A bearing fault diagnosis method based on the demodulation mechanism of harmonic summation signal model

Abstract

This invention discloses a bearing fault diagnosis method based on the demodulation mechanism of a harmonic additive signal model, comprising the following steps: By establishing a finite-order harmonic additive signal model, and using Hilbert transform and Taylor series expansion, the envelope square signal is rigorously derived, proving that the demodulation spectrum contains only the frequency interval components of any two harmonics of the original signal, and that the amplitude is proportional to the product of the amplitudes of the two harmonics. Based on this, the mechanism is applied to ordinary bearing inner ring faults where the impact amplitude is modulated by frequency conversion, clarifying the law that the demodulation spectrum amplitude decreases with order; further, it is extended to non-uniform crossed roller bearing outer ring faults, establishing an excitation force model containing three unequal impact intervals, revealing the diagnostic characteristics of modulation sideband aliasing and sudden increases in amplitude of specific harmonics. This invention overcomes the limitations of existing approximation methods based on harmonic multiplication models, strictly follows the mathematical principles of bearing signal demodulation, and can achieve accurate derivation of bearing demodulation spectrum characteristics for bearing fault diagnosis.

Description

Technical Field

[0001] This invention belongs to the field of mechanical fault diagnosis and signal processing technology, specifically relating to a bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model. Background Technology

[0002] As a core transmission component of rotating machinery, the operating condition of rolling bearings directly affects the reliability and safety of the equipment. In applications such as industrial robots and high-end machine tool spindles, where heavy loads and high precision are critical, crossed roller bearings are widely used because they can withstand multi-directional composite loads. When defects such as localized fatigue spalling occur in the bearing raceway, periodic impact excitations are generated during operation, triggering a high-frequency resonant response in the system. Performing Hilbert transform amplitude demodulation (envelope demodulation) on the vibration signal after resonant bandpass filtering is an effective means of extracting fault characteristic frequencies and diagnosing bearing faults.

[0003] In existing research, when performing Hilbert demodulation on the vibration response of bearings modulated by frequency conversion amplitude, the filtered response signal within the resonant frequency band is usually approximated as a harmonic multiplication (i.e., the product of the carrier wave and the modulating wave), and the frequency components of the demodulated spectrum are derived based on this. For example, a method, equipment and medium for modeling and fault diagnosis of rolling bearing vibration response (He Guolin; Liu Zihao; Li Weihua; Lin Huibin CN202510335319.8). However, this approximate simplification of harmonic multiplication has inherent limitations: First, after the bearing vibration response is bandpass filtered, the amplitudes of the spectral lines within the frequency band are not equal, and the simplified form of harmonic multiplication cannot reflect the true situation of the asymmetry of the amplitudes of each spectral line; Second, although the frequency components of the demodulated spectrum derived based on the harmonic multiplication form are consistent with the true demodulated spectrum, it cannot mathematically and rigorously explain the quantitative relationship between the magnitude of each frequency component in the demodulated spectrum and the amplitude of the original signal spectrum, resulting in the lack of rigor in the current theory's explanation of the magnitude of some frequency components in the demodulated spectrum.

[0004] Crossed roller bearings structurally replace traditional cages with spacers, and typically employ two types of spacers of different thicknesses symmetrically installed, resulting in a non-uniform circumferential distribution of rollers on the equivalent single-sided raceway. When a local fault exists in the outer ring, the impact time intervals generated by the rollers passing through the fault point sequentially are no longer constant, forming a periodic impact sequence with three unequal intervals. Furthermore, the impact excitation force is also modulated by the amplitude of the outer ring rotation frequency. The coupling of these two effects results in an excitation force spectrum structurally different from that of ordinary bearings: the Fourier coefficients of the unequal-interval impacts undergo phase superposition and amplification at specific orders, and because the fundamental frequency of the local fault in the outer ring is numerically smaller than the outer ring rotation frequency (modulation frequency), the modulation sidebands of adjacent fault harmonics overlap significantly. Existing methods based on harmonic multiplication approximations cannot rigorously explain the physical nature of the sudden increase in amplitude of specific harmonics in the demodulation spectrum under the above coupling effect, nor can they quantitatively describe the magnitude relationship of each frequency component amplitude under the condition of modulation sideband aliasing. Currently, a rigorous mathematical derivation and a systematic theoretical framework are lacking for the demodulation spectrum mechanism under such complex operating conditions. Summary of the Invention

