Establishment of asymmetric fault evolution model of ceramic rolling bearing and diagnosis method and system

Abstract

The application relates to an asymmetric fault evolution model establishment and diagnosis method of a ceramic rolling bearing, which comprises the following steps: S1. signal acquisition; S2. data preprocessing; S3. defect geometry modeling; S4. dynamic response simulation; S5. feature extraction; S6. feature matching and fault stage identification; and S7. fault early warning output. The application also provides an asymmetric fault evolution model establishment and diagnosis system of a ceramic rolling bearing. The application introduces asymmetric geometry representation and establishes a differential evolution model on both sides of a defect, so that the model can depict the profile difference between the entering side and the leaving side of the defect and the evolution law of the profile difference under different working conditions, thereby improving the representation capability of the real defect morphology of the ceramic bearing. The application provides a modeling and diagnosis method and system which can describe the asymmetric defect evolution law and is coupled with the vibration response characteristics, and the precision of the fault prediction and diagnosis of the ceramic bearing is improved.

Description

Technical Field

[0001] This invention relates to the field of bearing fault diagnosis technology, specifically to a method and system for establishing and diagnosing asymmetric fault evolution models of ceramic rolling bearings. Background Technology

[0002] Rolling bearings are among the most critical basic components of rotating machinery, and their health directly affects the safety and reliability of the equipment. With the continuous increase in spindle speed and load levels, ceramic materials, due to their high hardness, low density, and excellent wear resistance, are gradually replacing metal bearings in high-speed rotating systems. However, unlike traditional steel bearings, silicon nitride ceramic bearings are prone to asymmetric spalling defects on the outer raceway during operation. Due to the low fracture toughness and high brittleness of ceramic materials, the defect edges exhibit different evolution rates on both sides under the periodic impact of the rolling elements; one side becomes gentler, while the other side continues to expand, forming a sloping edge.

[0003] Most existing fault modeling methods are based on symmetry assumptions and only describe ideal geometric spalling morphology. These models cannot reflect the nonlinear contact characteristics of ceramic materials and the asymmetric evolution of defects, resulting in significant biases in the prediction of vibration response, especially in the early stages of defect identification.

[0004] Therefore, it is necessary to propose a modeling and diagnostic method that can describe the evolution law of asymmetric defects and couple it with vibration response characteristics in order to improve the accuracy of ceramic bearing fault prediction and diagnosis. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide a method and system for establishing and diagnosing an asymmetric fault evolution model of ceramic rolling bearings.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a method for establishing and diagnosing an asymmetric fault evolution model of ceramic rolling bearings, comprising the following steps: S1. Signal Acquisition: Acquire vibration and rotational speed signals during the operation of the rolling bearing; S2. Data preprocessing: The acquired vibration signal is sequentially filtered, denoised, resampled in the angular domain, and normalized to generate a preprocessed signal segment; S3. Defect Geometry Modeling: Constructing an asymmetric evolution geometric model and asymmetry coefficient for the outer ring spalling defect of the rolling bearing. or ( f ); S4. Dynamic Response Simulation: Establish a two-degree-of-freedom coupled dynamic equation, and numerically solve the asymmetric evolution geometric model based on the established two-degree-of-freedom coupled dynamic equation to generate theoretical eigenvectors, including the impact pulse train, envelope spectrum and STFT energy map; S5. Feature Extraction: Perform feature analysis on the preprocessed signal segment obtained in step S2, including envelope analysis, spectrum analysis and time-frequency analysis, and extract time-domain and frequency-domain features related to the theoretical feature vector; S6. Feature Matching and Fault Stage Identification: The feature vector obtained in step S5 is matched and compared with the theoretical feature vector output in step S4 to obtain the envelope spectrum error ΔA, centroid drift ΔC, and STFT similarity S. TF Pulse sequence similarity S imp And calculate feature similarity S According to the asymmetry coefficient or ( f and feature similarity S Comprehensive assessment of defects; S7. Fault warning output: The alarm level is divided according to the stage of the defect. The alarm levels include level 0, level 1, level 2 and level 3, and the corresponding fault warning signal is output.

[0007] Furthermore, in step S1, the vibration signal is acquired by an acceleration sensor mounted on the outer ring of the rolling bearing; the rotational speed signal is acquired by an encoder, grating, or magnetoelectric rotational speed sensor mounted on the spindle.

[0008] Furthermore, in step S2, the filtering process uses a 3BPFI to 10BPFI bandpass filter to process the vibration signal and suppress irrelevant frequency band noise. The denoising process is based on the wavelet transform method, and the vibration signal is subjected to 5-7 layers of wavelet denoising using the Daubechies or Symlets wavelet basis. Angular domain resampling converts the filtered and denoised vibration signal into an angular domain signal based on the rotation speed signal. The normalization process is as follows: based on the sliding window length T and the step size ΔT, the continuous angular domain signal is divided into several signal segments, the signal energy of each signal segment is calculated, and normalization is performed.

[0009] Furthermore, in step S3, when constructing the asymmetric evolution geometric model of the outer ring spalling defect of the rolling bearing, it is first assumed that the rolling bearing has an outer ring spalling defect, with the middle position of the outer ring spalling defect being a trapezoidal groove with an opening at the top. The first and second elevations of the trapezoidal groove have asymmetric defect entry and exit side slopes, respectively; an angular domain is used. f Describe the relative positional relationship between the rolling element and the outer ring spalling defect, defining the inclination angle at which the defect enters the lateral ramp as... i 1( f The angle of inclination of the defect away from the side slope is... i 2( fThe longitudinal wear depth of the defect entering the side slope is... h 1( f The longitudinal wear depth of the defect away from the side slope is... h 2( f The transverse wear width of the defect entering the side slope is... The 1 ( f The transverse wear width of the defect leaving the side slope is... The 2 ( f ); The asymmetric evolution geometric model for the spalling defect in the outer ring of a rolling bearing is constructed as follows: ; In equation (1), Indicates the longitudinal wear depth of the defect entering the side slope. h 1( f ) with angle domain f Changes; Indicates the longitudinal wear depth of the defect away from the side slope. h 2( f ) with angle domain f Changes; v 1( f () represents the relative sliding velocity of the rolling element on the inclined surface at the defect entry point; v 2( f () represents the relative sliding velocity of the rolling element on the slope surface after the defect leaves; ω is the angular velocity of the bearing; h 1( f () represents the longitudinal wear depth of the defect entering the side slope; h 2( f () represents the longitudinal wear depth of the defect as it leaves the side slope; k h This is the equivalent ceramic brittle damage evolution coefficient; p 0 Based on Hertz contact theory, this represents the maximum contact pressure between the rolling element and the outer raceway under defect-free conditions. Δ p 1( f () represents the increase in contact pressure as the defect enters the inclined plane; Δ p 2 ( f () represents the increase in contact pressure as the defect leaves the side slope; F n The equivalent normal load in the contact area between the rolling element and the defect entering or leaving the side slope; I The moment of inertia of the rolling element in the contact area between the rolling element and the defect entering or leaving the side slope. a The contact radius between the rolling element and the defect entering or leaving the side slope; ; R * The equivalent radius of curvature; E * It is the equivalent elastic modulus; i 1( f () represents the angle of inclination at which the defect enters the side slope; i 2( f () represents the angle of inclination of the defect away from the side slope; The 1 ( f () represents the transverse wear width of the defect entering the side slope; The 2 ( f () represents the transverse wear width of the defect as it leaves the side slope; The 1 ( f ), The 2 ( f Introducing second-order terms in ) and An equivalent characterization is performed for the length compensation induced by the curvature of the raceway. c The second-order geometric correction strength, reflecting the curvature / fitness of the raceway, has the dimension of 1 / length. This is applied when the curvature effect is negligible. c→ 0, the formula naturally degenerates into the planar slope approximation; asymmetric coefficient or ( f ) is represented as: ; In formula (3): or ( f )=0 indicates that the defect is symmetrical on both sides; or ( f →1 indicates that the height of the defect is asymmetrical on the left and right sides, that is, the expansion on one side is significant.

