy coefficient matrix Before Line and front The submatrix of columns, ,in, Represents the energy coefficient matrix No. Row and Elements of a column; Representation and Energy Function Independent generalized coordinate vectors The corresponding generalized external force vector is, ; Representation and Energy Function The generalized coordinate vector The corresponding generalized external force vector is, ; 通过运动平衡态构成情况a下的定常激励机电设备的吸引子模型；The attractor model of the electromechanical device with steady excitation in case a is formed by the motion equilibrium state; 对于情况b，通过令式（11）中的，获得情况b下的定常激励机电设备的吸引子模型，即：广义动量向量的收敛值，表达式为：For case b, by making (11) , we obtain the attractor model of the electromechanical device with steady excitation under case b, namely: the convergence value of the generalized momentum vector , the expression is: （12） (12) 对于情况c，通过令式（11）中的，可得情况c下的定常激励机电设备的吸引子模型，即：广义坐标向量的收敛值，表达式为：For case c, by making (11) , we can get the attractor model of the electromechanical device with steady excitation under case c, that is: the convergence value of the generalized coordinate vector , the expression is: （13） (13) 步骤2、构建定常激励下机电设备的吸引子模型中广义变量与机电设备对应物理量的映射；Step 2, constructing a mapping between generalized variables in an attractor model of electromechanical equipment under steady excitation and corresponding physical quantities of the electromechanical equipment; 步骤3，构建基于吸引子的定常激励下机电设备的退化模型；Step 3, constructing a degradation model of electromechanical equipment under steady excitation based on attractors; 步骤3.1，构建机电设备的微观参数退化模型，具体步骤如下：Step 3.1, construct the micro-parameter degradation model of electromechanical equipment. The specific steps are as follows: 分析导致机电设备性能退化的微观退化机理，将微观退化机理映射到机电设备的广义变量上获得导致机电设备性能退化的参数；Analyze the microscopic degradation mechanism that causes the performance degradation of electromechanical equipment, and map the microscopic degradation mechanism to the generalized variables of the electromechanical equipment to obtain the parameters that cause the performance degradation of the electromechanical equipment; 针对导致机电设备性能退化的参数构建微观参数退化模型；Construct a micro-parameter degradation model for the parameters that cause performance degradation of electromechanical equipment; 步骤3.2，基于吸引子模型和微观参数退化模型构建定常激励机电设备的吸引子退化模型；Step 3.2, constructing an attractor degradation model of a steady-state excitation electromechanical device based on the attractor model and the microscopic parameter degradation model; 步骤4，根据步骤2的映射关系，将待检测机电设备的物理量映射为广义变量；基于待检测机电设备的广义变量及定常激励机电设备的吸引子退化模型评价机电设备的寿命结果。Step 4: Map the physical quantities of the electromechanical equipment to be tested into generalized variables according to the mapping relationship in step 2; and evaluate the life results of the electromechanical equipment based on the generalized variables of the electromechanical equipment to be tested and the attractor degradation model of the electromechanical equipment with steady excitation. 2.根据权利要求1所述的性能退化评价方法，其特征在于，步骤3.1中构建机电设备的微观参数退化模型的具体步骤为：2. The performance degradation evaluation method according to claim 1 is characterized in that the specific steps of constructing the microscopic parameter degradation model of the electromechanical equipment in step 3.1 are: 分析导致机电设备性能退化的微观退化机理，并映射到机电设备的广义变量上；Analyze the microscopic degradation mechanisms that lead to the performance degradation of electromechanical equipment and map them to the generalized variables of electromechanical equipment; 针对导致机电设备性能退化的参数构建微观参数退化模型。A micro-parameter degradation model is constructed for the parameters that cause performance degradation of electromechanical equipment. 3.根据权利要求2所述的性能退化评价方法，其特征在于，机电设备性能退化的微观退化机理映射到机电设备的广义变量上表现为余能系数、能量系数和耗散系数的退化。3. The performance degradation evaluation method according to claim 2 is characterized in that the microscopic degradation mechanism of the performance degradation of the electromechanical equipment is mapped to the generalized variables of the electromechanical equipment and manifested as the degradation of the residual energy coefficient, energy coefficient and dissipation coefficient. 4.根据权利要求3所述的性能退化评价方法，其特征在于，微观参数退化模型的表达式为：4. The performance degradation evaluation method according to claim 3, characterized in that the expression of the micro-parameter degradation model is: 式中，为退化时间时会发生退化的广义变量的退化量；为会发生退化的广义变量的退化初始值；为表征会发生退化的广义变量退化方向的示性函数，性能随退化时间增大时，，性能随退化时间减小时，；为会发生退化的广义变量的性能退化速率；为会发生退化的广义变量退化的时间尺度函数。In the formula, Degradation time A generalized variable that will degenerate when The amount of degradation; is a generalized variable that may degenerate The degenerate initial value of To characterize the generalized variable that will degenerate Indicative function of degradation direction, performance changes with degradation time When increasing, , performance degradation over time When decreasing, ; is a generalized variable that may degenerate The performance degradation rate of is a generalized variable that may degenerate Time scale function of degradation. 5.根据权利要求4所述的性能退化评价方法，其特征在于，会发生退化的广义变量的性能退化速率的表达式为：5. The performance degradation evaluation method according to claim 4, characterized in that the generalized variable that will be degraded The performance degradation rate The expression is: 式中，表示不考虑外界应力影响时的退化速率参数；为第个影响会发生退化的广义变量退化的外界应力；表示外界应力对退化速率的影响程度参数；，u为影响会发生退化的广义变量退化的外界应力类型数；为外界应力的归一化函数。In the formula, It represents the degradation rate parameter without considering the influence of external stress; For the generalized variable whose effect will degenerate Degenerative external stress; Represents external stress Parameters of influence on degradation rate; , u is a generalized variable that affects the degradation Number of degenerate external stress types; External stress The normalization function of . 6.根据权利要求5所述的性能退化评价方法，其特征在于，根据会发生退化的广义变量的性能退化速率与第个影响会发生退化的广义变量退化的外界应力之间的关系，外界应力的归一化函数的表达式为：6. The performance degradation evaluation method according to claim 5, characterized in that the degradation is based on the generalized variables The performance degradation rate With generalized variable whose effect will degenerate Degenerative external stress The relationship between external stress The normalization function The expression is: 式中，和分别为机电设备的外界应力的上限和下限。In the formula, and The external stress of electromechanical equipment is upper and lower limits. 7.根据权利要求1-6任一项所述的性能退化评价方法，其特征在于，还基于定常激励机电设备的吸引子退化模型评价机电设备的功能状态。7. The performance degradation evaluation method according to any one of claims 1 to 6 is characterized in that the functional state of the electromechanical equipment is also evaluated based on an attractor degradation model of the electromechanical equipment under steady-state excitation.
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