A modeling method based on electromagnetic-dynamic coupling of induction motors

Abstract

The present invention relates to a modeling method based on electromagnetic-dynamic coupling of an induction motor, comprising the following steps: constructing a rotor-bearing dynamic model of the induction motor; obtaining a radial air gap length function between a stator and a rotor in the induction motor based on the rotor-bearing dynamic model and with a set fault state as input; obtaining a turn function of the stator and the rotor according to the winding structure of the induction motor, obtaining a winding function of the induction motor based on the turn function and the radial air gap length function, and calculating the self-inductance and mutual inductance of the stator and the rotor based on the turn function, the winding function, and the air gap length function; constructing a multi-loop model of the induction motor, and calculating motor parameters of the induction motor using the self-inductance and mutual inductance of the stator and the rotor as input; and feeding the obtained motor parameters back to the rotor-bearing dynamic model and repeating the aforementioned steps to implement numerical iterative calculation until a model with a preset iteration condition is output and a coupled model is output.

Description

Technical Field

[0001] The present invention relates to the technical field of induction motors, and in particular to a modeling method based on electromagnetic-dynamic coupling of induction motors. Background Art

[0002] According to statistics, about 44% of induction motor failure cases are related to bearings. Implementing effective condition monitoring and fault diagnosis of early bearing failures in induction motors is of practical significance for ensuring the smooth operation of industrial production activities.

[0003] Fault diagnosis approaches are generally categorized as data-driven and model-driven. Compared to data-driven approaches, model-based machine fault simulation can generate sufficient representative signals to meet the data volume requirements of data-driven approaches, avoiding the economical cost of extensive fault testing. Furthermore, the fault model's ability to simulate a variety of fault conditions facilitates the testing and comparison of diagnostic algorithms and helps understand the physical relationships within the machine. Most modeling approaches for diagnosing motor bearing faults focus on constructing a bearing dynamics model and then analyzing the time and frequency domain information in the vibration signal to identify signal signatures that reflect the fault type and severity. Compared to dynamic modeling and vibration signal analysis, there is relatively little research on establishing electromagnetic models and analyzing current signals for motors with bearing faults. Many of these studies use motor models to investigate bearing faults. However, most studies simplify the bearing's dynamics using signal models, ignoring the nonlinearities of bearing operation and oversimplifying the coupling between the electromagnetic and dynamic models.

[0004] The motor modeling methods used in existing general research are, from low to high complexity, the dq method, the multi-loop method, the magnetic equivalent method, and the finite element method. Models with low complexity, such as the dq model, face the difficulty of accurately simulating multiple types of motor faults. Complex models often mean higher computational accuracy and time costs, which is not conducive to the implementation of online fault diagnosis based on model-driven methods. For example, in the journal article "Induction machine model with space harmonics for fault diagnosis based on the convolution theorem" by Sapena-Bano et al., only calculating the motor inductance, the time consumed by the winding function method and the finite element method related to the multi-loop model was 7.571 seconds and 3 hours and 9 minutes respectively, but the calculation results were almost the same.

[0005] Furthermore, as a lumped parameter model, the multi-loop model's computational accuracy is lower than that of magnetic equivalent models and finite element models. However, its consideration of the motor's geometry and winding layout still makes it suitable for analyzing induction motors with arbitrary winding distributions and asymmetric conditions. For several possible mechanical and electrical faults, the multi-loop model offers a significant advantage in terms of the ratio of simulated fault types to computational cost. However, research on bearing fault modeling using multi-loop theory is limited to simulating bearing fault characteristics using a non-uniform air gap distribution signal model. This signal model ignores the various nonlinear factors within the bearing system and simplifies the dynamic response of the rotor-bearing system to a specific function, which is not conducive to obtaining a motor model output that reflects the actual physical conditions. By combining the motor's electromagnetic model with the dynamic model for coupled modeling, it is possible to construct a motor system model that better reflects the actual electromagnetic-magnetic-mechanical interaction conditions and avoid the simplification errors of the signal model. Research on coupled electromagnetic and dynamic models of electric motors is relatively limited. Han et al., in their journal article "Stator Current Model for Detecting Rolling Bearing Faults in Induction Motors Using Magnetic Equivalent Circuits," proposed a method for coupling magnetic equivalent and dynamic models. However, this method is computationally expensive and has complex parameters. Therefore, a method for applying multi-loop models to coupled models is urgently needed. Summary of the Invention

[0006] The object of the present invention is to provide a modeling method based on electromagnetic-dynamic coupling of an induction motor.

[0007] To achieve the above-mentioned object of the invention, the present invention provides a modeling method based on electromagnetic-dynamic coupling of an induction motor, comprising:

[0008] S1. Construct a rotor-bearing dynamics model for an induction motor;

[0009] S2. Based on the rotor-bearing dynamic model and with a set fault state as input, obtaining a radial air gap length function between the stator and rotor of the induction motor;

[0010] S3. Obtaining turns functions of the stator and the rotor according to the winding structure of the induction motor, obtaining a winding function of the induction motor based on the turns function and the radial air gap length function, and calculating self-inductance and mutual inductance of the stator and the rotor based on the turns function, the winding function, and the air gap length function;

[0011] S4. Constructing a multi-loop model of the induction motor and calculating the motor parameters of the induction motor using the self-inductance and mutual inductance of the stator and the rotor as inputs;

[0012] S5. Feedback the acquired motor parameters to the rotor-bearing dynamics model and repeat steps S3 to S5 to achieve coupling and numerical iterative calculation of the rotor-bearing dynamics model and the multi-loop model until the preset iteration conditions are reached to output the coupled rotor-bearing dynamics model and the multi-loop model.

[0013] According to one aspect of the present invention, in step S1, in the step of constructing a rotor-bearing dynamic model in an induction motor, the rotor-bearing dynamic model includes: a rotor-bearing vibration differential equation, a restoring force equation, and a ball contact deformation equation; wherein, the following equations are included:

[0014] Constructing the rotor-bearing vibration differential equation based on the rotor model and the bearing model in the induction motor;

[0015] The restoring force equation and the ball contact deformation equation are constructed based on the bearing model.