[0010] Furthermore, the aforementioned k h The expression is: ; In equation (2), k 0 represents an empirical coefficient; H ref , K IC,ref Used as a reference constant for dimensionless transformation; p , q It is a dimensionless sensitivity index used to characterize the hardness of ceramic bearings. H With fracture toughness K IC The effect of the removal rate of the equivalent brittle material on the strength is taken as follows: p = q =1; By setting initial conditions f =0, which can simulate the entire process of the defect evolving from an initial approximately symmetrical state to an asymmetrical morphology.

[0011] Furthermore, the dynamic equation for step S4 is: ; In equation (4), M For the equivalent mass of the outer ring of the rolling bearing, x This represents the radial displacement response of the outer ring of the rolling bearing relative to the stationary base; x The first and second derivatives are velocity With acceleration ; i Indicates the degrees of freedom for overturning and rotation. i The first and second derivatives are angular velocities, respectively. With angular acceleration ; Q Let be the moment of inertia of the outer ring of the rolling bearing relative to its center of mass; C x and C θ These are the equivalent damping coefficients for radial translation and tilting rotation, respectively; K xx ( f () represents the time-varying radial contact stiffness considering the effects of defects; K xθ ( f The displacement-rotation cross stiffness is... K θx ( f ) represents the rotation-displacement cross stiffness, used to characterize the translation-rotation coupling effect caused by the asymmetric evolution of defects; K θθ ( f () represents the equivalent rotational stiffness; Fx ( t )and M θ ( t These are the equivalent radial excitation force and equivalent overturning moment acting on the outer ring of the rolling bearing, respectively. K xx ( f ) is represented as: ; In equation (5), N b For the number of rolling elements, f j Indicates the first j The angular phase offset of each rolling element relative to the spalling defect on the outer ring of the rolling bearing; f+f j ) indicates the first j Each rolling element in the current angle domain f The absolute angular position below, For the first j Radial contact stiffness when a rolling element crosses the outer ring spalling defect area K xx ( f ) contributions; ; In equation (6), For the first j The displacement-rotation cross stiffness when a rolling element crosses the outer ring spalling defect area K xθ ( f ) contributions; For the first j The rotational-displacement cross stiffness when a rolling element crosses the outer ring spalling defect area K θx ( f ) contributions; For the first j When a rolling element crosses the outer ring spalling defect area, the equivalent rotational stiffness... K θθ ( f ) contributions; , and The expression is as follows: ; In equation (7), i 1( f+f j ) is the first jThe angle of inclination of the defect entry side slope when a rolling element crosses the outer ring spalling defect area; i 2( f+f j ) is the first j The angle of inclination of the defect away from the side slope when a rolling element crosses the outer ring spalling defect area; or ( f+f j ) is the first j The asymmetry coefficient when a rolling element crosses the outer ring spalling defect; ; ; In equation (8), α This is a dimensionless lever arm coefficient; L d ( f+f j ) is the first j The effective length of the rolling element across the spalling defect on the outer ring of the rolling bearing is expressed as: ; In equation (10), L The length of the bottom of the trapezoidal groove for the spalling defect on the outer ring of the rolling bearing; L e1 ( f+f j ) is the first j The lateral wear width of a rolling element crossing a defect into the side slope; L e2 ( f+f j ) is the first j The lateral wear width of a rolling element as it exits the defect from the side slope; In equations (5), (8), and (9), The expression is: ; In equation (11), D( f () is the time-varying displacement excitation function. β 1 represents the stiffness attenuation coefficient of the defect entering the inclined plane. β 2 represents the stiffness attenuation coefficient as the defect leaves the side slope; ; F x ( t )and M θ ( t The expression for ) is: ; In equation (12), For the first j Each rolling element corresponds to the equivalent radial excitation force. F x ( t The contribution of ) is expressed as follows: ; In equation (13), Δ F c =m b oh 2 Δ F c This represents the amplitude of the centrifugal force pulsation of the rolling element. m b The mass of a single rolling element; oh c The angular frequency of the periodic modulation excitation related to the rolling element; t Indicates time; M θ ( t The expression for ) is: ; In equation (14), For the first j Each rolling element has an overturning moment. M θ ( t The contribution of ) is expressed as follows: ; In equation (15), Δ h ( f )= h 1( f )- h 2( f ); p 1( f The contact pressure between the rolling element and the inclined surface where the defect enters is denoted as . p 2( f The contact pressure between the rolling element and the defect-leaning side slope is the pressure at which the rolling element leaves the defect. F c =m b oh 2 R b , F c For the centrifugal force of the rolling element, R b Where is the radius of the rolling element; β Centrifugal force of rolling elements F c Direction and overturning momentM θ ( t The angle between the directions of action.

[0012] Furthermore, the time-varying displacement excitation function D ( f The expression is: ; In equation (16), angle domain f Describes the relative positional relationship between the rolling element and the outer ring spalling defect. The entire process of a single rolling element passing through the outer ring spalling defect region is divided into four characteristic angles. f 1. f 2. f 3. f 4: ; d 1( f This indicates that the rolling element gradually enters the defect-entry side from the normal outer raceway, and its contact displacement smoothly transitions from 0 to the wear depth of the defect-entry side inclined surface. h 1( f To ensure the continuity of the displacement and its first derivative, a cosine transition function is used to describe the process: ; d 2( f This indicates the stage where the rolling element completely detaches from the side slope and falls into the bottom of the trapezoidal groove of the outer ring spalling defect. Its displacement is mainly due to… h 1( f ), h 2( f The combined effect of these factors determines that, considering the geometric flatness and dynamic continuity of the bottom of the trapezoidal groove due to the outer ring spalling defect, the displacement excitation can be approximated as: ; d 3( f This indicates the stage where the rolling element gradually rises from the bottom of the trapezoidal groove of the outer ring spalling defect and moves away from the defect departure side, with its displacement caused by... h 2( f The process smoothly recovers to 0; to maintain the same continuity conditions as the entry phase, a sinusoidal transition function is used to describe the process. .