[0005] To address the shortcomings of existing harmonic multiplication approximation methods in deriving Hilbert demodulation spectrum frequency components—namely, the lack of rigorous amplitude relationship verification and the absence of a complete theoretical framework for the demodulation spectrum mechanism of local faults in the outer ring of crossed roller bearings with non-uniform roller distribution—this invention provides a method for deriving and diagnosing bearing fault characteristic frequencies based on the Hilbert amplitude demodulation mechanism of a harmonic additive signal model. This invention rigorously establishes the Hilbert amplitude demodulation mechanism of harmonic additive signals from a mathematical perspective, revealing the sources and amplitude patterns of the demodulation spectrum frequency components. This mechanism is then applied sequentially to derive the characteristic frequencies of local faults in the inner ring of ordinary rolling bearings and in the outer ring of crossed roller bearings, providing a rigorous theoretical basis for fault diagnosis of these complex bearings. This method is particularly suitable for deriving and diagnosing the characteristic frequencies of local faults in the outer ring of crossed roller bearings with non-uniform roller distribution.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] A bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model includes the following steps: S1. Constructing a harmonic summation signal model: Performing resonant bandpass filtering on the bearing vibration acceleration signal, and characterizing the filtered impact response signal, which consists of a finite number of frequency domain spectral lines, as follows: A harmonic summing signal consisting of harmonics of different frequencies and amplitudes; S2. Derive the Hilbert amplitude demodulation mechanism: Perform Hilbert transform on the harmonic summation signal model to obtain the envelope square signal, perform Taylor series expansion on the envelope signal, and approximate the envelope signal in the form of linear harmonic summation. S3. Fault Feature Derivation and Diagnosis Guided by Mechanism: The demodulation mechanism in step S2 is applied to the derivation of the characteristic frequency of the vibration response of local bearing faults. An impact excitation force model is established by combining the bearing structural parameters and kinematic relationship. Based on the fault characteristic frequency distribution and amplitude law in the demodulation spectrum, the diagnosis of local bearing faults is realized.

[0008] Furthermore, in step S1, the harmonic summation signal model It can be represented as the sum of multiple harmonics with different frequencies and amplitudes, and its expression is:

[0009] In the formula This represents the number of harmonics contained in the harmonic summation signal model. , , The first The amplitude, frequency, and phase of each harmonic component; each harmonic satisfies And the frequency interval between any two adjacent harmonics Neither pair is entirely equal.

[0010] Furthermore, in step S2, the specific steps for Hilbert transform amplitude demodulation of the harmonic summation signal model are as follows: (1) Find the Hilbert transform pair for the harmonic summation signal model to obtain the envelope square signal. The DC component of the envelope square signal is the sum of the squares of the amplitudes of each harmonic, and the AC component is the sum of the cosine signals whose frequency is equal to the frequency difference between any two harmonics of the original signal and whose amplitude is twice the product of the amplitudes of the corresponding two harmonics. (2) Take the square root of the square envelope signal to obtain the envelope signal. In order to reveal the frequency component law of the envelope signal, use the Taylor series expansion theorem to perform a polynomial expansion on the envelope signal and analyze the frequency components introduced by each term step by step. (3) It can be concluded that the main frequency component of the demodulation spectrum is the frequency difference between any two harmonics of the original signal, and the amplitude of a certain frequency interval component in the demodulation spectrum is positively correlated with the product of the amplitudes of the two harmonics that constitute the corresponding frequency interval in the original signal; in addition to the main component, it also contains integer multiples of the frequency interval component and the mixing of multiple frequency interval components, but its amplitude decays step by step due to the convergence of the Taylor series coefficients.

[0011] Further, in step S3, when the diagnostic object is a local fault in the inner ring of a common rolling bearing with rotating inner ring and fixed outer ring, an impact excitation force model modulated by the inner ring rotation frequency amplitude is established, and the impact time interval is the reciprocal of the inner ring fault passing frequency; the excitation force spectrum is formed with the inner ring fault passing frequency and higher harmonics as the center frequency, and the inner ring rotation frequency as the interval to form a multi-order modulation sideband; after the vibration response signal is bandpass filtered by the resonant band, the filtered response is equivalent to a harmonic summation signal model, and it is determined according to the demodulation mechanism in step S2: the amplitude of the inner ring fault passing frequency and the modulation sideband component in the demodulation spectrum decreases with the increase of frequency order, and its physical essence is that the product of harmonic amplitudes corresponding to higher order frequencies decreases step by step.

[0012] Furthermore, in step S3, when the object of diagnosis is a local fault in the outer ring of a crossed roller bearing with a rotating outer ring and a fixed inner ring, two types of spacers of different thicknesses are symmetrically installed in the equivalent single-sided raceway of the bearing. This causes three impact time intervals to occur when adjacent rollers on the same side pass through the fault point of the outer ring in sequence: impact interval without spacers, impact interval with small spacers, and impact interval with large spacers. The above three impact time intervals constitute a complete impact cycle, and satisfy the condition that the cycle includes... The time-closed-loop accumulation conditions are as follows: one impact interval without spacers, one impact interval with small spacers, and one impact interval with large spacers. This represents the total number of rollers on an equivalent single-sided raceway.

