Rolling bearing vibration response modeling and fault diagnosis method, equipment and medium

Abstract

The invention discloses a rolling bearing vibration response modeling and fault diagnosis method, equipment and a medium. The method comprises the following steps: establishing an unequal-interval and amplitude-modulated exciting force sequence signal model; and modeling a vibration impact response signal, simulating an envelope demodulation numerical value, and diagnosing faults. According to the invention, the rolling bearing is taken as a research object, a vibration impact response signal model is established, the model is finer, and the vibration mechanism of the bearing can be simulated more accurately; the characteristics of impact excitation, response signals and envelope signals can be analyzed in detail in sequence, unequal interval and amplitude modulation characteristics of excitation force are decoupled from the vibration principle, fault characteristics of impact response and envelope are revealed, and rolling bearing fault diagnosis considering unequal interval and amplitude modulation excitation force can be realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of rolling bearing fault signal modeling and fault detection, and particularly relates to a rolling bearing vibration response modeling and fault diagnosis method, system, device and medium considering uneven intervals and amplitude modulation excitation forces. Background Art

[0002] As a core transmission component of rotating machinery, the operating state of a rolling bearing is directly related to the reliability and safety of the equipment. In high-precision equipment such as industrial robots and high-end machine tools, crossed roller bearings are widely used because they can withstand multi-directional composite loads. However, such bearings usually use spacer blocks to replace the cage to adjust the distribution of the rollers, resulting in uneven spacing between adjacent rollers and forming a unique uneven interval distribution characteristic. When there are local defects in the bearing, the impact signals generated when the rollers pass through the defect points usually exhibit the dual characteristics of unequal time intervals and dynamic amplitude modulation, which poses many challenges to traditional fault diagnosis methods under such complex working conditions. Specifically, it is manifested as follows:

[0003] Most existing studies are based on the assumption of equal roller spacing, and the established theoretical models are difficult to accurately describe the periodic mutation phenomenon of roller spacing caused by spacer blocks, thus unable to effectively capture the quasi-periodic distortion of the impact sequence caused thereby. In addition, under the coupled action of multi-physical fields such as time-varying loads and machining errors in rolling bearings, amplitude-modulated fault impacts will be generated, exacerbating the decoupling difficulty of excitation and response characteristics in the frequency domain. At present, there is no in-depth study on the vibration mechanism of rolling bearings under the action of uneven intervals and amplitude modulation excitation forces. The existing vibration response modeling methods are difficult to truly simulate the actual working conditions during the operation of the bearings, and there is a large room for improvement, resulting in a lack of sufficient theoretical support for the fault diagnosis methods of such bearings.

[0004] The existing technology focuses on the diagnosis of the non-modulation working conditions of rolling bearings with uneven roller intervals. For example, a method for analyzing the fault characteristic frequencies of rolling bearings with uneven roller intervals (Cai Zequan; Jing Lilong; He Guolin; Liu Xiaolong; Lu Wenbo; Li Weihua CN202410387551.1) analyzes the generation of complex fault characteristics caused by uneven interval impacts from the principle of signal processing for rolling bearings with uneven roller intervals. However, this model is only applicable to the ideal working conditions where the excitation force amplitude is constant and there is no rotational frequency modulation. In fact, industrial bearings generally have amplitude modulation phenomena related to the rotational frequency. The existing methods ignore the coupling effect between the fault passing frequency and the rotational frequency, resulting in the loss of key modulation components in the fault characteristic calculation process, which is not conducive to fully utilizing all fault characteristics for identification and diagnosis under weak faults. Summary of the Invention

[0005] To at least solve one of the problems existing in the prior art, the present invention provides a method for modeling the vibration response and fault diagnosis of a rolling bearing considering uneven intervals and amplitude modulation excitation forces, establishes a vibration response model of the rolling bearing under uneven intervals and amplitude modulation excitation forces, decouples the uneven interval and amplitude modulation characteristics of the excitation force from the vibration principle, reveals the fault characteristics of the impact response and envelope, and provides inspiration for subsequent rolling bearing fault diagnosis research and engineering applications.

[0006] To achieve the object of the present invention, a method for modeling the vibration response and fault diagnosis of a rolling bearing considering uneven intervals and amplitude modulation excitation forces provided by the present invention includes the following steps:

[0007] Step S1: Determine the vibration impact time interval according to the positional relationship of the rollers distributed at uneven intervals; introduce an amplitude modulation function to construct a signal model of the excitation force sequence with uneven intervals and amplitude modulation;

[0008] Step S2: Perform time-domain convolution analysis on the signal model of the excitation force sequence with uneven intervals and amplitude modulation by using the frequency response function to establish a vibration impact response signal model to characterize the fault characteristics and modulation mechanism; perform envelope demodulation on the impact response through Hilbert transform, and separate the spectral cluster characteristics formed by the coupling action of the modulation parameters and the time-varying impact in the demodulation spectrum;

[0009] Step S3: Conduct numerical simulation on the uneven intervals and amplitude modulation excitation force - vibration response - envelope signal of the bearing to reveal the bearing fault characteristics; compare the vibration acceleration data of the bearing to be diagnosed with the envelope spectrum characteristics of the simulation signal to obtain the fault diagnosis result of the bearing to be diagnosed.