[0013] Furthermore, in step S6, the feature similarity... S The calculation formula is: ; In equation (20): Δ A For envelope spectrum error, Δ C For center of mass drift, S TF for STFT Similarity S imp For pulse sequence similarity, oh 1~ oh 4 is the weighting coefficient, which satisfies oh 1+ oh 2+ oh 3+ oh 4 = 1; Based on the asymmetry coefficient or ( f and feature similarity S The comprehensive defect assessment stage specifically includes: (1) Initial peeling stage: or ( f )<0.1, S ≥0.8; (2) Asymmetric expansion stage: 0.1≤ or ( f )≤0.4, 0.7≤ S <0.8; (3) Stable wear stage: 0.4 or ( f )≤0.6, 0.5≤ S <0.7; (4) Failure shutdown phase: or ( f >0.6, S< 0.5.

[0014] Furthermore, in step S7, alarm levels are classified according to the defect stage, and corresponding fault warning signals are output, specifically as follows: (1) The alarm level in the initial peeling stage is level 0, and the fault warning signal is: signal normal; (2) The alarm level of the asymmetric expansion stage is level 1, and the fault warning signal is: it is necessary to pay close attention and arrange planned maintenance to avoid further expansion of defects; (3) The alarm level during the stable wear stage is level 2, and the fault warning signal is: it is necessary to immediately organize a shutdown inspection, assess the severity of the defect, and formulate a maintenance plan; (4) The alarm level during the failure shutdown stage is level 3. The fault warning signal is: emergency shutdown is required, and continued operation is strictly prohibited to prevent equipment damage or safety accidents.

[0015] This invention also provides a system for establishing and diagnosing an asymmetric fault evolution model of ceramic rolling bearings, comprising a data acquisition unit, a preprocessing unit, a defect geometry modeling unit, a dynamic analysis unit, a feature extraction unit, a model-measurement matching unit, and an early warning unit; the data acquisition unit is connected to the preprocessing unit, and the preprocessing unit is connected to the feature extraction unit; both the defect geometry modeling unit and the preprocessing unit are connected to the dynamic analysis unit, both the dynamic analysis unit and the feature extraction unit are connected to the model-measurement matching unit, and the model-measurement matching unit is connected to the early warning unit; The acquisition unit is used to acquire vibration signals and rotational speed signals during the operation of the rolling bearing; The preprocessing unit is used to sequentially filter, denoise, resample in the angular domain, and normalize the acquired vibration signal to generate a preprocessed signal segment. The defect geometry modeling unit is used to construct the asymmetric evolution geometric model and asymmetry coefficient of the outer ring spalling defect of the rolling bearing. or ( f ); The dynamic analysis unit is used to establish a two-degree-of-freedom coupled dynamic equation to simulate the entire process of a rolling element crossing an asymmetric defect. Based on the established two-degree-of-freedom coupled dynamic equation, the Runge-Kutta method is used to numerically solve the asymmetric evolution geometric model and generate theoretical eigenvectors, including impact pulse trains, envelope spectra, and STFT energy maps. The feature extraction unit is used to perform feature analysis on the preprocessed signal segments generated by the preprocessing unit, including envelope analysis, spectrum analysis and time-frequency analysis, to extract time-domain features and frequency-domain features related to the theoretical feature vector; The model-test matching unit is used to match and compare the time-domain and frequency-domain features extracted by the feature extraction unit with the theoretical feature vectors generated by the dynamic analysis unit, and calculate the envelope spectrum error ΔA, centroid drift ΔC, and STFT similarity S. TF Pulse sequence similarity S imp And calculate feature similarity S According to the asymmetry coefficient or ( f ) and similarity S Comprehensive assessment of defects; The early warning unit is used to classify the alarm level according to the defect stage determined by the model-measurement matching unit. The alarm levels include level 0, level 1, level 2 and level 3, and output a fault early warning signal.

[0016] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention introduces asymmetric geometric representation and establishes a differential evolution model on both sides of the defect, so that the model can characterize the difference in the contours of the defect entry side and the exit side and its evolution law with working conditions, thereby improving the ability to characterize the true defect morphology of ceramic bearings.

[0017] (2) The present invention constructs a dynamic model that simultaneously considers the coupling effect of radial translation and overturning rotation, and incorporates the coupling terms caused by asymmetric defects into the response calculation, so that the simulated signal is more consistent with the actual measurement in terms of impact pulse, sideband modulation and time-frequency energy transfer.

[0018] (3) The present invention establishes a model-driven feature matching mechanism to evaluate the consistency between theoretical response and measured signal in multiple domain features such as impact sequence, envelope spectrum, and time-frequency diagram, so that the diagnostic conclusion has a clear physical correspondence, which is convenient for engineers to review and track the cause of defect evolution.

[0019] (4) This invention combines asymmetric evolution parameters and multi-domain consistency index to achieve graded identification of different stages of initial spalling, asymmetric expansion, stable wear and failure shutdown, significantly improves the sensitivity to early weak impact and modulation enhancement process, and enhances the continuous monitoring capability of progressive degradation.

[0020] (5) The present invention outputs multi-level early warning results and forms a closed loop with alarm, recording, load reduction and shutdown actions, so that the ceramic bearing operation status assessment, maintenance strategy formulation and whole life cycle health management have an executable basis and engineering implementation. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the asymmetric model of the outer ring spalling defect of the rolling bearing of the present invention; Figure 2 This is a schematic diagram showing the displacement changes of the rolling element entering the outer ring of the rolling bearing as a spalling defect according to the present invention. Figure 3 The graph shows the comparison results of the rolling bearing experimental signal and the simulation signal of the asymmetric evolution geometric model of the present invention in the 1s time domain within 8.0~9.0s. Figure 4 for Figure 3 A magnified view of the area from 8.46 to 8.51 s. Figure 5 This is a comparison of the spectrum of the rolling bearing experimental signal and the simulation signal of the asymmetric evolution geometric model of this invention within the range of 0~500Hz; Figure 6 for Figure 5 Comparison results of the spectrum in the 0~300Hz range; Figure 7The structural framework diagram of the ceramic rolling bearing asymmetric fault evolution model establishment and diagnosis system of this invention is shown below; In the figure, 1-trapezoidal groove; 2-first elevation; 3-second elevation; 4-defect entering the side slope; 5-defect leaving the side slope; 6-rolling body. Detailed Implementation

[0022] The following examples are used to illustrate the present invention, but are not intended to limit the scope of the invention.

[0023] Example 1

[0024] like Figure 1 As shown, a method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings includes the following steps: S1. Signal Acquisition: Acquire vibration and rotational speed signals during the operation of the rolling bearing; In step S1, the vibration signal is acquired by an accelerometer installed on the outer ring of the rolling bearing; the accelerometer has an effective bandwidth of not less than 40kHz, and the sampling frequency of the vibration signal is not less than 20 times the passing frequency of the rolling element, so as to capture the high-frequency impact caused by the peeling defects of the outer ring of the ceramic bearing. The speed signal is acquired by an encoder, grating, or magnetoelectric speed sensor mounted on the spindle; S2. Data preprocessing: The acquired vibration signal is sequentially filtered, denoised, resampled in the angular domain, and normalized to generate a preprocessed signal segment; In step S2, the filtering process uses a 3BPFI to 10BPFI bandpass filter to process the vibration signal and suppress irrelevant frequency band noise. The denoising process is based on the wavelet transform method, and the vibration signal is subjected to 5-7 layers of wavelet denoising using the Daubechies or Symlets wavelet basis. Angular domain resampling converts the filtered and denoised vibration signal into an angular domain signal based on the rotation speed signal. The normalization process is as follows: based on the sliding window length T and the step size ΔT, the continuous angular domain signal is divided into several signal segments, the signal energy of each signal segment is calculated, and normalization is performed.