[0013] Furthermore, based on pulse sequences with unequal time intervals, a method using the bearing outer ring rotation frequency is introduced. The amplitude modulation function of the fundamental frequency Establish the time-domain function of the actual impact excitation force of a local fault in the outer ring of a crossed roller bearing. :

[0014]

[0015] In the formula, express The time-domain function of the actual impact excitation force modulated by the frequency conversion amplitude at any given moment; This represents the outer ring frequency shift amplitude modulation function; This represents a non-uniform impulse pulse sequence that is not modulated. This represents the highest truncation order of the Fourier series expansion of the amplitude modulation function; This is the harmonic order index of the amplitude modulation function; and These are the frequency modulation functions of the first generation. The amplitude and phase of the first-order component; The imaginary unit; This is the order index of the Fourier series of a non-uniform pulse sequence; To characterize the unequal interval impact characteristics of the first Fourier coefficients; This is the fundamental frequency of the characteristic sequence of local faults in the outer ring of the crossed roller bearing.

[0016] Furthermore, the impact excitation force is solved using the frequency domain convolution theorem and multiplied with the system frequency response function to obtain the system vibration response amplitude spectrum.

[0017] A system for implementing the bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model includes: The signal acquisition and filtering module is used to acquire bearing vibration acceleration signals and perform resonant bandpass filtering. The demodulation mechanism derivation module is used to perform envelope square derivation and frequency component analysis on the harmonic additive signal model based on Hilbert transform and Taylor series expansion. The fault feature extraction and diagnosis module is used to calculate the impact time interval and excitation force spectrum by combining bearing structural parameters, and output the bearing fault diagnosis results based on the main frequency distribution and amplitude law of the demodulation spectrum.

[0018] A computer device according to the present invention includes a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, which, when executed by the processor, causes the processor to implement the method described herein.

[0019] The present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor implements the method described herein. Compared with the prior art, the present invention has the following beneficial effects: (1) Rigor of demodulation mechanism derivation: Breaking through the limitations of existing harmonic multiplication approximation methods, through the derivation of envelope square of Hilbert transform and Taylor series expansion, the source of demodulation frequency components is rigorously proven from a mathematical perspective, and the quantitative relationship between the magnitude of each frequency component in demodulation spectrum and the magnitude of the original signal spectrum line is given.

[0020] (2) Interpretability of amplitude patterns: It reveals the "amplitude product effect" - that is, the amplitude of a certain frequency interval component in the demodulation spectrum is positively correlated with the product of the amplitudes of the two harmonics that constitute that frequency interval in the original signal, making the amplitude distribution of the demodulation spectrum mechanistically interpretable, and making up for the shortcomings of existing methods that can only qualitatively analyze frequency components and cannot quantitatively explain amplitude relationships.

[0021] (3) Rigorous Derivation of Fault Characteristics of Crossed Roller Bearing Outer Ring: For local faults in the outer ring of crossed roller bearings with non-uniform roller distribution, an excitation force model containing three unequal impact time intervals is established. Combined with the demodulation mechanism revealed in this invention, the even-numbered harmonics in the demodulation spectrum are rigorously derived as the first dominant frequency. The base frequency is the second main frequency. The fault diagnosis characteristics, such as severe sideband aliasing, provide a complete and rigorous theoretical basis for fault identification of this type of bearing.

[0022] (4) Universality: The established Hilbert amplitude demodulation mechanism for harmonic summation signals has universality and can be extended to the demodulation spectrum analysis and fault feature interpretation of vibration signals of various rotating machinery exhibiting amplitude modulation. Compared with the prior art, the beneficial effects of this invention are at least as follows: Taking ordinary rolling bearings and cross-roller bearings with non-uniform roller distribution as research objects, a rigorous demodulation model for harmonic summation signals is established, breaking through the limitations of the approximate simplification of harmonic multiplication in the prior art; the essence of Hilbert demodulation extracting frequency intervals is rigorously proven from the underlying mathematical logic, revealing the "amplitude product effect"; under complex working conditions, the sideband aliasing and specific harmonic amplitude jump characteristics under the coupling effect of unequal interval impact and frequency amplitude modulation are accurately decoupled, providing a high-precision and highly reliable theoretical judgment criterion for fault feature extraction and diagnosis of complex heterogeneous rolling bearings. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the principle of resonance demodulation analysis in an embodiment of the present invention. Figure 2 This is a schematic diagram of the amplitude spectrum of the harmonic summation signal model according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the local demodulated square spectrum of the harmonic summation signal model from 0 to 20 Hz according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the local demodulation spectrum of the harmonic summation signal model from 0 to 60 Hz in an embodiment of the present invention; Figure 5 This is a time-domain comparison diagram of the original signal and the envelope signal in an embodiment of the present invention; Figure 6 This is a time-domain comparison diagram of the theoretical envelope signal and the Taylor series expansion signal in an embodiment of the present invention; Figure 7 This is a comparison diagram of the theoretical demodulation spectrum and the Taylor series expansion amplitude spectrum of an embodiment of the present invention; Figure 8 This is a schematic diagram of the frequency domain amplitude spectrum of the impact excitation force of a local fault in the inner ring of a conventional rolling bearing according to an embodiment of the present invention. Figure 9This is a schematic diagram of the 0-200Hz local amplified demodulation spectrum of a local fault in the inner ring of a common rolling bearing according to an embodiment of the present invention; Figure 10 This is a time-domain waveform diagram of the impact excitation force of a local fault in the outer ring of a crossed roller bearing according to an embodiment of the present invention. Figure 11 This is a schematic diagram of the local magnified amplitude spectrum of the impact excitation force of the outer ring failure of the crossed roller bearing according to an embodiment of the present invention. Figure 12 This is a time-domain waveform diagram of the system vibration and shock response according to an embodiment of the present invention; Figure 13 This is a magnified view of the amplitude spectrum and resonance band of the system vibration and shock response according to an embodiment of the present invention. Figure 14 This is a schematic diagram of the theoretical demodulation spectrum of a local fault in the outer ring of a crossed roller bearing according to an embodiment of the present invention; Figure 15 This is a diagram showing the low-frequency local magnification and main frequency distribution of the demodulation spectrum in an embodiment of the present invention. Figure 16 This is a flowchart illustrating the application of the experimental diagnostic method for crossed roller bearings according to an embodiment of the present invention. Figure 17 As described in the embodiments of the present invention A schematic diagram of the global demodulation spectrum obtained experimentally under fault size; Figure 18 As described in the embodiments of the present invention Local magnification and feature annotation of the experimental demodulation spectrum under fault size; Figure 19 As described in the embodiments of the present invention A schematic diagram of the global demodulation spectrum obtained experimentally under fault size; Figure 20 As described in the embodiments of the present invention A magnified view of the experimental demodulation spectrum under fault size and its feature annotation. Detailed Implementation