[0010] Furthermore, in step S1, the spatial arrangement of the rollers of the rolling bearing is determined by a mathematical definition method, specifically including:

[0011] There are z rollers with a diameter of d in the bearing raceway, and y spacer blocks with a predetermined thickness d m are symmetrically arranged between the rollers. Based on the coordinate system, the angular position relationship between the centers of any two rollers is established, and its expression is:

[0012]

[0013] In the formula, y k and z k are the number of spacer blocks and rollers existing between two rollers in the rolling direction of the rollers; D is the pitch diameter of the roller center revolving around the axis.

[0014] Furthermore, step S1 includes the following sub-steps:

[0015] S1.1 Calculate the vibration and shock time interval: According to the expression of the angular position relationship between the centers of two rollers, calculate the vibration and shock time interval when the rollers pass through the raceway fault point in sequence, which can be expressed as:

[0016]

[0017] In the formula, f bo is the frequency of a single roller passing through the raceway fault point.

[0018] S1.2 Introduce the amplitude modulation function and establish the time-domain expression of the excitation force with unequal intervals and amplitude modulation within the revolution period of the roller:

[0019]

[0020] In the formula, a m , are respectively the amplitude and phase of the m-th component of the rotational frequency amplitude modulation function; f out is the rotational frequency of the bearing; n is the order of the excitation force within one period; A is the amplitude of the excitation force; t n is the impact moment of the excitation force.

[0021] Further, perform the Fourier transform on the excitation force function f(t), which can be expressed as:

[0022]

[0023] In the formula, b k represents the amplitude of the k-th Fourier series, f o represents the fundamental frequency of the local fault characteristic frequency, and δ represents the unit impulse function.

[0024] Furthermore, step S2 includes the following sub-steps:

[0025] S2.1 Use the frequency response function to perform time-domain convolution calculation on the unequal interval amplitude modulation excitation force described in S1, and establish a vibration and shock response signal model, whose amplitude spectrum can be expressed as:

[0026]

[0027] Ignore the frequency components with relatively small amplitudes far from the resonance peak in the response spectrum X(f), and intercept the frequency components with relatively large amplitudes near the l-th natural frequency. f l is a certain harmonic fundamental frequency as the starting frequency, which includes a total of N k harmonic fundamental frequencies, and the cut-off frequency is f l +(N k -1)f i , and approximately represent the response signal of the intercepted N-th order natural frequency in the form of an amplitude modulation multiplication signal. The time-domain signal of the system response is simplified to:

[0028]

[0029] In the formula, c l,k and respectively represent the amplitude and phase at the k-th harmonic passing frequency of the s-th natural frequency of the response signal. N m represents the order of the rotational frequency modulation in the intercepted signal.

[0030] S2.2 Perform Hilbert transform amplitude demodulation on the impulse response. The analytical signal and its amplitude spectrum of the response are expressed as:

[0031]

[0032] In the formula, z(t) represents the envelope of the response signal; represents the Hilbert transform pair of the time-domain signal of the system response; u m and v k respectively represent the amplitudes of the m-th order of δ(f ± mf out ) and the k-th order of δ(f - kf o ), and E k,m represents the amplitudes of the k-th and m-th order frequencies of |Z(f)|.

[0033] Furthermore, step S3 includes the following sub-steps:

[0034] S3.1 Conduct numerical simulation of the bearing vibration response based on the MATLAB platform. Generate fault excitation signals and response signals with unequal intervals and amplitude modulation according to the bearing geometry and operating condition parameters, and complete envelope demodulation analysis to reveal the bearing fault characteristics;

[0035] S3.2 Obtain the measured vibration response signal of the rolling bearing to be detected on the bearing fault test bench, perform envelope demodulation on the response signal using the same parameters, and qualitatively compare the envelope spectral characteristics between the experimental signal and the simulation signal to diagnose the bearing fault.

[0036] Furthermore, the time-domain and frequency-domain signal characteristics of the excitation force with unequal intervals and amplitude modulation include: (1) There are excitation force signals with multiple impact intervals in the time domain. The length of one cycle is T o , and the amplitude is periodically modulated by the rotational frequency. (2) Taking the reciprocal f o of T o as the fundamental frequency of the local fault characteristic frequency, there are the fundamental frequency and its high-order harmonics in the spectrum of the excitation force with unequal intervals and amplitude modulation, and there are multi-order amplitude modulations with the outer race rotational frequency as the interval for each order of local fault characteristic frequency. (3) The main frequency intervals between the large-amplitude components in the spectrogram are zkf o / 2 and (z + y)kf o / 2 times the fundamental frequency.

[0037] Furthermore, the impact response characteristics of the rolling bearing considering unequal interval and amplitude modulation excitation force include: (1) There are multiple impact response intervals in the time domain of the response. The length of one cycle is T o , and the impact response amplitude is periodically modulated by the rotation frequency. (2) The fundamental frequency and its high-order harmonics exist in the response spectrum. For each order of fault characteristic frequency, there are multiple orders of amplitude modulation at intervals of the rotation frequency. (3) There are frequency intervals such as zkf o / 2 and (z + y)kf o / 2 times the fundamental frequency between the high-amplitude components in the response spectrum.