[0016] According to one aspect of the present invention, the rotor-bearing vibration differential equation is expressed as:

[0017]

[0018]

[0019] Among them, m r is the rotor mass, c is the rotor damping, F bxi (i=1,2) is the restoring force of the i-th bearing in the x direction, F byi (i=1,2) is the contact force of the i-th bearing in the y direction, and g is the acceleration due to gravity;

[0020] The restoring force equation is constructed based on Hertz contact theory and is expressed as:

[0021]

[0022]

[0023] Among them, F bx Indicates the number of balls is n ball The total restoring force of the bearing in the x direction; F by Indicates the number of balls is n ball The total restoring force of the bearing in the y direction; δ j is the contact deformation of the jth ball; j is the contact coefficient of the jth ball; when δj >0 when λ j =1, otherwise λ j =0;K c is the contact stiffness; θ j is the position of the jth ball angle;

[0024] The ball contact deformation equation is expressed as:

[0025] δ j =x sinθ j +y cosθ j -c l -c lj

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] Among them, δ j is the contact deformation of the jth ball; c1 is the radial clearance of the bearing; c 1j It is the additional radial clearance when the ball passes the peeling position; d b is the ball diameter; D b is the bearing pitch diameter; ω b is the ball track angular velocity; α is the contact angle; ω r is the rotor angular velocity; h is the equivalent spalling depth considering that the ball does not contact the spalling bottom, w apall is the peeling width, R0 is the bearing outer ring radius, θ spall is the peeling starting angle position, Δθ spall is the peeling angle.

[0032] According to one aspect of the present invention, in step S2, the step of obtaining a radial air gap length function between a stator and a rotor in the induction motor based on the rotor-bearing dynamics model and taking a set fault state as input includes:

[0033] Input a set fault state and calculate the contact deformation of each ball in the bearing according to the ball contact deformation equation;

[0034] Obtaining the restoring force of the rotor in the X and Y directions based on the contact deformation, the current rotor angular velocity of the rotor, and the restoring force equation;

[0035] Inputting the obtained restoring force into the rotor-bearing vibration differential equation to obtain the eccentricity and eccentricity angle of the rotor in the X and Y directions;

[0036] A radial air gap length function between the stator and the rotor is obtained based on the obtained eccentricity and eccentricity angle.

[0037] According to one aspect of the present invention, the step of obtaining a radial air gap length function between the stator and the rotor based on the obtained eccentricity and eccentricity angle includes:

[0038] A generalized expression for the air gap length between the stator and the rotor when a bearing fault occurs is obtained, which is expressed as:

[0039]

[0040]

[0041] Among them, θ s is the stator mechanical angle, g0 is the uniform air gap length when there is no eccentricity, e is the eccentricity introduced by the bearing fault, and ψ(t) is the angular position function introduced to take into account the change of the defect position with the rotation of the bearing inner ring;

[0042] Obtain the eccentricity and eccentricity angle of the rotor in the X and Y directions; wherein the eccentricity and the eccentricity angle are respectively expressed as:

[0043]

[0044]

[0045] The eccentricity and the eccentricity angle are introduced into the generalized expression of the air gap length to obtain a radial air gap length function between the stator and the rotor, which is expressed as:

[0046] g(θ s ,t)=g0-d ecc cos(θ ecc -θ s ).

[0047] According to one aspect of the present invention, in step S3, the step of obtaining the turns functions of the stator and the rotor according to the winding structure of the induction motor, and obtaining the winding function of the induction motor based on the turns functions and the radial air gap length function includes:

[0048] The turns functions of the stator and the rotor are obtained respectively; wherein, for a stator with a single-layer winding distribution, the turns function of each phase winding is expressed as:

[0049] i=1:1:p / 2

[0050] n start =2Q s (i-1) / p

[0051]

[0052] Among them, Z s is the number of turns per stator winding; Q pp is the number of slots per pole and per phase, Q s is the total number of stator slots;

[0053] For a rotor with a single rotor bar, the turns function of a single rotor bar is expressed as:

[0054]

[0055] Among them, θ bar is the mechanical angular position of the rotor bars, α r is the mechanical angle between adjacent rotor bars;

[0056] The winding function of the induction motor is obtained based on the turns functions of the stator and the rotor and the radial air gap length function, which is expressed as:

[0057]

[0058] Among them, 〈g -1 (θ s )〉 represents the average value of the inverse function of the air gap length.

[0059] According to one aspect of the present invention, in step S3, the step of calculating the self-inductance and mutual inductance of the stator and the rotor based on the turns function, the winding function and the air gap length function includes:

[0060] Based on Gauss's law and Ampere's law, the mutual inductance formula between any coil C1 and coil C2 between the stator and the rotor is obtained, which is expressed as:

[0061]

[0062] Where μ0 is the air gap permeability, r is the air gap center radius, l is the lamination length, n C1 (θ s ) is the turns function of winding C1, N C2 (θ s ) is the winding function of winding C2, g -1 (θ s ) is the inverse function of the air gap length;

[0063] The rotor mechanical angle of the rotor is introduced, and the mutual inductance formula is converted to:

[0064]

[0065] or,

[0066]

[0067] Among them, θ r represents the rotor mechanical angle;

[0068] The self-inductance and mutual inductance of the stator and the rotor are obtained based on the turns function, the winding function, the air gap length function, and the mutual inductance formula.

[0069] According to one aspect of the present invention, in step S4, in the step of constructing a multi-loop model of the induction motor, the multi-loop model includes: a voltage equation, a flux equation, an electromagnetic torque equation, and a dynamic equation of the induction motor; wherein,

[0070] The voltage equation is expressed as:

[0071]

[0072]

[0073]

[0074]

[0075] Among them, U s is the stator voltage vector; I s,r 、R s,r and λ s,r are the current vector, resistance matrix and flux vector of the stator and rotor respectively; U sa，sb，sc is the three-phase voltage of the stator, i sa，sb，sc is the stator three-phase winding current, Rs is the single-phase stator winding resistance under the assumption of stator symmetry, λ sa，sb，sc is the flux linkage on the three-phase stator winding, n b is the number of rotor bars, R b is the resistance of a single rotor bar, R e is the end ring resistance, i ri (i=1,2,…,n b ) and λ ri (i=1,2,…,n b ) are the current and flux passing through the i-th rotor circuit, i e and λ e are the current and flux through the end ring respectively;

[0076] The magnetic flux equation is expressed as:

[0077] λ s =Lss I s +L sr I r

[0078]

[0079]

[0080]

[0081] Among them, L ss and L rr are the stator self-inductance matrix and the rotor self-inductance matrix respectively; L sr and L rs The stator-rotor mutual inductance matrix and the rotor-stator mutual inductance matrix are respectively, where ;L sisj (i=1,2,3;j=1,2,3) is the mutual inductance between stator phase i and stator phase j, L sirj (i=a,b,c;j=1,2,…,n b ) is the mutual inductance between stator phase i and the jth rotor circuit, L rirj (i=1,2,…,n b ; j=1,2,…,n b ) is the mutual inductance between the i-th and j-th rotor circuits, L b and L e are the rotor bar and end ring leakage inductances respectively;

[0082] The electromagnetic torque equation is expressed as:

[0083]

[0084] Where P is the number of motor poles, θ e is the electrical angle;

[0085] The kinetic equation is expressed as:

[0086]

[0087] Where J is the rotor moment of inertia, ω r is the rotor angular velocity, and T1 is the load torque.

[0088] According to one aspect of the present invention, in step S4, in the step of calculating the motor parameters of the induction motor using the self-inductance and mutual inductance of the stator and the rotor as input, the motor parameters include: rotor angular velocity;

[0089] In step S5, the acquired motor parameters are fed back to the rotor-bearing dynamics model and steps S3 to S5 are repeatedly executed to realize coupling and numerical iterative calculation of the rotor-bearing dynamics model and the multi-loop model. In the step, the rotor angular velocity in the motor parameters is fed back to the rotor-bearing dynamics model and steps S3 to S5 are repeatedly executed to realize coupling and numerical iterative calculation of the rotor-bearing dynamics model and the multi-loop model.

[0090] According to one aspect of the present invention, in step S2, the fault state is at least one of an outer ring fault, an inner ring fault, and a ball fault of the bearing.

[0091] According to one solution of the present invention, the present invention proposes a coupled modeling method based on the multi-loop model of the induction motor and the rotor-bearing system dynamics model. At the same time, an electromagnetic model of the induction motor and a rotor-bearing dynamics model that takes into account nonlinear factors such as bearing radial clearance and Hertzian contact are established. The radial air gap length and the rotor angular velocity are used as coupling parameters for iterative solution. Because the multi-loop model is a lumped parameter model, while taking into account the motor geometry and winding layout, the number of parameters is less than that of the magnetic equivalent model and the finite element model, and the model complexity is lower. Therefore, it can effectively save computing resources and simulate the dynamic response characteristics of the motor under common electrical and mechanical faults. It is conducive to providing rapid data support for fault mechanism research and online intelligent diagnosis methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 is a block diagram schematically showing steps of a modeling method according to one embodiment of the present invention;

[0093] Figure 2 is a flow chart schematically illustrating a modeling method according to one embodiment of the present invention;

[0094] Figure 3 is a structural diagram schematically showing an induction motor according to an embodiment of the present invention;

[0095] Figure 4 is a schematic diagram showing the structure of a rotor-bearing system according to an embodiment of the present invention;

[0096] Figure 5 is a structural diagram schematically showing a bearing outer ring fault according to an embodiment of the present invention;

[0097] Figure 6 is a structural diagram schematically showing bearing fault types according to an embodiment of the present invention;

[0098] Figure 71 is a diagram schematically showing a stator and rotor air gap distribution diagram according to an embodiment of the present invention;

[0099] Figure 8 is a diagram schematically showing an equivalent circuit of a stator winding according to an embodiment of the present invention;

[0100] Figure 9 is a diagram schematically showing a rotor multi-circuit model according to an embodiment of the present invention;

[0101] Figure 10 1 is a diagram schematically showing a comparison of rotor Y-direction vibration spectra (10 Hz) under outer ring fault simulation according to an embodiment of the present invention;

[0102] Figure 11 1 is a diagram schematically showing a comparison of stator current simulation signal spectra (10 Hz) under an outer ring fault according to an embodiment of the present invention;

[0103] Figure 12 1 is a diagram schematically showing a comparison of stator current simulation signal spectra (20 Hz) under an outer ring fault according to an embodiment of the present invention;

[0104] Figure 13 1 is a diagram schematically showing a comparison of rotor Y-direction vibration spectra (10 Hz) under inner race fault simulation according to an embodiment of the present invention;

[0105] Figure 14 1 is a diagram schematically showing a comparison of stator current simulation signal spectra (10 Hz) under an inner ring fault according to an embodiment of the present invention;

[0106] Figure 15 1 is a diagram schematically showing a comparison of stator current simulation signal spectra (20 Hz) under an inner ring fault according to an embodiment of the present invention;

[0107] Figure 16 1 is a diagram schematically showing a comparison of signal spectra (10 Hz) of a motor end cover vibration experiment under an outer race fault according to an embodiment of the present invention;

[0108] Figure 17 1 is a diagram schematically showing a comparison of stator current experimental signal spectra (10 Hz) under an outer ring fault according to an embodiment of the present invention;

[0109] Figure 18 1 is a diagram schematically showing a comparison of signal spectra (20 Hz) of a motor end cover vibration experiment under an outer race fault according to an embodiment of the present invention;

[0110] Figure 19 1 is a diagram schematically showing a comparison of stator current experimental signal spectra (20 Hz) under an outer ring fault according to an embodiment of the present invention. DETAILED DESCRIPTION

[0111] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be derived from these drawings without inventive effort.

[0112] When describing the embodiments of the present invention, the orientation or positional relationship expressed by the terms "longitudinal", "transverse", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside" and "outside" are based on the orientation or positional relationship shown in the relevant drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the above terms should not be understood as limiting the present invention.

[0113] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described one by one here, but the embodiments of the present invention are not limited to the following embodiments.

[0114] Combine Figure 1 and Figure 2 As shown, according to one embodiment of the present invention, a modeling method based on electromagnetic-dynamic coupling of an induction motor includes:

[0115] S1. Construct a rotor-bearing dynamics model for an induction motor;

[0116] S2. Based on the rotor-bearing dynamics model and taking the set fault state as input, obtain a radial air gap length function between the stator and rotor of the induction motor;

[0117] S3. Obtaining the turns function of the stator and rotor according to the winding structure of the induction motor, and obtaining the winding function of the induction motor based on the turns function and the radial air gap length function, and calculating the self-inductance and mutual inductance of the stator and rotor based on the turns function, the winding function and the air gap length function;

[0118] S4. Construct a multi-loop model of the induction motor and calculate the motor parameters of the induction motor using the self-inductance and mutual inductance of the stator and rotor as inputs.