[0024] To make the technical solutions and objectives of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific implementation steps described herein are only used to better illustrate the application of the present invention, but the technical features involved in the embodiments of the present invention are not limited thereto.

[0025] like Figure 1 As shown in the figure, a rolling bearing fault diagnosis method based on the demodulation mechanism of the harmonic addition model in this embodiment includes the following steps: S1. Construct a harmonic summation signal model.

[0026] In rolling bearing fault diagnosis, when a local fault occurs in the bearing raceway, the impact excitation force generated during operation will induce a high-frequency resonant response in the system. A bandpass filter is applied to a specific resonant frequency band of the acquired vibration acceleration signal. The filtered fault impact response signal consists of a finite number of spectral lines in the frequency domain, which can be considered as the sum of a finite number of harmonic signals, i.e., a harmonic summation signal model. Without loss of generality, a model is established using... Harmonic summation signal model composed of harmonic signals of different frequencies with unequal intervals between adjacent frequencies. :

[0027] In the formula, , , The first The amplitude, frequency, and phase of each harmonic component; each harmonic frequency satisfies The frequency domain amplitude spectrum of this harmonic summation signal model is as follows: Figure 2 As shown, the frequency spacing of each adjacent harmonic component The fact that not all pairs are equal reflects the general situation of non-equal spacing of spectral lines within the filter band.

[0028] S2. Using the Hilbert amplitude demodulation mechanism of the harmonic summation signal model, perform a Hilbert transform on the established harmonic summation signal model to obtain the analytic signal, and solve for the envelope square signal. for:

[0029] In the formula, For the amplitudes of the two original harmonics, , These are the two harmonic frequencies. , For the two harmonic phases, for Number of mid-spectral lines This is the envelope signal.

[0030] As shown in the above equation, the envelope squared signal contains only a zero-frequency (DC) component and a frequency that is the difference between any two harmonic frequencies. The AC component, and the magnitude of this AC component directly depends on the magnitude of the product of the amplitudes of the original two harmonics. .

[0031] Prove that the frequency of the AC component of the envelope squared signal is composed of the frequency difference between any two harmonics of the original signal, and that its amplitude is proportional to the product of the amplitudes of the corresponding two harmonics: Envelope signal for Take the square root. Since the envelope signal is a real signal, based on the Taylor series expansion formula, the envelope signal can be expanded to approximate it, revealing the demodulation mechanism that the main frequency components in the demodulation spectrum are frequency interval components, and their amplitudes are positively correlated with the product of the amplitudes of the corresponding two harmonics. Mathematical derivation proves that the main frequency components in the envelope signal are still the frequency interval components of any two harmonics in the original harmonic summation signal model. Furthermore, its amplitude is positively correlated with the product of the initial amplitudes of the two harmonics that make up the frequency interval in the original response signal. This is the "amplitude product effect" disclosed in this invention. In addition, secondary frequency components such as higher harmonics and multi-order mixing will also be derived.