[0038] Furthermore, the Hilbert transform demodulation spectrum characteristics of the rolling bearing considering unequal interval and amplitude modulation excitation force include: 1) There are frequency components of the fundamental frequency f o of the local fault characteristic frequency of the raceway and its high-order harmonics. For each order of fault characteristic frequency, there are multiple orders of amplitude modulation at intervals of the rotation frequency; 2) The amplitudes are relatively large at frequencies of 2kf o , zkf o / 2 and (z + y)kf o / 2, which are the main frequency components; 3) There is a modulation phenomenon with all the local fault characteristic frequencies in 1) and 2) as the center frequencies and multiple orders of rotation frequencies as the modulation frequencies.

[0039] The present invention also provides a rolling bearing vibration response modeling and fault diagnosis system considering unequal interval and amplitude modulation excitation force.

[0040] The present invention also provides a computer device.

[0041] The present invention also provides a computer-readable storage medium.

[0042] Compared with the prior art, the beneficial effects of the present invention are at least as follows:

[0043] Taking the rolling bearing as the research object, the constructed model is more refined and can more accurately simulate the vibration mechanism of the bearing; the characteristics of the impact excitation, response signal, and envelope signal are analyzed in detail in sequence, decoupling the unequal interval and amplitude modulation characteristics of the excitation force from the vibration principle, revealing the fault characteristics of the impact response and envelope, and realizing the fault diagnosis of the rolling bearing considering unequal interval and amplitude modulation excitation force. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is the overall flowchart of the vibration response modeling and fault diagnosis in the embodiment of the present invention.

[0045] Figure 2 is the schematic diagram of the distribution of the roller and the spacer block in the embodiment of the present invention.

[0046] Figure 3 It is a schematic diagram of the bearing rolling in the embodiment of the present invention.

[0047] Figure 4 It is a schematic diagram of the uneven interval distribution of the rollers in the embodiment of the present invention.

[0048] Figure 5 It is a time-domain diagram of the excitation force simulation signal in the embodiment of the present invention.

[0049] Figure 6 It is a partially enlarged frequency-domain diagram of the excitation force simulation signal in the embodiment of the present invention.

[0050] Figure 7 It is a time-domain diagram of the impact response simulation signal in the embodiment of the present invention.

[0051] Figure 8 It is a frequency-domain diagram of the impact response simulation signal in the embodiment of the present invention.

[0052] Figure 9 It is a partially enlarged frequency-domain diagram of the impact response simulation signal in the embodiment of the present invention.

[0053] Figure 10 It is a partially enlarged frequency-domain diagram of the impact response simulation signal in the embodiment of the present invention.

[0054] Figure 11 It is a local diagram of the envelope demodulation spectrum of the impact response simulation signal in the embodiment of the present invention from 0 to 200 Hz.

[0055] Figure 12 It is a local diagram of the envelope demodulation spectrum of the impact response simulation signal in the embodiment of the present invention from 20 to 90 Hz.

[0056] Figure 13 It is 1 mm of the outer ring in the embodiment of the present invention 2 Local diagram of the envelope demodulation spectrum of the fault experiment from 0 to 200 Hz.

[0057] Figure 14 It is 1 mm of the outer ring in the embodiment of the present invention 2 Local diagram of the envelope demodulation spectrum of the fault experiment from 20 to 90 Hz.

[0058] Figure 15 It is 2 mm of the outer ring in the embodiment of the present invention 2 Local diagram of the envelope demodulation spectrum of the fault experiment from 0 to 200 Hz.

[0059] Figure 16 It is 2 mm of the outer ring in the embodiment of the present invention 2 Local diagram of the envelope demodulation spectrum of the fault experiment from 20 to 90 Hz. Specific implementation manner

[0060] To make the technical solutions and objectives of the present invention clearer and more understandable, 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 implementation manner of the present invention are not limited thereto.

[0061] As Figure 1 shown, a rolling bearing vibration response modeling and fault diagnosis method considering unequal interval and amplitude modulation excitation force provided by an embodiment of the present invention includes the following steps:

[0062] S1: Establish an excitation force sequence signal model with unequal interval and amplitude modulation: Determine the vibration impact time interval according to the positional relationship of rollers with unequal interval distribution; introduce an amplitude modulation function and derive the expression of the excitation force sequence with unequal interval and amplitude modulation.

[0063] Determine the spatial arrangement of the rolling bearing rollers through mathematical definition, specifically including: There are z rollers with a diameter of d in the bearing raceway, and y spacer blocks with a predetermined thickness d m are symmetrically arranged between the rollers. Based on the coordinate system, establish the angular position relationship between the centers of any two rollers, and its expression is:

[0064]

[0065] In the formula, y k and z k are the number of spacer blocks and rollers existing between two rollers in the rolling direction of the rollers; D is the pitch diameter of the roller center revolving around the axis.