[0119] S5. Feedback the acquired motor parameters to the rotor-bearing dynamics model and repeat steps S3 to S5 to achieve coupling and numerical iterative calculation of the rotor-bearing dynamics model and the multi-loop model until the preset iteration conditions are reached to output the coupled rotor-bearing dynamics model and the multi-loop model.

[0120] like Figure 3 As shown, according to one embodiment of the present invention, in step S1, during the step of constructing a rotor-bearing dynamic model for an induction motor, a motor model of a three-phase, four-pole induction motor is constructed. Based on this motor model, a structural analysis of the rotor and bearings mounted on the rotor is performed. It is found that rotor rotation failures are typically caused by distributed or localized defects on the bearing. Distributed defects often exist at various locations on the bearing assembly and are difficult to characterize using specific frequency characteristics. Therefore, single-point defects, or other localized faults with specific characteristic frequencies, are generally considered for bearing fault research.

[0121] In this embodiment, bearing failures can be divided into three categories: outer ring failure, inner ring failure, and ball failure. Figure 4 As shown in the figure, the rotor-bearing system is separated from the induction motor model, and the rotor-bearing dynamic model is constructed by taking the outer ring fault of the bearing as an example.

[0122] In this embodiment, the rotor-bearing dynamics model includes: a rotor-bearing vibration differential equation, a restoring force equation, and a ball contact deformation equation; wherein:

[0123] The rotor-bearing vibration differential equation is constructed based on the rotor model and bearing model of the induction motor. The rotor-bearing vibration differential equation is expressed as:

[0124]

[0125]

[0126] Among them, m r is the rotor mass, c is the rotor damping, F bxi (i=1,2) is the restoring force of the i-th bearing in the x direction, F byi (i=1,2) is the contact force of the i-th bearing in the y direction, and g is the acceleration due to gravity;

[0127] The restoring force equation and ball contact deformation equation are constructed based on the bearing model; see Figure 5 As shown, the restoring force equation is constructed based on Hertz contact theory, which is expressed as:

[0128]

[0129]

[0130] Among them, F bx Indicates the number of balls is n ball The total restoring force of the bearing in the x direction; F by Indicates the number of balls is nball The total restoring force of the bearing in the y direction; δ j is the contact deformation of the jth ball; j is the contact coefficient of the jth ball; when δ j >0 when λ j =1, otherwise λ j =0;K c is the contact stiffness; θ j is the position of the jth ball angle;

[0131] In this embodiment, the ball contact deformation equation is constructed based on the pure rolling condition of the bearing, which is expressed as:

[0132] δ j =x sinθ j +y cosθ j -c l -c lj

[0133]

[0134]

[0135]

[0136]

[0137]

[0138] Among them, δ j is the contact deformation of the jth ball; c1 is the radial clearance of the bearing; c 1j is the additional radial clearance when the ball passes through the peeling position, which is obtained by simulating the half-wave sine function; d b is the ball diameter; D b is the bearing pitch diameter; ω b is the ball track angular velocity; α is the contact angle; ω r is the rotor angular velocity; h is the equivalent spalling depth considering that the ball does not contact the spalling bottom, w apall is the peeling width, R0 is the bearing outer ring radius, θ spall is the peeling starting angle position, Δθ spall is the peeling angle.

[0139] like Figure 6 As shown, according to one embodiment of the present invention, in step S2, the fault state is at least one of a bearing outer ring fault, an inner ring fault, and a ball fault. In this embodiment, the fault state is input in the initial stage of the model in the form of data on the peeling component (inner ring, outer ring, ball), the peeling position (angle), and the peeling width.

[0140] In this embodiment, since a bearing fault may cause a change in the air gap between the stator and the rotor, thereby affecting the stator-rotor (ie, stator and rotor) inductance and thus the stator current, the bearing fault state may be used as an input.

[0141] Combine Figure 1 and Figure 2 As shown, according to an embodiment of the present invention, in step S2, the step of obtaining the radial air gap length function between the stator and the rotor of the induction motor based on the rotor-bearing dynamics model and taking the set fault state as input includes:

[0142] Input the set fault state and calculate the contact deformation of each ball in the bearing according to the ball contact deformation equation;

[0143] Based on the contact deformation, the current rotor angular velocity, and the restoring force equation, the restoring force of the rotor in the X and Y directions is obtained;

[0144] The obtained restoring force is input into the rotor-bearing vibration differential equation to obtain the eccentricity and eccentricity angle of the rotor in the X and Y directions;

[0145] The radial air gap length function between the stator and the rotor is obtained based on the obtained eccentricity and eccentricity angle. In this embodiment, see Figure 7 As shown, the radial displacement of the rotor in two directions, which is decomposed into the air gap distribution between the stator and the rotor in the dynamic model of the bearing-rotor system, determines the distribution of the air gap between the stator and the rotor. Strictly speaking, due to manufacturing errors and other reasons, the air gap of the induction motor in actual operation is often uneven, and the additional radial displacement of the rotor caused by the bearing fault aggravates this situation. As the induction motor runs, the restoring force pulsation caused by the bearing fault causes the dynamic eccentricity of the rotor, and then a time-varying air gap is obtained. The distribution of the air gap can be calculated in successive numerical iterations. In this embodiment, the coupling path between the electromagnetic-dynamic model in the induction motor is realized by obtaining the radial air gap length function, which includes:

[0146] The generalized expression for the air gap length between the stator and the rotor when the bearing fault occurs is obtained as follows:

[0147]

[0148]

[0149] Among them, θ sis the stator mechanical angle, g0 is the uniform air gap length when there is no eccentricity, e is the eccentricity introduced by the bearing fault (the eccentricity is the magnitude of the eccentric displacement caused by the bearing running to the defect position. Since this part is the theoretical derivation of the characteristic frequency of the stator current due to the bearing fault, the eccentricity is only an assumed constant), ψ(t) is the angular position function introduced to take into account the change of the defect position with the rotation of the bearing inner ring; in this embodiment, the expression formula for the air gap length when a bearing fault exists under ideal conditions is obtained.