[0032] The demodulated square spectrum contains only the zero-frequency component and the frequency interval components; make ,verify Established, among which This represents the AC component function of the normalized envelope squared signal, which is obtained by transforming the envelope squared signal... The ratio of AC to DC components in the model is used to construct a model that satisfies the convergence condition of the Taylor series expansion. This represents the total number of harmonic components included in the harmonic summation signal model. , These represent the first harmonic in the original harmonic summation signal model. The and the first The amplitude of each harmonic component. , These represent the first harmonic in the original harmonic summation signal model. The and the first The frequency of each harmonic component. and These represent the first harmonic in the original harmonic summation signal model. The and the first The initial phase of each harmonic component. In the original harmonic summation signal model, the first harmonic is represented by the second harmonic. The amplitude of each harmonic component. The coefficients representing the power terms in the Taylor series expansion are used in the derivation of the Hilbert amplitude demodulation mechanism in this invention, due to the envelope signal. It is the squared envelope signal The arithmetic square root, therefore take .

[0033] Using Taylor series to transform envelope signals Expand:

[0034]

[0035] By analyzing the frequency components introduced by each term at each order, it can be concluded that the main frequency component of the demodulated spectrum is the frequency difference between any two harmonics of the original signal. Furthermore, the magnitude of a certain frequency interval component in the demodulation spectrum is positively correlated with the product of the amplitudes of the two harmonics constituting that frequency interval in the original signal; in addition to the main components, it also contains integer multiples of the frequency interval components and the mixing of multiple frequency interval components by addition and subtraction, but its amplitude decays step by step due to the convergence of the Taylor series coefficients.

[0036] To verify the above demodulation mechanism, a simulated signal consisting of the sum of four harmonics was constructed. The simulation parameters are set as follows: the frequencies are respectively , , , The corresponding amplitudes are respectively , , , All phases are set to 0, and the sampling frequency is... Sampling duration .

[0037] For simulation signals Perform Hilbert amplitude demodulation to obtain the demodulated square spectrum as follows: Figure 3 As shown. By Figure 3 It can be seen that the spectral lines appearing in the demodulated squared spectrum are exactly the original signal. The frequency interval components of any two harmonics (4, 5, 7, 9, 12, 16 Hz, etc.) in the original signal are analyzed, and no other frequency components are found in the demodulated square spectrum. This verifies the derivation that the envelope square signal contains only the zero-frequency component and the frequency interval components. Further observation of the amplitude of each frequency interval component reveals that in the original signal... and The product of amplitudes is the largest, and the amplitude is also the largest in the demodulated square spectrum at a frequency interval of 7Hz. and The product of amplitudes is the smallest, which corresponds to the smallest amplitude in the demodulated square spectrum at 4Hz, perfectly matching the derivation conclusion.

[0038] The corresponding demodulation spectrum is as follows Figure 4 As shown. By Figure 4 As can be seen, the demodulated spectrum also contains all the aforementioned frequency interval components as main frequency components, and the relative relationship of the amplitudes of each main frequency component is consistent with the demodulated square spectrum, verifying the "amplitude product effect": the larger the product of the amplitudes of the two harmonics in the original signal, the larger the amplitude of the corresponding frequency interval component in the demodulated spectrum. In addition to the main frequency components, the demodulated spectrum also contains a small number of harmonic and mixing components with smaller amplitudes, consistent with the theoretical derivation.

[0039] Time-domain comparison of the corresponding envelope signal and the original signal, for example Figure 5As shown, it can be seen that due to the simulation signal adjacent frequency spacing That is, the simplest ratio of adjacent frequency intervals can be reduced to coprime integers, and the envelope signal For a periodic signal with a minimum positive period of 1 second, Hilbert amplitude demodulation in the time domain essentially involves solving for the positive envelope. Furthermore, regarding the envelope signal A 10th-order Taylor series expansion approximation is performed, and the time-domain comparison between the theoretical envelope signal and the expansion result is shown below. Figure 6 As shown, the demodulation spectrum pairs are as follows: Figure 7 As shown, the two are in high agreement, verifying the effectiveness of the Taylor series expansion approximation.

[0040] S3. Analysis and diagnosis of bearing fault characteristics under the guidance of implementation mechanism: The demodulation mechanism in step S2 is applied to the fault diagnosis of ordinary rolling bearings and crossed roller bearings respectively.

[0041] For a localized fault in the inner ring of a conventional rolling bearing, a single-degree-of-freedom bearing system with a rotating inner ring and a fixed outer ring is taken as the research object. The simulation parameters are set as follows: inner ring fault passage frequency. Inner ring frequency First-order undamped natural frequency Damping ratio sampling frequency Sampling time .

[0042] Impact excitation force is affected by the inner ring rotation frequency Amplitude modulation, modulation function by The fundamental frequency is expanded into a Fourier series, and the excitation force spectrum is formed as follows: Centered on its higher harmonics, with For multi-order modulation sidebands with intervals, such as Figure 8 As shown.

[0043] After performing bandpass filtering on the system vibration response, 12 center frequency spectral lines near the natural frequency and their modulation sidebands are used to construct a harmonic summation signal model. Hilbert amplitude demodulation is then performed according to the demodulation mechanism in step S2, resulting in the demodulated spectrum as shown below. Figure 9 As shown.