[0066] In some embodiments of the present invention, the crossed roller bearing has a total of 4 spacer blocks, which are divided into 2 types of sizes and are symmetrically installed in pairs, as shown. Due to the introduction of the spacer blocks, the rollers of the crossed roller bearing are divided into two symmetrical parts by spacer blocks with different thicknesses. The rollers and the spacer blocks are closely arranged on the raceway, and the following structural relationship is satisfied on the bearing pitch circle:

[0067] πD = 2zd + 2d1 + 2d2

[0068] where D is the pitch diameter of the bearing, z is the number of rolling elements on one side of the crossed roller bearing, d is the diameter of the rolling element, and d1 and d2 are the thicknesses of the two types of spacer blocks respectively.

[0069] When a local fault occurs on the outer ring of a crossed roller bearing with 4 spacer blocks symmetrically installed in pairs, every time the rolling element rotates one circle relative to the outer ring, two groups of identical signals containing unequal interval impacts will be generated, which is equivalent to half a circle of rotation relative to the outer ring as a period. Therefore, the fundamental frequency f o of the local fault characteristic frequency of the outer ring is the frequency f of a single roller passing through the fault point of the racewaybo Twice that of, is:

[0070]

[0071] α is the contact angle of the bearing;

[0072] In some embodiments of the present invention, due to Figure 2 the uneven interval distribution of the rolling elements as shown, there will be 3 impact time intervals when the rolling elements pass through the local fault point on the outer ring.

[0073] (1) Impact time interval between two adjacent rollers on the same side without an interval block:

[0074]

[0075] f r [[ID=2,3]]is the revolution frequency of the rolling element, is the angle between two adjacent rollers on the same side without an interval block relative to the bearing axis.

[0076] (2) Impact time interval between two adjacent rollers on the same side with a small interval block d1:

[0077]

[0078] represents the angle between two adjacent rollers on the same side with a small interval block d1 relative to the bearing axis.

[0079] (3) Impact time interval between two adjacent rollers on the same side with a large interval block d2:

[0080]

[0081] represents the angle between two adjacent rollers on the same side with a small interval block d2 relative to the bearing axis.

[0082] (4) The roller has three impact intervals within a period T o (when the rolling element revolves half a turn) and satisfies:

[0083]

[0084] When there is a local fault point on the outer ring, the position of the fault point will change as the outer ring rotates. Impact will only occur when the fault point is in the load zone. The amplitude of the impact excitation force changes with the load. The amplitude of the impact excitation force is very small or zero in the non-load zone. Therefore, there is a phenomenon of rotational frequency amplitude modulation for the impact excitation force. The modulation function is a periodic function with the rotational frequency as the fundamental frequency and can be expanded by Fourier series, and the order is relatively high. Starting from the first roller after a certain large interval block d2, within a period T oInside, when the rolling element passes through the local fault point of the outer ring, an excitation force with unequal intervals and amplitude modulation is generated, and the excitation force function is:

[0085]

[0086] where a m and are respectively the amplitude and phase of the m-th order component of the rotational frequency amplitude modulation function; n is the order of the excitation force within one period; A is the amplitude of the excitation force; t n is the impact moment of the excitation force within one period; t is the time independent variable of the excitation force with unequal intervals and amplitude modulation; δ is the unit impulse function, and δ(t - t n ) is the impulse sequence of the excitation force function at the moment t n .

[0087]

[0088] Performing the Fourier series expansion of the excitation force function f(t) in exponential form gives:

[0089]

[0090] where b k represents the amplitude of the k-th order Fourier series, and j is the imaginary unit;

[0091]

[0092] Performing the Fourier transform on the excitation force function f(t) with unequal intervals and amplitude modulation gives:

[0093]

[0094] The excitation force function with one period extended to infinity is:

[0095]

[0096] In the formula, f represents the frequency independent variable in the spectrum, t' n represents the impact moment of the excitation force for an infinite long time, DIV(n, z / 2) represents the integer part of n divided by z / 2, and REM(n, z / 2) represents the remainder of n divided by z / 2.

[0097] S2: Vibration shock response signal modeling and envelope demodulation: Performing time-domain convolution analysis on the excitation force function with unequal intervals and amplitude modulation in step S1 using the frequency response function, establishing a vibration shock response signal model to characterize the fault features and modulation mechanism; performing envelope demodulation on the shock response through Hilbert transform, and separating the spectral cluster features formed by the coupling action of the modulation parameters and time-varying shocks in the demodulation spectrum.

[0098] For a damped vibration system, its unit impulse response function h(t) can be expressed as

[0099]

[0100] Among them, ξ b 、f n,b and f d are the b-th order damping ratio, undamped natural frequency and damped natural frequency of the system respectively; A h,b and are the amplitude and phase angle of the b-th order of the system respectively; N b is the order of the system's natural frequency.

[0101] The vibration response function of the system is:

[0102]

[0103] In the formula Represents the convolution operation.

[0104] The Fourier transform of the vibration response function is:

[0105] X(f)=F(f)H(f)

[0106] H(f) is the frequency response function of the damped vibration system.