[0150] Obtain the eccentricity and eccentricity angle of the rotor in the X and Y directions; wherein, the eccentricity and eccentricity angle of the rotor are obtained respectively by the displacement of the rotor in the two directions at time t, wherein the eccentricity and eccentricity angle are respectively expressed as:

[0151]

[0152]

[0153] Introducing the eccentricity and eccentricity angle into the generalized expression of the air gap length can obtain the radial air gap length function between the stator and the rotor, which is expressed as:

[0154] g(θ s ,t)=g0-d ecc cos(θ ecc -θ s ).

[0155] In this embodiment, the displacement x in two directions calculated by the dynamic model is r 、y r (i.e. the variable x required to calculate the radial air gap length function of the rotor-bearing vibration differential equation r 、y r ) Calculate the eccentricity d ecc and eccentricity angle θ ecc , and then calculate the radial air gap length function g(θ s ,t).

[0156] According to the present invention, by associating the obtained radial air gap length function with the inductance obtained in subsequent steps, the stator current can be influenced in the multi-loop model. This is a clear path for coupling the rotor-bearing system dynamics model to the multi-loop model of the induction motor. Accordingly, the dynamic behavior of the multi-loop model is fed back to the rotor-bearing dynamics model through the transmission of rotor speed parameters. Therefore, the present invention couples the induction motor multi-loop model with the rotor-bearing dynamics model through the air gap length distribution and speed, thereby obtaining an electromagnetic-dynamic coupling model of the induction motor.

[0157] Combine Figure 1 and Figure 2As shown, according to one embodiment of the present invention, accurate inductance calculation is the basis for the correct establishment of the multi-loop model. The leakage inductance of the stator, rotor bars and end rings can be calculated using the motor geometric parameters, but the time-varying self-inductance and mutual inductance of the stator and rotor are usually difficult to measure or accurately estimate. Considering that the winding structure determines the motor magnetomotive force and most of the air gap magnetic permeance, the winding function method provides an effective way to calculate the inductance using the motor winding and air gap length distribution. Similarly, based on the assumptions of the multi-loop model, the winding function method also expands some necessary assumptions:

[0158] 1. The magnetic flux passes through the air gap radially, that is, the axial magnetic flux is negligible;

[0159] 2. The magnetic permeability of magnetic materials is infinite;

[0160] 3. The cogging effect is negligible.

[0161] Furthermore, based on the above assumptions, the calculation process of the self-inductance and mutual inductance of the stator and rotor is carried out. Specifically, in step S3, the steps of obtaining the turns function of the stator and rotor according to the winding structure of the induction motor, and obtaining the winding function of the induction motor based on the turns function and the radial air gap length function include:

[0162] Obtain the turns functions of the stator and rotor respectively; for a stator with a single-layer winding distribution, the turns function of each phase winding is expressed as:

[0163] i=1:1:p / 2

[0164] n start =2Q s (i-1) / p

[0165]

[0166] Among them, Z s is the number of turns per stator winding; Q pp is the number of slots per pole and per phase, Q s is the total number of stator slots;

[0167] For a rotor with a single rotor bar, the turns function of a single rotor bar is expressed as:

[0168]

[0169] Among them, θ bar is the mechanical angular position of the rotor bars, α r is the mechanical angle between adjacent rotor bars;

[0170] The winding function of the induction motor is obtained based on the turns function of the stator and rotor and the radial air gap length function. In the calculation of the winding function method, the winding distribution of the motor stator and rotor is represented by the turns function. The turns function represents the spatial distribution of the number of turns of a stator winding or rotor loop on one side of the motor, while the winding function represents the spatial distribution of the magnetomotive force generated by the current passing through a stator winding or rotor loop. Obviously, the winding function is a function of the turns function and the air gap length. Therefore, the winding function is expressed as:

[0171]

[0172] Among them, 〈g -1 (θ s )〉 represents the average value of the inverse function of the air gap length.

[0173] Combine Figure 1 and Figure 2 As shown, according to one embodiment of the present invention, in step S3, the step of calculating the self-inductance and mutual inductance of the stator and the rotor based on the turns function, the winding function and the air gap length function includes:

[0174] Based on Gauss's law and Ampere's law, the mutual inductance formula between any coil C1 and coil C2 between the stator and rotor is obtained, which is expressed as:

[0175]

[0176] Where μ0 is the air gap permeability, r is the air gap center radius, l is the lamination length, n C1 (θ s ) is the turns function of winding C1, N C2 (θ s ) is the winding function of winding C2, g -1 (θ s ) is the inverse function of the air gap length;

[0177] In the motor, considering the relative motion between the stator and the rotor, the rotor mechanical angle is introduced, and the mutual inductance formula is converted to:

[0178]

[0179] Or, rewritten as a function of time t:

[0180]

[0181] Among them, θ r represents the rotor mechanical angle;

[0182] Furthermore, the self-inductance and mutual inductance of the stator and rotor are obtained based on the turns function, winding function, air gap length function and mutual inductance formula obtained above.

[0183] Combine Figure 1 and Figure 2 As shown, according to one embodiment of the present invention, in addition to obtaining the self-inductance and mutual inductance of the stator and rotor, it is further necessary to construct a multi-loop model of the induction motor to achieve coupling between the rotor-bearing dynamics model and the multi-loop model. In this embodiment, the establishment of the multi-loop model relies on the following assumptions:

[0184] 1. The motor is a linear system powered by a balanced three-phase voltage source;

[0185] 2. Ignore saturation, eddy current loss and friction loss;

[0186] 3. The rotor bars are insulated from each other.

[0187] Then, in step S4, in the step of constructing a multi-loop model of the induction motor, the multi-loop model establishment process is described based on the above assumptions. In this embodiment, the multi-loop model includes: the voltage equation, flux equation, electromagnetic torque equation, and dynamic equation of the induction motor.