[0044] As can be seen from the demodulation spectrum, there is an inner-track fault passing frequency in the demodulation spectrum. And its higher harmonics, as well as the inner frequency rotation centered on each harmonic. The signal consists of multiple modulated sidebands spaced apart, with the amplitude of each main frequency and sideband strictly decreasing with increasing order. Based on the "amplitude product effect," the essence of this decreasing law lies in the fact that the higher the frequency of the two harmonics constituting a certain demodulated frequency component, the smaller the initial amplitude product within the resonant band, and therefore the smaller the amplitude of that frequency component in the demodulated spectrum. For a local fault in the inner ring of a common rolling bearing: the impact excitation force is modulated by the inner ring rotational frequency amplitude, presenting equally spaced impacts. Combining the "amplitude product effect" in step S2, since the number of harmonic pairs corresponding to higher-order harmonics within the resonant band is small and their initial amplitude is low, the amplitude of the fundamental frequency of the inner ring fault and its modulated sidebands in the demodulated spectrum must exhibit a strict, progressively decreasing attenuation law.

[0045] For localized faults in the outer ring of crossed roller bearings: Crossed roller bearings have rollers arranged in a cross pattern, equivalent to the superposition of two sets of single-row roller bearings. To control clearance, four spacers (available in large and small sizes) are symmetrically installed between the vertically arranged rollers. ( The rollers and spacers satisfy the following on the pitch circle:

[0046] In the formula, For the diameter of the node, This is the equivalent number of rollers on one side. The diameter is the roller diameter. The inner ring is fixed, and the outer ring rotates at a constant frequency. Under rotating conditions, due to the presence of the spacer, three different impact time intervals occur when the rollers on the same side pass the outer ring fault point in sequence: (1) Impact interval without spacer Corresponding central angle , ; (2) Impact interval with small spacer blocks Corresponding central angle , ; (3) Impact gap containing large spacer blocks Corresponding central angle , ; In the formula, The relative passing frequency of a single roller relative to the outer ring. These represent the thickness of the spacers in two different specifications.

[0047] In a complete shock cycle (The rolling element revolves relative to the outer ring for half a revolution) satisfies:

[0048] In the formula, This represents the total number of rollers on an equivalent single-sided raceway.

[0049] Based on pulse sequences with unequal time intervals, a method is introduced to measure the bearing outer ring frequency. The amplitude modulation function of the fundamental frequency Establish the time-domain function of the actual impact excitation force of a local fault in the outer ring of a crossed roller bearing. :

[0050] In the formula For outer ring frequency switching, The fundamental frequency for a local fault in the outer ring; These represent the amplitude and phase of the frequency conversion amplitude modulation function, respectively. To characterize the unequal interval impact characteristics of the first Fourier coefficients, This represents the order index of the Fourier series expansion of an unmodulated, non-uniform impulse pulse sequence. This represents the highest truncation order of the Fourier series expansion of the outer ring frequency shift amplitude modulation function. This indicates that after the frequency conversion amplitude modulation function is expanded by Fourier series, the th... The amplitude of the first harmonic component, Represents the imaginary unit (i.e.) ).

[0051] The impact excitation force is solved using the frequency domain convolution theorem and compared with the system frequency response function. Multiplying them together yields the amplitude spectrum of the system's vibration response. :

[0052] In the formula, The Dirac impulse function is used to characterize the discrete spectral impulse characteristics of a signal in the frequency domain. The frequency independent variable represents the frequency domain. This indicates the harmonic order index (i.e., the order of the modulation sideband) of the outer ring frequency switching amplitude modulation function. This represents the frequency response function of the bearing vibration system.

[0053] This indicates that the system's frequency response function is affected by characteristic coefficients with non-uniform impact. Discrete sampling with unequal amplitude and non-equal frequency intervals.

[0054] Setting the outer ring frequency The outer ring has a partial fault in the fundamental frequency. The corresponding calculation yields , , .

[0055] The system response of the bearing rotor system in this simulation embodiment is solved, and the time-domain waveform of the impact excitation force is obtained as follows: Figure 10 As shown, the excitation force amplitude spectrum is as follows Figure 11 As shown; the system response time-domain signal is as follows Figure 12 As shown, the response amplitude spectrum is as follows Figure 13 As shown.

[0056] After the system vibration response is filtered by the resonant bandpass filter, it is equivalent to a harmonic summation signal model. Hilbert amplitude demodulation is then performed according to the demodulation mechanism in step S2, and the resulting theoretical envelope demodulation spectrum is as follows: Figure 14 and local magnification Figure 15 As shown, the obtained demodulation spectrum has the following fault diagnosis characteristics: 1) There is a local fault in the outer ring of the fundamental frequency. Its higher harmonics, and each harmonic has an outer ring frequency conversion on both sides. The multi-stage modulation sidebands are spaced out.