[0107] The amplitude spectrum of the system vibration response considering unequal intervals and amplitude modulation excitation is:

[0108]

[0109] δ is the unit pulse function, δ(kf o ±mf out ) indicates that the spectrum is in kf o ±mf out The pulse sequence at the position; H is the frequency response function, H(kf o ±mf out ) indicates kf o ±mf out The frequency response function is sampled at unequal intervals; the frequency components with larger amplitude near the lth order natural frequency in the response spectrum X(f) are intercepted, f l is a harmonic fundamental frequency as the starting frequency, which contains N k Harmonic fundamental frequency, cutoff frequency is f l +(N k -1)f i , the response signal of the intercepted N-order natural frequency is approximately expressed in the form of an amplitude modulated multiplied signal. The response time domain signal can be approximately simplified as follows:

[0110]

[0111] Among them, c l,k 、 respectively represent the amplitude and phase at the passing frequency of the k-th harmonic of the s-th natural frequency of the response signal. N m represents the order of the outer race rotation frequency modulation in the intercepted signal.

[0112] Perform Hilbert transform amplitude demodulation on the impulse response. Simplify the derivation taking the envelope demodulation of the first resonance peak as an example. Let N = 1, and the response signal x1(t) is expressed as:

[0113]

[0114] c 1,k and respectively represent the amplitude and phase at the passing frequency of the k-th harmonic near the first natural frequency of the response signal, and f1 represents the starting frequency near the first natural frequency intercepted.

[0115] Its Hilbert transform pair is:

[0116] <,

[0117] The envelope z(t) of the intercepted response signal can be obtained as:

[0118]

[0119] z(t) represents the envelope of the response signal; and represent the time-domain signal of the system response of the frequency component with a larger amplitude near the first natural frequency intercepted and its Hilbert transform pair;

[0120] are all harmonic functions, and the periods are 1 / f out and 1 / f o , respectively. According to the convolution theorem, the amplitude spectrum of the envelope z(t), that is, the Hilbert transform demodulation amplitude spectrum of the response, can be expressed as:

[0121]

[0122] In the formula, δ(f ± mf out ) represents a pulse sequence with an interval of f out ; δ(f - kf o ) represents a pulse sequence with an interval of f o ; δ(f - kf o ± mf out ) represents a pulse sequence with a center frequency of kf o and an interval frequency of mf out ; um represents the amplitude of the m-th order frequency component of δ(f ± mf out ), v k represents the amplitude of the k-th order frequency component of δ(f - kf o ); E k,m represents the amplitudes of the k-th and m-th order frequencies of the amplitude spectrum |Z(f)|, C p , C q and C k are the amplitudes of each harmonic, p and q are the fundamental frequency harmonics of each harmonic, are the phases of each harmonic.

[0123] The demodulation spectrum of the response signal intercepting the components near the first natural frequency is composed of modulation spectral lines with the fundamental frequencies of each fault feature as the center frequencies and the rotation frequency as the modulation frequency. The demodulation spectrum of the rolling bearing impact response considering unequal intervals and amplitude modulation excitation forces intercepting multiple natural frequency components further generalized is also composed of modulation spectral lines with the fundamental frequencies of each fault feature as the center frequencies and the rotation frequency as the modulation frequency.

[0124] S3: Conduct numerical simulations of the bearing unequal interval and amplitude modulation excitation force - vibration response - envelope signal to reveal the bearing fault characteristics; compare the envelope spectrum characteristics of the vibration acceleration data of the bearing to be diagnosed and the simulation signal to obtain the fault diagnosis result of the bearing to be diagnosed, and realize the fault diagnosis of the rolling bearing under the action of unequal interval and amplitude modulation excitation force.

[0125] Numerical simulation and fault diagnosis: Based on the MATLAB platform, conduct numerical simulations of the bearing unequal interval and amplitude modulation excitation force - vibration response - envelope signal to obtain simulation signals and reveal the bearing fault characteristics; measure the vibration acceleration data of the bearing fault test bench, qualitatively compare the envelope spectrum characteristics of the measured signal (vibration acceleration data) and the simulation signal, and realize the fault diagnosis of the rolling bearing under the action of unequal interval and amplitude modulation excitation force.

[0126] S3.1 Carry out numerical simulations of the bearing vibration response based on the MATLAB platform, generate unequal interval and amplitude modulation fault excitation signals and response signals according to the bearing geometric parameters and working condition parameters, and complete envelope demodulation analysis to reveal the bearing fault characteristics;

[0127] S3.2 Obtain the measured vibration response signal (vibration acceleration data) of the bearing to be detected on the bearing fault test bench, perform envelope demodulation on the vibration response signal using the same geometric parameters and working condition parameters, qualitatively compare the envelope frequency spectrum characteristics between the experimental signal and the simulation signal, and diagnose the bearing fault. The bearing to be detected can be one, or two or more.

[0128] In a specific example, the numerical simulation parameters determined according to the actual size and working condition parameters of the cross-roller bearing of model SW-HG-20 in actual tests, the rotational speed is 334 rpm, the size and working condition parameters are shown in Table 1, and the impact time interval and fundamental frequency when the outer ring fails are shown in Table 2.

[0129] Table 1 Actual size and working condition parameters of the cross-roller bearing

[0130]

[0131] Table 4 Impact time interval and passing frequency when the outer ring of the cross-roller bearing has a local fault

[0132]

[0133] Let the intensity A of the excitation force be 1, and at this time the excitation force is a unit impulse excitation force. The excitation force simulation signal and its Fourier series are as Figure 4 and Figure 5 shown.