[0025] S3. Defect Geometry Modeling: Constructing an asymmetric evolution geometric model and asymmetry coefficient for the outer ring spalling defect of the rolling bearing. or ( f ); Reference Figure 1 and Figure 2In step S3, when constructing the asymmetric evolution geometric model of the outer ring spalling defect of the rolling bearing, it is first assumed that the rolling bearing has an outer ring spalling defect. The middle position of the outer ring spalling defect is a trapezoidal groove 1 with an opening at the top. Above the first elevation 2 and the second elevation 3 of the trapezoidal groove 1, there are asymmetric defect entry slope 4 and defect exit slope 5, respectively. (When there are local defects on the raceway surface of the outer ring of the ceramic bearing, during the operation of the bearing, the edges of the local defects will undergo elastoplastic deformation or spalling under the periodic impact force of the rolling elements, causing changes in the morphological characteristics of the edges of the defects and further expanding the area of ​​the defects. The sharp edges on both sides of the initial defects are deformed into planes under the periodic impact force of the rolling elements. The defect edges that undergo elastoplastic deformation can be assumed to have a smooth planar morphology. See the paper Branch NA, Arakere NK, Forster Net al. Critical stresses and strains at the spall edge of a case hardened bearing due to ball impact. International Journal of Fatigue, 2013, 47:) 268-278.); using the angle domain f Describe the relative positional relationship between the rolling element 6 and the outer ring spalling defect, and define the inclination angle at which the defect enters the side slope 4 as . i 1( f The angle of inclination of the defect away from the side slope 5 is... i 2( f The longitudinal wear depth of the defect entering the side slope 4 is... h 1( f The longitudinal wear depth of the defect away from the side slope 5 is... h 2( f The transverse wear width of the defect entering the side slope 4 is... The 1 ( f The transverse wear width of the defect away from the side slope 5 is... The 2 ( f ); The asymmetric evolution geometric model for the spalling defect in the outer ring of a rolling bearing is constructed as follows: ; In equation (1), Indicates the longitudinal wear depth of the defect entering the side slope. h 1( f ) with angle domain f Changes; Indicates the longitudinal wear depth of the defect away from the side slope. h 2( f ) with angle domain f Changes; v 1( f ) represents the relative sliding speed of the rolling element 6 on the inclined surface 4 on the side where the defect enters; v 2( f The relative sliding speed of the rolling element 6 on the inclined surface 5 on the side where the defect leaves is; ω is the angular velocity of the bearing; h 1( f () represents the longitudinal wear depth of the defect entering the side slope 4; h 2( f ) represents the longitudinal wear depth of the defect as it leaves the side slope 5; k h This is the equivalent ceramic brittle damage evolution coefficient; p 0 Based on Hertz contact theory, this represents the maximum contact pressure between rolling element 6 and the outer raceway under defect-free conditions. Δ p 1( f ) represents the contact pressure increment when the defect enters the inclined surface 4; Δ p 2 ( f ) represents the increase in contact pressure as the defect leaves the inclined plane 5; F n The equivalent normal load in the contact area between the rolling element 6 and the defect entering the side slope 4 or the defect leaving the side slope 5; I The moment of inertia of the rolling element 6 in the contact area with the defect entering the inclined plane 4 or the defect leaving the inclined plane 5; a The contact radius between the rolling element 6 and the side slope 4 where the defect enters or the side slope 5 where the defect leaves; ; R * The equivalent radius of curvature; E * It is the equivalent elastic modulus; Calculate Δ p 1( f )hour, F n , I , aThe values ​​are all taken as the values ​​of rolling element 6 and defect entry side slope 4; Calculate Δ p 2( f )hour, F n , I , a The values ​​are all taken as the values ​​of the rolling element 6 and the defect departure side slope 5; i 1( f ) represents the angle of inclination at which the defect enters the side slope 4; i 2( f ) represents the angle of inclination of the defect away from the side slope 5; The 1 ( f ) represents the transverse wear width of the defect entering the side slope 4; The 2 ( f ) represents the transverse wear width of the defect away from the side slope 5; The 1 ( f ), The 2 ( f Introducing second-order terms in ) and An equivalent characterization is performed for the length compensation induced by the curvature of the raceway. c The second-order geometric correction strength, reflecting the curvature / fitness of the raceway, has the dimension of 1 / length. This is applied when the curvature effect is negligible. c→ 0, the formula naturally degenerates into the planar slope approximation; The k h The expression is: ; In equation (2), k 0 represents an empirical coefficient; H ref , K IC,ref Used as a reference constant for dimensionless transformation; p , q It is a dimensionless sensitivity index used to characterize the hardness of ceramic bearings. H With fracture toughness K IC The effect of the removal rate of the equivalent brittle material on the strength is taken as follows: p = q =1; This relationship reflects: when the fracture toughness of ceramic materials... K ICReduced (increased brittleness) or decreased hardness H At this time, the defect edges are more prone to micro-fracture and material peeling, thus increasing the macroscopic degradation rate; By setting initial conditions f =0, which can simulate the entire process of the outer ring peeling defects evolving from an initial approximately symmetrical state to an asymmetrical morphology; asymmetric coefficient or ( f ) is represented as: ; In formula (3): or ( f )=0 indicates that the defect is symmetrical on both sides; or ( f →1 indicates that the height of the defect is asymmetrical on both sides, that is, the expansion on one side is significant; S4. Dynamic Response Simulation: A two-degree-of-freedom coupled dynamic equation is established to simulate the entire process of the rolling element 6 crossing the outer ring spalling defect. Based on the established two-degree-of-freedom coupled dynamic equation, the Runge-Kutta method (existing technology) is used to numerically solve the asymmetric evolution geometric model and generate theoretical eigenvectors, including impact pulse train, envelope spectrum and STFT energy map. The dynamic equation for step S4 is: ; In equation (4), M For the equivalent mass of the outer ring of the rolling bearing, x This represents the radial displacement response of the outer ring of the rolling bearing relative to the stationary base; x The first and second derivatives are velocity With acceleration ; i Indicates the degrees of freedom for overturning and rotation. i The first and second derivatives are angular velocities, respectively. With angular acceleration ; Q Let be the moment of inertia of the outer ring of the rolling bearing relative to its center of mass; C x and C θ These are the equivalent damping coefficients for radial translation and tilting rotation, respectively; K xx ( f () represents the time-varying radial contact stiffness considering the effects of defects; K xθ ( f The displacement-rotation cross stiffness is... K θx ( f ) represents the rotation-displacement cross stiffness, used to characterize the translation-rotation coupling effect caused by the asymmetric evolution of defects; K θθ ( f () represents the equivalent rotational stiffness; F x ( t )and M θ ( t These are the equivalent radial excitation force and equivalent overturning moment acting on the outer ring of the rolling bearing, respectively. This invention employs the angle domain f The equivalent superposition modeling method within the inner ring treats the contact stiffness disturbance caused by the interaction between each rolling element 6 and the outer ring spalling defect as occurring in the angular domain. f The function with phase translation characteristics is superimposed in the system stiffness term, so as to effectively characterize the influence of multiple rolling bodies 6 acting simultaneously on the system dynamic response while keeping the structure of the two-degree-of-freedom coupled dynamic model unchanged. in, K xx ( f ) is represented as: ; In equation (5), N b The number of rolling elements is 6. f j Indicates the first j The angular phase offset of each rolling element 6 relative to the spalling defect on the outer ring of the rolling bearing; f+f j ) indicates the first j The rolling element 6 is in the current angle domain f The absolute angular position below, For the first j When the rolling element 6 crosses the outer ring spalling defect area, the radial contact stiffness... K xx ( f ) contributions; As can be seen from the above formula, when two or more rolling elements 6 simultaneously enter / leave the outer ring spalling defect within a similar angle range and come into contact with the edge of the outer ring spalling defect, their stiffness disturbance contribution will be naturally superimposed in the total stiffness of the system through a summation form, thus effectively characterizing the overlapping effect of "multiple rolling elements acting simultaneously". Similarly, the cross stiffness term, equivalent rotational stiffness, and equivalent excitation term can also be constructed using the same phase translation-summation method to obtain their equivalent totals: ; In equation (6), For the firstj When the rolling element 6 crosses the outer ring spalling defect area, the displacement-rotation cross stiffness is affected. K xθ ( f ) contributions; For the first j When the rolling element 6 crosses the outer ring spalling defect area, the rotational-displacement cross stiffness is affected. K θx ( f ) contributions; For the first j When the rolling element 6 crosses the outer ring spalling defect area, the equivalent rotational stiffness... K θθ ( f ) contributions; , and The expression is as follows: ; In equation (7), i 1( f+f j ) is the first j The angle of inclination of the defect entry side slope 4 when the rolling element 6 crosses the outer ring spalling defect area; i 2( f+f j ) is the first j The angle of inclination of the side slope 5 where the rolling element 6 is located when it crosses the outer ring spalling defect area; or ( f+f j ) is the first j The asymmetry coefficient of a rolling element 6 when it crosses the outer ring spalling defect; ; ; In equation (8), α This is a dimensionless lever arm coefficient; L d ( f+f j ) is the first j The effective length of each rolling element 6 across the spalling defect on the outer ring of the rolling bearing is expressed as: ; In equation (10), L The length of the bottom of the trapezoidal groove 1 for the peeling defect on the outer ring of the rolling bearing; L e1 ( f+f j ) is the first jThe rolling element 6 crosses the defect and enters the lateral wear width of the side slope 4; L e2 ( f+f j ) is the first j Each rolling element 6 spans the lateral wear width of the defect as it leaves the side slope 5; In equations (5), (8), and (9), The expression is: ; In equation (11), D ( f () is the time-varying displacement excitation function. β 1 represents the stiffness attenuation coefficient of the defect entering the inclined plane 4. β 2 is the stiffness attenuation coefficient when the defect leaves the side slope 5; ; F x ( t )and M θ ( t The expression for ) is: ; In equation (12), For the first j Each rolling element has 6 pairs of equivalent radial excitation forces. F x ( t The contribution of ) is expressed as follows:

[0026] In equation (13), Δ F c =m b oh 2 Δ F c The amplitude of centrifugal force pulsation of rolling element 6. m b The mass of a single rolling element 6; oh c The angular frequency of the periodic modulation excitation associated with the rolling element 6; t Indicates time; M θ ( t The expression for ) is: ; In equation (14), For the first j Each rolling element has 6 pairs of overturning moments. Mθ ( t The contribution of ) is expressed as follows: ; In equation (15), Δ h ( f )= h 1( f )- h 2( f ); p 1( f The contact pressure between the rolling element 6 and the inclined surface 4 where the defect enters is ( ). p 2( f The contact pressure between the rolling element 6 and the defect-free side slope 5 is the pressure applied between the rolling element 6 and the defect-free side slope 5. F c =m b oh 2 R b , F c For the centrifugal force of rolling element 6, R b The radius of the rolling element is 6. β Centrifugal force for rolling element 6 F c Direction and overturning moment M θ ( t The angle between the directions of action.

[0027] The time-varying displacement excitation function D ( f The expression is: ; In equation (16), Reference Figure 2 , angle domain f Describe the relative positional relationship between the rolling element 6 and the outer ring spalling defect. The entire process of a single rolling element 6 passing through the outer ring spalling defect region is divided into four characteristic angles. f 1. f 2. f 3. f 4: ; d 1( f This indicates that the rolling element 6 gradually enters the defect entry side stage from the normal outer raceway, and its contact displacement smoothly transitions from 0 to the wear depth of the defect entry side inclined surface 4. h 1( f To ensure the continuity of the displacement and its first derivative, a cosine transition function is used to describe the process: ; d 2( f This indicates the stage where the rolling element 6 completely detaches from the side slope 4 and falls into the bottom of the trapezoidal groove 1 of the outer ring spalling defect. Its displacement is mainly caused by... h 1( f ), h 2( f The combined effect determines that, considering the geometric flatness and dynamic continuity of the bottom of the trapezoidal groove 1 with outer ring spalling defects, the displacement excitation can be approximated as: ; d 3( f This indicates that the rolling element 6 gradually rises from the bottom of the trapezoidal groove 1 of the outer ring spalling defect and moves away from the side where the outer ring spalling defect leaves, and its displacement is due to... h 2( f The process smoothly recovers to 0; to maintain the same continuity conditions as the entry phase, a sinusoidal transition function is used to describe the process. ; S5. Feature Extraction: Perform feature analysis on the preprocessed signal segment obtained in step S2, including envelope analysis, spectrum analysis and time-frequency analysis, and extract time-domain and frequency-domain features related to the theoretical feature vector; S6. Feature Matching and Fault Stage Identification: The feature vector obtained in step S5 is matched and compared with the theoretical feature vector output in step S4 to obtain the envelope spectrum error ΔA, centroid drift ΔC, and STFT similarity S. TF Pulse sequence similarity S imp And calculate feature similarity S According to the asymmetry coefficient or ( f and feature similarity S Comprehensive assessment of defects; Feature similarity in step S6 S The calculation formula is: ; In equation (20): Δ A For envelope spectrum error, Δ C For center of mass drift, S TF for STFT Similarity S imp For pulse sequence similarity, oh 1~ oh 4 is the weighting coefficient, which satisfies oh 1+ oh2+ oh 3+ oh 4 = 1; Where, Δ A、 Δ C、S TF 、S imp All results were obtained using conventional normalization calculation methods in the field of signal processing.

[0028] Based on the asymmetry coefficient or ( f and feature similarity S The comprehensive defect assessment stage specifically includes: (1) Initial peeling stage: or ( f )<0.1, S ≥0.8; (2) Asymmetric expansion stage: 0.1≤ or ( f )≤0.4, 0.7≤ S <0.8; (3) Stable wear stage: 0.4 or ( f )≤0.6, 0.5≤ S <0.7; (4) Failure shutdown phase: or ( f >0.6, S< 0.5.