[0188] Among them, see Figure 8 and Figure 9 By equating each phase of the stator winding to a series circuit of resistance and leakage inductance, and considering the cage rotor as a loop uniformly distributed in space, the voltage equation for a three-phase squirrel cage induction motor with star connection can be expressed as:

[0189]

[0190]

[0191]

[0192]

[0193] Among them, U s is the stator voltage vector; I s,r 、R s,r and λ s,r are the current vector, resistance matrix and flux vector of the stator and rotor respectively; U sa，sb，sc is the three-phase voltage of the stator, i sa，sb，sc is the stator three-phase winding current, Rs is the single-phase stator winding resistance under the assumption of stator symmetry, λ sa，sb，sc is the flux linkage on the three-phase stator winding, n b is the number of rotor bars, R b is the resistance of a single rotor bar, R e is the end ring resistance, i ri (i=1,2,…,n b ) and λ ri(i=1,2,…,n b ) are the current and flux passing through the i-th rotor circuit, i e and λ e are the current and flux through the end ring respectively;

[0194] Furthermore, the stator and rotor flux equations are expressed as:

[0195] λ s =L ss I s +L sr I r

[0196]

[0197]

[0198]

[0199] Among them, L ss and L rr are the stator self-inductance matrix and the rotor self-inductance matrix respectively; L sr and L rs The stator-rotor mutual inductance matrix and the rotor-stator mutual inductance matrix are respectively, where ;L sisj (i=1,2,3;j=1,2,3) is the mutual inductance between stator phase i and stator phase j, L sirj (i=a,b,c;j=1,2,…,n b ) is the mutual inductance between stator phase i and the jth rotor circuit, L rirj (i=1,2,…,n b ; j=1,2,…,n b ) is the mutual inductance between the i-th and j-th rotor circuits, L b and L e are the rotor bar and end ring leakage inductances respectively;

[0200] Furthermore, the matrix form of the electromagnetic torque equation can be derived from the magnetic energy formula of the linear motor system, which is expressed as:

[0201]

[0202] Where P is the number of motor poles, θ e is the electrical angle;

[0203] Furthermore, the kinetic equation is expressed as:

[0204]

[0205] Where J is the rotor moment of inertia, ωr is the rotor angular velocity, and T1 is the load torque.

[0206] According to the present invention, in a multi-loop model, inductance couples with current through flux linkage, while the air gap length distribution influences the stator and rotor inductance matrices. Air gap length fluctuations can be solved using the bearing-rotor dynamics model. Therefore, the air gap length can be considered a common parameter for both the multi-loop model and the dynamics model, enabling numerical calculations of the multi-loop and bearing-rotor dynamics coupled models through parameter transfer.

[0207] According to one embodiment of the present invention, in step S4, in the step of calculating the motor parameters of the induction motor using the self-inductance and mutual inductance of the stator and the rotor as input, the motor parameters include: rotor angular velocity;

[0208] In step S5, the acquired motor parameters are fed back to the rotor-bearing dynamics model and steps S3 to S5 are repeatedly executed to realize the coupling and numerical iterative calculation of the rotor-bearing dynamics model and the multi-loop model. In the step, the rotor angular velocity in the motor parameters is fed back to the rotor-bearing dynamics model and steps S3 to S5 are repeatedly executed to realize the coupling and numerical iterative calculation of the rotor-bearing dynamics model and the multi-loop model.

[0209] To verify the effectiveness of the coupled model, we simulated a bearing fault on a three-phase, two-pole induction motor (Marathon D391) used in the experiment. The stator winding structure of the induction motor is single-layer. The parameters of the multi-loop model and the rotor-bearing system model are given in Table 1 (induction motor multi-loop model parameters) and Table 2 (rotor-bearing dynamic model parameters), respectively.

[0210]

[0211]

[0212] Table 1

[0213]

[0214] Table 2

[0215] For the SKF6203 bearing parameters given in Table 2, its fault characteristic frequency can be calculated using the aforementioned single point defect classification and its characteristic frequency formula. The outer ring fault frequency of the bearing is f om =3.0681f r , the inner race fault frequency is f im =4.9319f r , the ball failure frequency is f bm =4.0594f rIn the coupled model, two fault types, outer race fault and inner race fault, are simulated, where the spalling position of the outer race fault is set to θ spall = 0° to ensure effective contact between the ball and the spalling location. Since the spalling on the inner ring rotates with the rotor, the inner ring failure is not affected by the initial location of the spalling.

[0216] Firstly, the outer ring fault was simulated and analyzed. Figure 10 The vibration spectrum of the rotor in the Y direction (equivalent to the Y direction of the bearing inner ring) when powered by a 10Hz power supply is shown, comparing the normal and outer ring fault conditions. The comparison shows that the overall vibration amplitude of the bearing dynamic model with an outer ring fault is higher than the normal condition, with prominent amplitudes at the outer ring fault frequency and its harmonics. This phenomenon is consistent with the vibration characteristics of a real bearing outer ring fault. Notably, the vibration spectrum under normal conditions also has prominent amplitudes at the characteristic frequency of the outer ring fault, which is due to the inherent characteristics of the bearing. During the circumferential motion of the rolling elements in the bearing, the arrangement of the rolling elements in the bearing repeats when the subsequent rolling element j moves to the position of the previous rolling element j+1, indicating a certain periodicity in the bearing's compliance (or stiffness). Therefore, relevant literature refers to this as varying compliance (VC) vibration. In single-row bearings, the VC frequency is exactly equal to the ball passing frequency and the bearing outer ring fault frequency.

[0217] Figure 11 and Figure 12 The stator current frequency domain images obtained by simulating the electromagnetic-dynamic coupling model at two power supply frequencies are presented, comparing the normal and outer race fault conditions. The comparison shows that the bearing fault frequency is reflected in the stator current spectrum through the coupling path. In addition to the power supply frequency and its harmonic components, although the outer race fault characteristic frequency is close to some power supply harmonic frequencies due to bearing parameters, the current spectrum under the outer race fault condition is still significantly higher than the normal condition at some characteristic frequencies. Some characteristic frequencies, such as f om -f s ,2f om +f s ,3f om +f s Etc., it has good performance in reflecting outer race faults at both power supply frequencies.

[0218] Secondly, the inner ring fault is simulated and analyzed. The vibration spectrum of the rotor in the Y direction under the condition of inner ring fault is as follows: Figure 13As shown in the figure, the characteristic frequency of the inner race fault and its multiples have significant amplitudes. Because the inner race spalling rotates at the rotor speed during bearing operation, numerous modulation sidebands are present around the characteristic frequency of the inner race fault and its multiples. The intervals between these modulation sidebands are exactly the rotor rotation frequency. Furthermore, the inner race fault does not cause a significant amplitude gain at the VC frequency, indirectly reflecting the overlap between the outer race fault frequency and the VC frequency.