[0057] In this embodiment, due to a local fault in the outer ring, the fundamental frequency... Numerically smaller than the outer ring rotation frequency The modulation sideband spacing of adjacent fault harmonics ( ) smaller than the modulation sideband width ( When the frequency bands of adjacent sidebands overlap, a significant spectral characteristic that distinguishes crossed roller bearings from ordinary bearings will inevitably occur.

[0058] 2) Due to the combined effects of non-uniform impulse modulation and the "amplitude product effect" during demodulation, the demodulated spectrum breaks the conventional decreasing attenuation pattern and exhibits abrupt jumps in magnitude: the even-numbered fundamental frequency components in the demodulated spectrum are the first dominant frequency components. Doubling the fundamental frequency ( (The equivalent number of rollers on one side of the raceway) is the second dominant frequency component, and , It exhibits a large value characteristic at specific harmonic frequencies.

[0059] In this embodiment, the even-numbered fundamental frequency components are the first major frequency components. (i.e., the multiplier of half the number of rollers) is the second main frequency component, and , and Certain order harmonics exhibit an unusually large group of dominant frequency characteristics.

[0060] 3) There is an outer ring frequency shift in the low-frequency region. And its higher harmonic components.

[0061] Experimental verification To verify the correctness of the above theory and numerical simulation, a fault simulation test bench and testing system for crossed roller bearings were built. The following methods were employed: Figure 16 The application process of the fault diagnosis method shown is as follows: After the measured vibration signal is acquired, the signal undergoes preprocessing such as time-domain truncation and noise reduction, followed by bandpass filtering to obtain a certain order high-frequency resonance peak. After envelope demodulation, the fault transmission frequency in the demodulated spectrum is compared with the theoretical value of the fault characteristic frequency calculated using the bearing's structural geometric parameters and rotational speed, thereby achieving fault type diagnosis. The bearing used in this experiment is SW-HG-20 type, and its dimensions and test conditions are strictly consistent with the simulation conditions (outer ring rotational speed). (Hz, sampling frequency 25600Hz). Local faults were artificially implanted into the outer raceway using wire cutting technology.

[0062] Example 1: Implantation area ,deep The outer ring exhibits a localized fault. The measured acceleration response was bandpass filtered from 2000Hz to 6000Hz and then demodulated using a Hilbert envelope. The resulting global demodulated spectrum is shown below. Figure 17 , local magnification and feature annotation diagram as follows Figure 18 As shown.

[0063] Example 2: Implantation area ,deep The outer ring has a local fault. Similarly, filtering and demodulation are performed, and the resulting local demodulated spectrum is as follows: Figure 19 , Local magnified feature annotation diagram as follows Figure 20 As shown.

[0064] As can be seen from the above embodiments, regardless of the fault size, the measured signal envelope demodulation spectrum clearly shows the outer ring frequency shift. This refers to the sideband aliasing phenomenon of the modulation frequency; simultaneously, it perfectly replicates the first main frequency component (even-fold fundamental frequency) and the second main frequency component ( )as well as , , The distribution pattern of anomalous amplitude jumps at the fundamental frequency was observed. The low-frequency region also independently exhibits rotational frequency and its higher harmonics. The distribution pattern is completely consistent with the "amplitude product effect" mechanism derived in this invention and the numerical simulation results, successfully achieving high-precision diagnosis of outer ring faults in crossed roller bearings.

[0065] It should be noted that although the present invention has been described in detail with reference to examples, those skilled in the art will readily understand that any modifications, substitutions, and improvements made without departing from the spirit and principles of the invention as set forth in the appended claims should be included within the scope of protection of the present invention.

Claims

1. A bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model, characterized in that, Includes the following steps: S1. Constructing a harmonic summation signal model: Performing resonant bandpass filtering on the bearing vibration acceleration signal, and characterizing the filtered impact response signal, which consists of a finite number of frequency domain spectral lines, as follows: A harmonic summing signal consisting of harmonics of different frequencies and amplitudes; S2. Derive the Hilbert amplitude demodulation mechanism: Perform Hilbert transform on the harmonic summation signal model to obtain the envelope square signal, perform Taylor series expansion on the envelope signal, and approximate the envelope signal in the form of linear harmonic summation. S3. Fault Feature Derivation and Diagnosis Guided by Mechanism: The demodulation mechanism in step S2 is applied to the derivation of the characteristic frequency of the vibration response of local bearing faults. An impact excitation force model is established by combining the bearing structural parameters and kinematic relationship. Based on the fault characteristic frequency distribution and amplitude law in the demodulation spectrum, the diagnosis of local bearing faults is realized.

2. The bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model according to claim 1, characterized in that: In step S1, the harmonic summation signal model It can be represented as the sum of multiple harmonics with different frequencies and amplitudes, and its expression is: In the formula This represents the number of harmonics contained in the harmonic summation signal model. , , The first The amplitude, frequency, and phase of each harmonic component; each harmonic satisfies And the frequency interval between any two adjacent harmonics Neither pair is entirely equal.