[0029] S7. Fault warning output: The alarm level is divided according to the stage of the defect. The alarm levels include level 0, level 1, level 2 and level 3, and a fault warning signal is output.

[0030] In step S7, alarm levels are classified according to the defect stage, and corresponding fault warning signals are output, specifically as follows: (1) The alarm level in the initial peeling stage is level 0, and the fault warning signal is: signal normal; (2) The alarm level of the asymmetric expansion stage is level 1, and the fault warning signal is: it is necessary to pay close attention and arrange planned maintenance to avoid further expansion of defects; (3) The alarm level during the stable wear stage is level 2, and the fault warning signal is: it is necessary to immediately organize a shutdown inspection, assess the severity of the defect, and formulate a maintenance plan; (4) The alarm level during the failure shutdown stage is level 3. The fault warning signal is: emergency shutdown is required, and continued operation is strictly prohibited to prevent equipment damage or safety accidents.

[0031] To verify the effectiveness of the asymmetric evolutionary geometric model established in this invention, a silicon nitride ceramic rolling bearing was selected as the test object using a ceramic rolling bearing fault simulation test bench. The time-domain and frequency-domain signals of the rolling bearing experiment were collected and compared with the simulation signals of the asymmetric evolutionary geometric model of this invention, resulting in the following... Figure 3 The comparison results of the 1-second time domain within the range of 8.0~9.0s are shown in the figure, and Figure 4 The image shown is a magnified view of the local area from 8.46 to 8.51 s. Figure 3 and Figure 4 It can be seen that the simulated signal of the asymmetric evolution geometric model is close to the experimental results in terms of overall fluctuation intensity and the rhythm of the occurrence of impact clusters, indicating that the model can reproduce the non-stationary response caused by defect excitation and can capture the transient response characteristics of the defect passage zone on a short time scale.

[0032] At the same time, such as Figure 5 The results show a comparison of the spectral frequencies within the range of 0-500Hz. It can be seen that... f BPFO The experimental signal and the simulated signal from the asymmetric evolution geometric model show good consistency at characteristic frequency positions. f BPFO and its second harmonic 2 f BPFO The presence of distinct spectral peaks at all locations indicates that the asymmetric evolutionary geometry model can effectively reconstruct the dominant frequency components corresponding to the excitation of outer-ring spalling defects. Although the amplitudes of some non-characteristic peaks differ, the positions of the main peak frequencies are consistent with the relative energy distribution, which can meet the requirements for fault characteristic interpretation and model verification.

[0033] Figure 6 Further, spectral comparison results within the 0–300 Hz range are provided. From Figure 6 It can be seen from this that, except f BPFO Outside the main peak, the experimental signal and the simulated signal are... f BPFO -2f r , f BPFO -f r , f BPFO +f r and f BPFO +2f rThe corresponding sideband components can be identified at each location, indicating that the model can reproduce the sideband structure under frequency conversion modulation. This result shows that the asymmetric evolution geometric model of the present invention can not only characterize the defect through the frequency itself, but also capture the modulation characteristics formed by its coupling with the frequency conversion, thereby supporting an equivalent description of the asymmetric evolution vibration mechanism at the frequency domain level.

[0034] Example 2

[0035] Reference Figure 7 A system for establishing and diagnosing an asymmetric fault evolution model of ceramic rolling bearings includes an acquisition unit, a preprocessing unit, a defect geometry modeling unit, a dynamic analysis unit, a feature extraction unit, a model-measurement matching unit, and an early warning unit. The acquisition unit is connected to the preprocessing unit, and the preprocessing unit is connected to the feature extraction unit. The defect geometry modeling unit and the preprocessing unit are both connected to the dynamic analysis unit, the dynamic analysis unit and the feature extraction unit are both connected to the model-measurement matching unit, and the model-measurement matching unit is connected to the early warning unit. The acquisition unit is used to acquire vibration signals and rotational speed signals during the operation of the rolling bearing; The preprocessing unit is used to sequentially filter, denoise, resample in the angular domain, and normalize the acquired vibration signal to generate a preprocessed signal segment. The defect geometry modeling unit is used to construct the asymmetric evolution geometric model and asymmetry coefficient of the outer ring spalling defect of the rolling bearing. or ( f ); The dynamic analysis unit is used to establish a two-degree-of-freedom coupled dynamic equation to simulate the entire process of a rolling element crossing an asymmetric defect. Based on the established two-degree-of-freedom coupled dynamic equation, the Runge-Kutta method is used to numerically solve the asymmetric evolution geometric model and generate theoretical eigenvectors, including impact pulse trains, envelope spectra, and STFT energy maps. The feature extraction unit is used to perform feature analysis on the preprocessed signal segments generated by the preprocessing unit, including envelope analysis, spectrum analysis and time-frequency analysis, to extract time-domain features and frequency-domain features related to the theoretical feature vector; The model-test matching unit is used to match and compare the time-domain and frequency-domain features extracted by the feature extraction unit with the theoretical feature vectors generated by the dynamic analysis unit, and calculate the envelope spectrum error ΔA, centroid drift ΔC, and STFT similarity S. TF Pulse sequence similarity S imp And calculate feature similarity S According to the asymmetry coefficient or ( f ) and similarity S Comprehensive assessment of defects; The early warning unit is used to classify the alarm level according to the defect stage determined by the model-measurement matching unit. The alarm levels include level 0, level 1, level 2 and level 3, and output a fault early warning signal.

[0036] It is understood that, although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings, characterized in that, Includes the following steps: S1. Signal Acquisition: Acquire vibration and rotational speed signals during the operation of the rolling bearing; S2. Data preprocessing: The acquired vibration signal is sequentially filtered, denoised, resampled in the angular domain, and normalized to generate a preprocessed signal segment; S3. Defect Geometry Modeling: Constructing an asymmetric evolution geometric model and asymmetry coefficient for the outer ring spalling defect of the rolling bearing. η ( φ ); S4. Dynamic Response Simulation: Establish a two-degree-of-freedom coupled dynamic equation, and numerically solve the asymmetric evolution geometric model based on the established two-degree-of-freedom coupled dynamic equation to generate theoretical eigenvectors, including the impact pulse train, envelope spectrum and STFT energy map; S5. Feature Extraction: Perform feature analysis on the preprocessed signal segment obtained in step S2, including envelope analysis, spectrum analysis and time-frequency analysis, and extract time-domain and frequency-domain features related to the theoretical feature vector; S6. Feature Matching and Fault Stage Identification: The feature vector obtained in step S5 is matched and compared with the theoretical feature vector output in step S4 to obtain the envelope spectrum error ΔA, centroid drift ΔC, and STFT similarity S. TF Pulse sequence similarity S imp And calculate feature similarity S According to the asymmetry coefficient η ( φ and feature similarity S Comprehensive assessment of defects; S7. Fault warning output: The alarm level is divided according to the stage of the defect. The alarm levels include level 0, level 1, level 2 and level 3, and the corresponding fault warning signal is output.