[0134] According to the system vibration response simulation parameters in Table 3, the system is subjected to a simulation operation under the action of an excitation force with unequal intervals and amplitude modulation, and the time-domain waveform x(t) of the response function is obtained as Figure 6 shown, and the response amplitude spectrum and its partial enlarged views are shown in Figures 8, 9 and 10.

[0135] Table 3 System vibration response simulation parameters

[0136]

[0137] Select the frequency range 2000 - 6000 Hz in the system response spectrum that contains the first-order and second-order natural frequencies, form a harmonic signal that is the sum of equal-frequency intervals and modulated spectral lines, and perform Hilbert transform amplitude demodulation simulation analysis on it to obtain the envelope spectrum as Figure 7 and 12 shown. 1) Only the fundamental frequency f o of the local fault characteristic frequency of the outer ring and its high-order multiples, as well as multiple modulation frequencies centered on each order of fault characteristic frequency and spaced by multiple orders of rotational frequencies; 2) 2kf o , zkf o / 2 and the amplitudes of the 12th, 22nd, and 32nd times of the fundamental frequency are relatively large; 3) The characteristics of the simulation signal are consistent with the theoretical modeling, verifying that the vibration shock response signal model described in step S2 is effective and reliable.

[0138] The following provides a detailed description of the verification tests for the two embodiments provided by the present invention:

[0139] In the embodiment of the present invention, the outer ring of the bearing is connected to the input shaft through a coupling, and the inner ring of the bearing is fixedly connected to the load arm, and the load arm simulates an overturning moment and a vertical downward radial static load applied to the bearing. In the embodiment of the present invention, the Miller BBM-PAK data acquisition and analysis system is adopted, and the vibration acceleration sensor is installed near the rolling bearing, and the sensor is connected to the data acquisition system, where the sampling frequency is 25,600 Hz and the sampling duration is 200 s.

[0140] Example 1: Artificial implantation of 1 mm in the crossed roller bearing 2 Analysis of the vibration signal of the faulty outer ring

[0141] A local fault area of 1 mm × 1 mm = 1 mm is introduced into the outer ring raceway 2 and the depth is 0.05 mm. The vibration acceleration response containing multiple resonance peaks is band-pass filtered at 2000 - 6000 Hz, and Hilbert transform envelope demodulation is performed to obtain the demodulation spectrum as shown in Figure 11 and 14 There is a modulation phenomenon with the first main frequency component 2kf o , the second main frequency component zkf o / 2 and 12, 22 and 32 times the fundamental frequency as the center frequencies and multiple order rotational frequencies as the modulation frequencies, and there are also rotational frequency and its high-order multiple frequency components. The distribution law is consistent with the foregoing theoretical derivation and numerical simulation, and it is diagnosed as a fault of the outer ring of the bearing.

[0142] Example 2: Artificial implantation of 2 mm in the crossed roller bearing 2 Analysis of the vibration signal of the faulty outer ring

[0143] A local fault area of 1 mm × 2 mm = 2 mm is introduced into the outer ring raceway 2 and the depth is 0.05 mm. The vibration acceleration response containing multiple resonance peaks is band-pass filtered at 2000 - 6000 Hz, and Hilbert transform envelope demodulation is performed to obtain the demodulation spectrum as shown in Figure 13 Figure 15 and 16 There is also a modulation phenomenon with the first main frequency component 2kf o , the second main frequency component zkf o / 2 and 12, 22 and 32 times the fundamental frequency as the center frequencies and multiple order rotational frequencies as the modulation frequencies, and there are also rotational frequency and its high-order multiple frequency components. The distribution law is consistent with the foregoing theoretical derivation and numerical simulation, and it is diagnosed as a fault of the outer ring of the bearing.

[0144] As can be seen from all the above embodiments, the analysis conclusion of the method proposed by the present invention is in good agreement with the experimental results, verifying the feasibility of the method of the present invention.

[0145] Example 3

[0146] This embodiment provides a rolling bearing vibration response modeling and fault diagnosis system considering unequally spaced and amplitude-modulated excitation forces, which is used to implement the method provided in the foregoing embodiment. The system includes the following modules:

[0147] An unequally spaced and amplitude-modulated excitation force sequence signal model establishment module, which is used to determine the vibration impact time interval according to the positional relationship of unequally spaced rollers; introduce an amplitude modulation function to construct an unequally spaced and amplitude-modulated excitation force sequence signal model;

[0148] A vibration impact response signal modeling and envelope demodulation module, which is used to perform time-domain convolution analysis on the unequally spaced and amplitude-modulated excitation force sequence signal model using a frequency response function, establish a vibration impact response signal model to characterize fault characteristics and modulation mechanisms; perform envelope demodulation on the impact response through Hilbert transform, and separate the spectral cluster characteristics formed by the coupling action of modulation parameters and time-varying impacts in the demodulation spectrum;

[0149] A fault diagnosis module, which is used to perform numerical simulation of the bearing unequally spaced and amplitude-modulated excitation force-vibration response-envelope signal, reveal the bearing fault characteristics; compare the vibration acceleration data of the bearing to be diagnosed with the envelope spectrum characteristics of the simulation signal to obtain the fault diagnosis result of the bearing to be diagnosed.