[0219] Figure 14 and Figure 15 The stator current spectrum for an inner race fault, as shown in Figure 1, has more complex frequency components than that for an outer race fault, which is related to the speed modulation present in the inner race fault. Several bearing fault characteristic frequencies, including those in the aforementioned formulas (the stator current fault characteristic frequency formula and the inner race fault characteristic frequency formula), can be found in the spectrum, such as f im -f s -f r ,f im +f s The validity of these characteristic frequency formulas is verified to a certain extent. Furthermore, because speed modulation disperses the limited energy originally concentrated at the characteristic frequency of inner race faults into other frequency components, the amplitude of the characteristic frequency and its harmonics of inner race faults is lower than that of outer race faults. The lower vibration amplitude, reflected in the air gap fluctuations, also results in lower amplitudes of the characteristic frequency components in the stator current. This means that detecting inner race faults based on characteristic frequency amplitudes is more difficult than detecting outer race faults.

[0220] In order to further verify the effectiveness of the coupling model of the present invention, an experimental platform was constructed.

[0221] In this embodiment, the test was conducted on a comprehensive mechanical failure simulation test bench. The test bench primarily consists of an induction motor, a frequency converter, a brake, and a photoelectric sensor. The photoelectric sensor is used to obtain the motor rotor speed. A FLUKE i200s AC current clamp is used to measure the current signals in the three-phase stator windings. The vibration signal of the motor end cover is measured using an IMI 608A11 accelerometer. A 3mm spalling fault is simulated by cutting a groove on the inner side of the outer raceway.

[0222] Figure 16 and Figure 17The vibration spectrum and stator current spectrum of the motor drive end cover at a power supply frequency of 10Hz are shown respectively. In the vibration spectrum, in addition to the rotation frequency and its multiples, significant characteristic components of the bearing outer ring fault can be observed, that is, the outer ring peeling shows significant dynamic characteristics. Since the measurement system is not completely grounded, a 50Hz sensor power supply frequency is introduced. In the stator current spectrum, due to the non-ideal sinusoidal waveform of the power supply voltage output by the inverter, the amplitude of the multiple frequency component of the power supply fundamental frequency is significantly higher than the simulation spectrum. The modulation sidebands around the power supply related frequencies may be caused by torque fluctuations. Excluding the above-mentioned interference components, the amplitude gain at the characteristic frequency of the bearing outer ring fault is still visible. Although the characteristic frequency amplitude in the experimental signal is lower than that of the simulation signal due to reasons that are difficult to consider in the simulation model, such as noise, the characteristic frequencies of the experimental signal and the simulation signal are in good agreement. Characteristic frequency f om -f s ,2f om +f s ,4f om +f s There is a relatively obvious amplitude gain caused by the outer ring fault. Under the same experimental conditions, the power supply frequency is 20Hz, and the vibration spectrum and stator current spectrum are as follows: Figure 18 、 19 As shown in the figure. The vibration spectrum still clearly shows the outer ring fault characteristics. In the stator current spectrum, the characteristic frequency f om -f s ,3f om -f s ,4f om +f s The above experimental results preliminarily verify the effectiveness of the derivation of the motor bearing fault characteristic frequency and the electromagnetic-dynamic coupling model.

[0223] The above contents are merely examples of specific solutions of the present invention. For devices and structures not described in detail, it should be understood that they can be implemented by adopting general devices and methods available in the art.

[0224] The above description is merely one embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A modeling method based on electromagnetic-dynamic coupling of induction motor, characterized in that: include: S1. Constructing a rotor-bearing dynamics model for an induction motor; wherein the rotor-bearing dynamics model includes: a rotor-bearing vibration differential equation, a restoring force equation, and a ball contact deformation equation; wherein, including: Constructing the rotor-bearing vibration differential equation based on the rotor model and the bearing model in the induction motor; Constructing the restoring force equation and the ball contact deformation equation based on the bearing model; S2. Based on the rotor-bearing dynamic model and with a set fault state as input, obtaining a radial air gap length function between the stator and rotor of the induction motor; S3. Obtaining turns functions of the stator and the rotor according to the winding structure of the induction motor, obtaining a winding function of the induction motor based on the turns function and the radial air gap length function, and calculating self-inductance and mutual inductance of the stator and the rotor based on the turns function, the winding function, and the air gap length function; S4. Constructing a multi-loop model of the induction motor, and calculating the motor parameters of the induction motor using the self-inductance and mutual inductance of the stator and the rotor as input; S5. Feeding back the acquired motor parameters to the rotor-bearing dynamics model and repeating steps S3 to S5 to achieve coupling and numerical iterative calculation of the rotor-bearing dynamics model and the multi-loop model until a preset iteration condition is reached and the coupled rotor-bearing dynamics model and the multi-loop model are output; The rotor-bearing vibration differential equation is expressed as: Among them, m r is the rotor mass, c is the rotor damping, F bxi (i=1,2) is the restoring force of the i-th bearing in the x direction, F byi (i=1,2) is the contact force of the i-th bearing in the y direction, and g is the acceleration due to gravity; The restoring force equation is constructed based on Hertz contact theory and is expressed as: Among them, F bx Indicates the number of balls is n ball The total restoring force of the bearing in the x direction; F by Indicates the number of balls is n ball The total restoring force of the bearing in the y direction; δ j is the contact deformation of the jth ball; j is the contact coefficient of the jth ball; when δ j >0 when λ j =1, otherwise λ j =0;K c is the contact stiffness; θ j is the position of the jth ball angle; The ball contact deformation equation is expressed as: d j =xsinθ j +ycosθ j -c l -c lj Among them, δ j is the contact deformation of the jth ball; c1 is the radial clearance of the bearing; c 1j It is the additional radial clearance when the ball passes the peeling position; d b is the ball diameter; D b is the bearing pitch diameter; ω b is the ball track angular velocity; α is the contact angle; ω r is the rotor angular velocity; h is the equivalent spalling depth considering that the ball does not contact the spalling bottom, w apall is the peeling width, R0 is the bearing outer ring radius, θ spall is the peeling starting angle position, Δθ spall is the peeling angle.