2. The method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings as described in claim 1, characterized in that, In step S1, the vibration signal is acquired by an acceleration sensor installed on the outer ring of the rolling bearing; the rotational speed signal is acquired by an encoder, grating, or magnetoelectric rotational speed sensor installed on the spindle.

3. The method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings as described in claim 1, characterized in that, In step S2, the filtering process uses a 3BPFI to 10BPFI bandpass filter to process the vibration signal and suppress irrelevant frequency band noise. The denoising process is based on the wavelet transform method, and the vibration signal is subjected to 5-7 layers of wavelet denoising using the Daubechies or Symlets wavelet basis. Angular domain resampling converts the filtered and denoised vibration signal into an angular domain signal based on the rotation speed signal. The normalization process is as follows: based on the sliding window length T and the step size ΔT, the continuous angular domain signal is divided into several signal segments, the signal energy of each signal segment is calculated, and normalization is performed.

4. The method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings as described in claim 1, characterized in that, In step S3, when constructing the asymmetric evolution geometric model of the outer ring spalling defect of the rolling bearing, the rolling bearing is first assumed to have an outer ring spalling defect. The middle position of the outer ring spalling defect is a trapezoidal groove with an opening at the top. Above the first and second elevations of the trapezoidal groove, there are asymmetric defect entry and defect exit side slopes, respectively. An angular domain is used. φ Describe the relative positional relationship between the rolling element and the outer ring spalling defect, defining the inclination angle at which the defect enters the lateral ramp as... θ 1( φ The angle of inclination of the defect away from the side slope is... θ 2( φ The longitudinal wear depth of the defect entering the side slope is... h 1( φ The longitudinal wear depth of the defect away from the side slope is... h 2( φ The transverse wear width of the defect entering the side slope is... Le 1 ( φ The transverse wear width of the defect leaving the side slope is... Le 2 ( φ ); The asymmetric evolution geometric model for the spalling defect in the outer ring of a rolling bearing is constructed as follows: ； In equation (1), Indicates the longitudinal wear depth of the defect entering the side slope. h 1( φ ) with angle domain φ Changes; Indicates the longitudinal wear depth of the defect away from the side slope. h 2( φ ) with angle domain φ Changes; v 1( φ () represents the relative sliding velocity of the rolling element on the inclined surface at the defect entry point; v 2( φ () represents the relative sliding velocity of the rolling element on the slope surface after the defect leaves; ω is the angular velocity of the bearing; h 1( φ () represents the longitudinal wear depth of the defect entering the side slope; h 2( φ () represents the longitudinal wear depth of the defect as it leaves the side slope; k h This is the equivalent ceramic brittle damage evolution coefficient; p 0 Based on Hertz contact theory, this represents the maximum contact pressure between the rolling element and the outer raceway under defect-free conditions. Δ p 1( φ () represents the increase in contact pressure as the defect enters the inclined plane; Δ p 2 ( φ () represents the increase in contact pressure as the defect leaves the side slope; F n The equivalent normal load in the contact area between the rolling element and the defect entering or leaving the side slope; I The moment of inertia of the rolling element in the contact area between the rolling element and the defect entering or leaving the side slope. a The contact radius between the rolling element and the defect entering or leaving the side slope; ; R * The equivalent radius of curvature; E * It is the equivalent elastic modulus; θ 1( φ () represents the angle of inclination at which the defect enters the side slope; θ 2( φ () represents the angle of inclination of the defect away from the side slope; Le 1 ( φ () represents the transverse wear width of the defect entering the side slope; Le 2 ( φ () represents the transverse wear width of the defect as it leaves the side slope; Le 1 ( φ ), Le 2 ( φ Introducing second-order terms in ) and An equivalent characterization is performed for the length compensation induced by the curvature of the raceway. γ The second-order geometric correction strength, reflecting the curvature / fitness of the raceway, has the dimension of 1 / length. This is applied when the curvature effect is negligible. γ→ 0, the formula naturally degenerates into the planar slope approximation; asymmetric coefficient η ( φ ) is represented as: ； In formula (3): η ( φ )=0 indicates that the defect is symmetrical on both sides; η ( φ →1 indicates that the height of the defect is asymmetrical on the left and right sides, that is, the expansion on one side is significant.

5. The method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings as described in claim 4, characterized in that, The k h The expression is: ； In equation (2), k 0 represents an empirical coefficient; H ref , K IC,ref Used as a reference constant for dimensionless transformation; p , q It is a dimensionless sensitivity index used to characterize the hardness of ceramic bearings. H With fracture toughness K IC The effect of the removal rate of the equivalent brittle material on the strength is taken as follows: p = q =1; By setting initial conditions φ =0, which can simulate the entire process of the defect evolving from an initial approximately symmetrical state to an asymmetrical morphology.

6. The method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings as described in claim 1, characterized in that, The dynamic equation for step S4 is: ； In equation (4), M For the equivalent mass of the outer ring of the rolling bearing, x This represents the radial displacement response of the outer ring of the rolling bearing relative to the stationary base; x The first and second derivatives are velocity With acceleration ; θ Indicates the degrees of freedom for overturning and rotation. θ The first and second derivatives are angular velocities, respectively. With angular acceleration ; Q Let be the moment of inertia of the outer ring of the rolling bearing relative to its center of mass; C x and C θ These are the equivalent damping coefficients for radial translation and tilting rotation, respectively; K xx ( φ () represents the time-varying radial contact stiffness considering the effects of defects; K xθ ( φ The displacement-rotation cross stiffness is... K θx ( φ ) represents the rotation-displacement cross stiffness, used to characterize the translation-rotation coupling effect caused by the asymmetric evolution of defects; K θθ ( φ () represents the equivalent rotational stiffness; F x ( t )and M θ ( t These are the equivalent radial excitation force and equivalent overturning moment acting on the outer ring of the rolling bearing, respectively. K xx ( φ ) is represented as: ； In equation (5), N b For the number of rolling elements, φ j Indicates the first j The angular phase offset of each rolling element relative to the spalling defect on the outer ring of the rolling bearing; φ+φ j ) indicates the first j Each rolling element in the current angle domain φ The absolute angular position below, For the first j Radial contact stiffness when a rolling element crosses the outer ring spalling defect area K xx ( φ ) contributions; ； In equation (6), For the first j The displacement-rotation cross stiffness when a rolling element crosses the outer ring spalling defect area K xθ ( φ ) contributions; For the first j The rotational-displacement cross stiffness when a rolling element crosses the outer ring spalling defect area K θx ( φ ) contributions; For the first j When a rolling element crosses the outer ring spalling defect area, the equivalent rotational stiffness... K θθ ( φ ) contributions; , and The expression is as follows: ； In equation (7), θ 1( φ+φ j ) is the first j The angle of inclination of the defect entry side slope when a rolling element crosses the outer ring spalling defect area; θ 2( φ+φ j ) is the first j The angle of inclination of the defect away from the side slope when a rolling element crosses the outer ring spalling defect area; η ( φ+φ j ) is the first j The asymmetry coefficient when a rolling element crosses the outer ring spalling defect; ； ； In equation (8), α This is a dimensionless lever arm coefficient; L d ( φ+φ j ) is the first j The effective length of the rolling element across the spalling defect on the outer ring of the rolling bearing is expressed as: ； In equation (10), L The length of the bottom of the trapezoidal groove for the spalling defect on the outer ring of the rolling bearing; L e1 ( φ+φ j ) is the first j The lateral wear width of a rolling element crossing a defect into the side slope; L e2 ( φ+φ j ) is the first j The lateral wear width of a rolling element as it exits the defect from the side slope; In equations (5), (8), and (9), The expression is: ； In equation (11), D ( φ () is the time-varying displacement excitation function. β 1 represents the stiffness attenuation coefficient of the defect entering the inclined plane. β 2 represents the stiffness attenuation coefficient as the defect leaves the side slope; ; F x ( t )and M θ ( t The expression for ) is: ； In equation (12), For the first j Each rolling element corresponds to the equivalent radial excitation force. F x ( t The contribution of ) is expressed as follows: ； In equation (13), Δ F c =m b ω 2 Δ F c This represents the amplitude of the centrifugal force pulsation of the rolling element. m b The mass of a single rolling element; ω c The angular frequency of the periodic modulation excitation related to the rolling element; t Indicates time; M θ ( t The expression for ) is: ； In equation (14), For the first j Each rolling element has an overturning moment. M θ ( t The contribution of ) is expressed as follows: ； In equation (15), Δ h ( φ )= h 1( φ )- h 2( φ ); p 1( φ The contact pressure between the rolling element and the inclined surface where the defect enters is denoted as . p 2( φ The contact pressure between the rolling element and the defect-leaning side slope is the pressure at which the rolling element leaves the defect. F c =m b ω 2 R b , F c For the centrifugal force of the rolling element, R b Where is the radius of the rolling element; β Centrifugal force of rolling elements F c Direction and overturning moment M θ ( t The angle between the directions of action.