[0150] Embodiment 4

[0151] This embodiment provides a computer device, which includes a processor and a memory. The memory is used to store instructions or computer programs, and the processor is used to execute the instructions or computer programs in the memory so that the device executes the steps of the method described in the foregoing embodiment.

[0152] Embodiment 5

[0153] This embodiment provides a computer-readable storage medium, in which instructions are stored. When the instructions run on a device, the device is caused to execute the steps of the method described in the foregoing embodiment.

[0154] The embodiment of the present invention establishes a rolling bearing vibration response model considering unequally spaced and amplitude-modulated excitation forces. The model is more refined and can more accurately simulate the vibration mechanism of the bearing; the characteristics of the impact excitation, response signal, and envelope signal are analyzed in detail in turn, decoupling the unequally spaced and amplitude-modulated characteristics of the excitation force from the vibration principle, revealing the fault characteristics of the impact response and envelope, and realizing the fault diagnosis of rolling bearings considering unequally spaced and amplitude-modulated excitation forces.

[0155] It should be noted that although the implementation of the present invention has been described in detail with reference to examples, those skilled in the art can easily understand that any modifications, substitutions, improvements, etc. made within the spirit and principles of the present invention as set forth in the appended claims should be included within the protection scope of the present invention.

Claims

1. A rolling bearing vibration response modeling and fault diagnosis method considering unequal interval and amplitude modulation excitation force, characterized in that, It includes the following steps: According to the positional relationship of rollers with unequal intervals, determine the vibration impact time interval; introduce an amplitude modulation function to construct an excitation force sequence signal model with unequal intervals and amplitude modulation; Perform time-domain convolution analysis on the excitation force sequence signal model with unequal intervals and amplitude modulation using the frequency response function, and establish a vibration impact response signal model to characterize the fault characteristics and modulation mechanism; perform envelope demodulation on the impact response through Hilbert transform, and separate the spectral cluster characteristics formed by the coupling effect of modulation parameters and time-varying impacts in the demodulation spectrum; Conduct numerical simulation of the excitation force-vibration response-envelope signal of the bearing with unequal intervals and amplitude modulation to reveal the bearing fault characteristics; compare the vibration acceleration data of the bearing to be diagnosed with the envelope spectrum characteristics of the simulation signal to obtain the fault diagnosis result of the bearing to be diagnosed.

2. The rolling bearing vibration response modeling and fault diagnosis method according to claim 1, which takes into account unequal intervals and amplitude modulation excitation forces, is characterized in that The method for determining the positional relationship of the rollers with unequal intervals is as follows: There are z rollers with a diameter of d in the bearing raceway, and y spacer blocks with a predetermined thickness d are symmetrically arranged between the rollers. Based on the coordinate system, the angular position relationship between the centers of any two rollers is established, and its expression is: m The size of the spacer block, based on the coordinate system, the angular position relationship between the centers of any two rollers is established, and its expression is: where y k and z k are the number of spacer blocks and rollers existing between two rollers in the rolling direction of the rollers; D is the pitch diameter of the roller center revolving around the axis.

3. The rolling bearing vibration response modeling and fault diagnosis method according to claim 2, which takes into account the unequally spaced and amplitude-modulated excitation force, is characterized in that According to the angular positional relationship expression between the centers of two rollers, determine the vibration impact time interval when the rollers pass through the raceway fault point in sequence, expressed as: where t k is the vibration shock time interval, and f bo is the frequency of a single roller passing through the fault point of the raceway.

4. A rolling bearing vibration response modeling and fault diagnosis method considering unequally spaced and amplitude modulation excitation forces according to claim 3, characterized in that The introduction of the amplitude modulation function to construct the excitation force sequence signal model with unequal intervals and amplitude modulation includes: Introduce an amplitude modulation function to establish the time-domain expression of the excitation force with unequal intervals and amplitude modulation within the revolution period of the roller: where \(f(t)\) is the excitation force function with unequal intervals and amplitude modulation; \(a\) m and are the amplitude and phase of the \(m\)-th order component of the rotational frequency amplitude modulation function respectively; \(f\) out is the rotational frequency of the bearing; \(n\) is the order of the excitation force within one period; \(A\) is the amplitude of the excitation force; \(t\) n is the impact moment of the excitation force; \(t\) is the time independent variable of the excitation force function with unequal intervals and amplitude modulation; \(\delta\) is the unit impulse function, and \(\delta(t - t\) n ) is the impulse sequence of the excitation force function at the moment \(t\) n ; Perform Fourier transform on the excitation force function f(t), expressed as: Wherein, F(f) represents the Fourier transform of the excitation force function f(t), and b k represents the amplitude of the k-th order Fourier series, and f o represents the fundamental frequency of the local fault characteristic frequency, and δ[f - (kf o ± mf out )] is the impulse sequence of the Fourier transform of the excitation force function at the frequency of kf o ± mf out , and f represents the frequency independent variable in the spectrum.