3. The bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model according to claim 2, characterized in that: In step S2, the specific steps for Hilbert transform amplitude demodulation of the harmonic summation signal model are as follows: (1) Find the Hilbert transform pair for the harmonic summation signal model to obtain the envelope square signal. The DC component of the envelope square signal is the sum of the squares of the amplitudes of each harmonic, and the AC component is the sum of the cosine signals whose frequency is equal to the frequency difference between any two harmonics of the original signal and whose amplitude is twice the product of the amplitudes of the corresponding two harmonics. (2) Take the square root of the square envelope signal to obtain the envelope signal. In order to reveal the frequency component law of the envelope signal, use the Taylor series expansion theorem to perform a polynomial expansion on the envelope signal and analyze the frequency components introduced by each term step by step. (3) It can be concluded that the main frequency component of the demodulation spectrum is the frequency difference between any two harmonics of the original signal, and the amplitude of a certain frequency interval component in the demodulation spectrum is positively correlated with the product of the amplitudes of the two harmonics that constitute the corresponding frequency interval in the original signal; in addition to the main component, it also contains integer multiples of the frequency interval component and the mixing of multiple frequency interval components, but its amplitude decays step by step due to the convergence of the Taylor series coefficients.

4. The bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model according to claim 1, characterized in that: In step S3, when the diagnostic object is a local fault in the inner ring of a common rolling bearing with rotating inner ring and fixed outer ring, an impact excitation force model modulated by the inner ring rotation frequency amplitude is established, and the impact time interval is the reciprocal of the inner ring fault passing frequency; the excitation force spectrum is formed with the inner ring fault passing frequency and higher harmonics as the center frequency and the inner ring rotation frequency as the interval to form a multi-order modulation sideband; after the vibration response signal is bandpass filtered by the resonant band, the filtered response is equivalent to a harmonic summation signal model, and it is determined according to the demodulation mechanism in step S2: the amplitude of the inner ring fault passing frequency and the modulation sideband component in the demodulation spectrum decreases with the increase of frequency order, and its physical essence is that the product of harmonic amplitudes corresponding to higher order frequencies decreases step by step.

5. The bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model according to claim 1, characterized in that: In step S3, when the object of diagnosis is a local fault in the outer ring of a crossed roller bearing with a rotating outer ring and a fixed inner ring, two types of spacers of different thicknesses are symmetrically installed in the equivalent single-sided raceway of the bearing. This causes three impact time intervals to occur when adjacent rollers on the same side pass through the fault point of the outer ring in sequence: impact interval without spacers, impact interval with small spacers, and impact interval with large spacers. The above three impact time intervals constitute a complete impact cycle, and satisfy the condition that the cycle includes... The time-closed-loop accumulation conditions are as follows: one impact interval without spacers, one impact interval with small spacers, and one impact interval with large spacers. This represents the total number of rollers on an equivalent single-sided raceway.

6. The bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model according to claim 5, characterized in that: Based on pulse sequences with unequal time intervals, a method is introduced to measure the bearing outer ring frequency. The amplitude modulation function of the fundamental frequency Establish the time-domain function of the actual impact excitation force of a local fault in the outer ring of a crossed roller bearing. : In the formula, express The time-domain function of the actual impact excitation force modulated by the frequency conversion amplitude at any given moment; This represents the outer ring frequency shift amplitude modulation function; This represents a non-uniform impulse pulse sequence that is not modulated. This represents the highest truncation order of the Fourier series expansion of the amplitude modulation function; This is the harmonic order index of the amplitude modulation function; and These are the frequency modulation functions of the first generation. The amplitude and phase of the first-order component; The imaginary unit; This is the order index of the Fourier series of a non-uniform pulse sequence; To characterize the unequal interval impact characteristics of the first Fourier coefficients; This is the fundamental frequency of the characteristic sequence of local faults in the outer ring of the crossed roller bearing.

7. The bearing fault diagnosis method based on the demodulation mechanism of a harmonic summation signal model according to claim 6, characterized in that: The impact excitation force is solved using the frequency domain convolution theorem and multiplied with the system frequency response function to obtain the system vibration response amplitude spectrum.

8. A system for implementing the method according to any one of claims 1 to 7, characterized in that, include: The signal acquisition and filtering module is used to acquire bearing vibration acceleration signals and perform resonant bandpass filtering. The demodulation mechanism derivation module is used to perform envelope square derivation and frequency component analysis on the harmonic additive signal model based on Hilbert transform and Taylor series expansion. The fault feature extraction and diagnosis module is used to calculate the impact time interval and excitation force spectrum by combining bearing structural parameters, and output the bearing fault diagnosis results based on the main frequency distribution and amplitude law of the demodulation spectrum.

9. A computer device comprising a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, characterized in that: When the computer program is executed by the processor, it causes the processor to implement the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor implements the method as described in any one of claims 1 to 8.

Images