7. The method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings as described in claim 6, characterized in that, The time-varying displacement excitation function D ( φ The expression is: ； In equation (16), the angle domain φ Describes the relative positional relationship between the rolling element and the outer ring spalling defect. The entire process of a single rolling element passing through the outer ring spalling defect region is divided into four characteristic angles. φ 1. φ 2. φ 3. φ 4: ； d 1( φ This indicates that the rolling element gradually enters the defect-entry side from the normal outer raceway, and its contact displacement smoothly transitions from 0 to the wear depth of the defect-entry side inclined surface. h 1( φ To ensure the continuity of the displacement and its first derivative, a cosine transition function is used to describe the process: ； d 2( φ This indicates the stage where the rolling element completely detaches from the side slope and falls into the bottom of the trapezoidal groove of the outer ring spalling defect. Its displacement is mainly due to… h 1( φ ), h 2( φ The combined effect of these factors determines that, considering the geometric flatness and dynamic continuity of the bottom of the trapezoidal groove due to the outer ring spalling defect, the displacement excitation can be approximated as: ； d 3( φ This indicates the stage where the rolling element gradually rises from the bottom of the trapezoidal groove of the outer ring spalling defect and moves away from the defect departure side, with its displacement caused by... h 2( φ The process smoothly recovers to 0; to maintain the same continuity conditions as the entry phase, a sinusoidal transition function is used to describe the process. 。 8. The method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings as described in claim 1, characterized in that, Feature similarity in step S6 S The calculation formula is: ； In equation (20): Δ A For envelope spectrum error, Δ C For center of mass drift, S TF for STFT Similarity S imp For pulse sequence similarity, ω 1~ ω 4 is the weighting coefficient, which satisfies ω 1+ ω 2+ ω 3+ ω 4 = 1; Based on the asymmetry coefficient η ( φ and feature similarity S The comprehensive defect assessment stage specifically includes: (1) Initial peeling stage: η ( φ )<0.1, S ≥0.8; (2) Asymmetric expansion stage: 0.1≤ η ( φ )≤0.4, 0.7≤ S <0.8; (3) Stable wear stage: 0.4 η ( φ )≤0.6, 0.5≤ S <0.7; (4) Failure shutdown phase: η ( φ >0.6, S< 0.

5.

9. The method for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings as described in claim 1, characterized in that, In step S7, alarm levels are classified according to the defect stage, and corresponding fault warning signals are output, specifically as follows: (1) The alarm level in the initial peeling stage is level 0, and the fault warning signal is: signal normal; (2) The alarm level of the asymmetric expansion stage is level 1, and the fault warning signal is: it is necessary to pay close attention and arrange planned maintenance to avoid further expansion of defects; (3) The alarm level during the stable wear stage is level 2, and the fault warning signal is: it is necessary to immediately organize a shutdown inspection, assess the severity of the defect, and formulate a maintenance plan; (4) The alarm level during the failure shutdown stage is level 3. The fault warning signal is: emergency shutdown is required, and continued operation is strictly prohibited to prevent equipment damage or safety accidents.

10. A system for establishing and diagnosing an asymmetric fault evolution model for ceramic rolling bearings, characterized in that, It includes an acquisition unit, a preprocessing unit, a defect geometry modeling unit, a dynamic analysis unit, a feature extraction unit, a model-measurement matching unit, and an early warning unit; the acquisition unit is connected to the preprocessing unit, and the preprocessing unit is connected to the feature extraction unit; the defect geometry modeling unit and the preprocessing unit are both connected to the dynamic analysis unit, the dynamic analysis unit and the feature extraction unit are both connected to the model-measurement matching unit, and the model-measurement matching unit is connected to the early warning unit; The acquisition unit is used to acquire vibration signals and rotational speed signals during the operation of the rolling bearing; The preprocessing unit is used to sequentially filter, denoise, resample in the angular domain, and normalize the acquired vibration signal to generate a preprocessed signal segment. The defect geometry modeling unit is used to construct the asymmetric evolution geometric model and asymmetry coefficient of the outer ring spalling defect of the rolling bearing. η ( φ ); The dynamic analysis unit is used to establish a two-degree-of-freedom coupled dynamic equation to simulate the entire process of a rolling element crossing an asymmetric defect. Based on the established two-degree-of-freedom coupled dynamic equation, the Runge-Kutta method is used to numerically solve the asymmetric evolution geometric model and generate theoretical eigenvectors, including impact pulse trains, envelope spectra, and STFT energy maps. The feature extraction unit is used to perform feature analysis on the preprocessed signal segments generated by the preprocessing unit, including envelope analysis, spectrum analysis and time-frequency analysis, to extract time-domain features and frequency-domain features related to the theoretical feature vector; The model-test matching unit is used to match and compare the time-domain and frequency-domain features extracted by the feature extraction unit with the theoretical feature vectors generated by the dynamic analysis unit, and calculate the envelope spectrum error ΔA, centroid drift ΔC, and STFT similarity S. TF Pulse sequence similarity S imp And calculate feature similarity S According to the asymmetry coefficient η ( φ ) and similarity S Comprehensive assessment of defects; The early warning unit is used to classify the alarm level according to the defect stage determined by the model-measurement matching unit. The alarm levels include level 0, level 1, level 2 and level 3, and output a fault early warning signal.

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