2. The modeling method according to claim 1, characterized in that In step S2, the step of obtaining a radial air gap length function between the stator and the rotor of the induction motor based on the rotor-bearing dynamics model and taking a set fault state as input includes: Input a set fault state and calculate the contact deformation of each ball in the bearing according to the ball contact deformation equation; Obtaining the restoring force of the rotor in the X and Y directions based on the contact deformation, the current rotor angular velocity of the rotor, and the restoring force equation; Inputting the obtained restoring force into the rotor-bearing vibration differential equation to obtain the eccentricity and eccentricity angle of the rotor in the X and Y directions; A radial air gap length function between the stator and the rotor is obtained based on the obtained eccentricity and eccentricity angle.

3. The modeling method according to claim 2, characterized in that The step of obtaining a radial air gap length function between the stator and the rotor based on the obtained eccentricity and eccentricity angle includes: A generalized expression for the air gap length between the stator and the rotor when a bearing fault occurs is obtained, which is expressed as: Among them, θ s is the stator mechanical angle, g0 is the uniform air gap length when there is no eccentricity, e is the eccentricity introduced by the bearing fault, and ψ(t) is the angular position function introduced to take into account the change of the defect position with the rotation of the bearing inner ring; Obtain the eccentricity and eccentricity angle of the rotor in the X and Y directions; wherein the eccentricity and the eccentricity angle are respectively expressed as: The eccentricity and the eccentricity angle are introduced into the generalized expression of the air gap length to obtain a radial air gap length function between the stator and the rotor, which is expressed as: g(θ s ,t)=g0-d ecc cos(θ ecc -θ s )。 4. The modeling method according to claim 3, characterized in that In step S3, the steps of obtaining the turns functions of the stator and the rotor according to the winding structure of the induction motor, and obtaining the winding function of the induction motor based on the turns functions and the radial air gap length function include: The turns functions of the stator and the rotor are obtained respectively; wherein, for a stator with a single-layer winding distribution, the turns function of each phase winding is expressed as: i=1:1:p / 2 n start =2Q s (i-1) / p Among them, Z s is the number of turns per stator winding; Q pp is the number of slots per pole and per phase, Q s is the total number of stator slots; For a rotor with a single rotor bar, the turns function of a single rotor bar is expressed as: Among them, θ bar is the mechanical angular position of the rotor bars, α r is the mechanical angle between adjacent rotor bars; The winding function of the induction motor is obtained based on the turns functions of the stator and the rotor and the radial air gap length function, which is expressed as: Among them, 〈g -1 (θ s )〉 represents the average value of the inverse function of the air gap length.

5. The modeling method according to claim 4, characterized in that: In step S3, the step of calculating the self-inductance and mutual inductance of the stator and the rotor based on the turns function, the winding function and the air gap length function includes: Based on Gauss's law and Ampere's law, the mutual inductance formula between any coil C1 and coil C2 between the stator and the rotor is obtained, which is expressed as: Where μ0 is the air gap permeability, r is the air gap center radius, l is the lamination length, n C1 (θ s ) is the turns function of winding C1, N C2 (θ s ) is the winding function of winding C2, g -1 (θ s ) is the inverse function of the air gap length; The rotor mechanical angle of the rotor is introduced, and the mutual inductance formula is converted to: or, Among them, θ r represents the rotor mechanical angle; The self-inductance and mutual inductance of the stator and the rotor are obtained based on the turns function, the winding function, the air gap length function, and the mutual inductance formula.

6. The modeling method according to claim 5, characterized in that: In step S4, in the step of constructing a multi-loop model of the induction motor, the multi-loop model includes: a voltage equation, a flux equation, an electromagnetic torque equation, and a dynamic equation of the induction motor; wherein, The voltage equation is expressed as: Among them, U s is the stator voltage vector; I s,r 、R s,r and λ s,r are the current vector, resistance matrix and flux vector of the stator and rotor respectively; U sa，sb，sc is the three-phase voltage of the stator, i sa，sb，sc is the stator three-phase winding current, Rs is the single-phase stator winding resistance under the assumption of stator symmetry, λ sa，sb，sc is the flux linkage on the three-phase stator winding, n b is the number of rotor bars, R b is the resistance of a single rotor bar, R e is the end ring resistance, i ri (i=1,2,…,n b ) and λ ri (i=1,2,…,n b ) are the current and flux passing through the i-th rotor circuit, i e and λ e are the current and flux through the end ring respectively; The magnetic flux equation is expressed as: λ s =L ss AND s +L sr AND r Among them, L ss and L rr are the stator self-inductance matrix and the rotor self-inductance matrix respectively; L sr and L rs The stator-rotor mutual inductance matrix and the rotor-stator mutual inductance matrix are respectively, where L sisj (i=1,2,3;j=1,2,3) is the mutual inductance between stator phase i and stator phase j, L sirj (i=a,b,c;j=1,2,…,n b ) is the mutual inductance between stator phase i and the jth rotor circuit, L rirj (i=1,2,…,n b ; j=1,2,…,n b ) is the mutual inductance between the i-th and j-th rotor circuits, L b and L e are the rotor bar and end ring leakage inductances respectively; The electromagnetic torque equation is expressed as: Where P is the number of motor poles, θ e is the electrical angle; The kinetic equation is expressed as: Where J is the rotor moment of inertia, ω r is the rotor angular velocity, and T1 is the load torque.

7. The modeling method according to claim 6, characterized in that: In step S4, in the step of calculating the motor parameters of the induction motor using the self-inductance and mutual inductance of the stator and the rotor as input, the motor parameters include: rotor angular velocity; In step S5, the acquired motor parameters are fed back to the rotor-bearing dynamics model and steps S3 to S5 are repeatedly executed to realize coupling and numerical iterative calculation of the rotor-bearing dynamics model and the multi-loop model. In the step, the rotor angular velocity in the motor parameters is fed back to the rotor-bearing dynamics model and steps S3 to S5 are repeatedly executed to realize coupling and numerical iterative calculation of the rotor-bearing dynamics model and the multi-loop model.

8. The modeling method according to any one of claims 1 to 7, characterized in that: In step S2, the fault state is at least one of an outer ring fault, an inner ring fault, and a ball fault of the bearing.

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