5. The rolling bearing vibration response modeling and fault diagnosis method that considers unequal interval and amplitude modulation excitation force according to claim 1, characterized in that The use of the frequency response function to perform time-domain convolution analysis on the excitation force sequence signal model with unequal intervals and amplitude modulation to establish a vibration impact response signal model to characterize the fault characteristics and modulation mechanism includes: Perform time-domain convolution calculation on the excitation force sequence signal model with unequal intervals and amplitude modulation using the frequency response function to establish a vibration impact response signal model, and the amplitude spectrum of the vibration impact response is expressed as: where \(H(f)\) is the frequency response function of the damped vibration system, \(H(kf o \pm mf out ) represents the unequally spaced sampling of the frequency response function with \(kf o \pm mf out , \(b k \) represents the amplitude of the \(k\)-th order Fourier series, \(f o \) represents the fundamental frequency of the local fault characteristic frequency, \(a m \) is the amplitude of the \(m\)-th order component of the rotational frequency amplitude modulation function, \(f out \) is the rotational frequency of the bearing, \(\delta [f-(kf o \pm mf out )]\) is the impulse sequence of the Fourier transform of the excitation force function at the frequency \(kf o \pm mf out , and \(\delta (kf o \pm mf out )\) represents the impulse sequence at \(kf o \pm mf out \) in the spectrum; Ignore the frequency components with small amplitudes far from the resonance peaks in the response spectrum X(f), and intercept the frequency components with large amplitudes near the l-th natural frequency, f l is a certain harmonic fundamental frequency as the starting frequency, and a total of N k harmonic fundamental frequencies, and the cut-off frequency is f l +(k - 1)f o , and approximately represent the response signal of the intercepted N-th order natural frequency in the form of an amplitude-modulated multiplication signal. The time-domain signal of the system response is simplified as: where c l,k , represent the amplitude and phase at the k-th harmonic passing frequency of the l-th natural frequency of the response signal, respectively; N m represents the order of the rotational frequency modulation in the intercepted signal, is the phase of the m-th order component of the rotational frequency amplitude modulation function.

6. A method for modeling the vibration response of a rolling bearing considering unequally spaced and amplitude-modulated excitation forces and fault diagnosis according to claim 5, characterized in that The separation of the spectral cluster characteristics formed by the coupling effect of modulation parameters and time-varying impacts in the demodulation spectrum through envelope demodulation of the impact response by Hilbert transform includes: Perform amplitude demodulation on the impact response by Hilbert transform, and the envelope and its amplitude spectrum of the response are expressed as: where \(z(t)\) represents the envelope of the response signal; and represent the time-domain signal of the system response and its Hilbert transform pair that intercept the frequency components with larger amplitudes near the first natural frequency; \(u\) m represents the amplitude of the \(m\)-th order frequency of \(\delta(f\pm mf\) out ), and \(\delta(f\pm mf\) out ) represents a pulse sequence with an interval of \(f\) out ; \(v\) k represents the amplitude of the \(k\)-th order frequency of \(\delta(f - kf\) o ), and \(\delta(f - kf\) o ) represents a pulse sequence with an interval of \(f\) o ; \(E\) k,m represents the amplitudes of the \(k\)-th and \(m\)-th order frequencies of the amplitude spectrum \(|Z(f)|\); \(C\) p , \(C\) q and \(C\) k are the amplitudes of each harmonic; \(p\) and \(q\) are the fundamental frequency harmonics of each harmonic, and \(\varphi\) is the phase of each harmonic.

7. A rolling bearing vibration response modeling and fault diagnosis method considering unequally spaced and amplitude-modulated excitation forces according to any one of claims 1-6, characterized in that Conduct numerical simulation of the excitation force-vibration response-envelope signal of the bearing with unequal intervals and amplitude modulation to reveal the bearing fault characteristics; compare the vibration acceleration data of the bearing to be diagnosed with the envelope spectrum characteristics of the simulation signal to obtain the fault diagnosis result of the bearing to be diagnosed, including: Based on the MATLAB platform, conduct numerical simulation of the bearing vibration response, generate fault excitation signals and response signals with unequal intervals and amplitude modulation according to the bearing geometry and operating conditions parameters, and perform envelope demodulation analysis to reveal the bearing fault characteristics; Obtain the measured vibration response signals of different damaged components on the bearing fault test bench, perform envelope demodulation on the response signals using the same parameters, and qualitatively compare the envelope spectral characteristics between the experimental signals and the simulation signals to diagnose the bearing faults.

8. A rolling bearing vibration response modeling and fault diagnosis system considering unequal interval and amplitude modulation excitation force, characterized in that, For implementing the method described in any one of claims 1-7, the system includes the following modules: An excitation force sequence signal model establishment module with unequal intervals and amplitude modulation, which is used to determine the vibration impact time interval according to the positional relationship of rollers with unequal intervals; introduce an amplitude modulation function to construct an excitation force sequence signal model with unequal intervals and amplitude modulation; Vibration shock response signal modeling and envelope demodulation module, which is used to perform time-domain convolution analysis on the excitation force sequence signal model with unequal intervals and amplitude modulation by using the frequency response function, establish a vibration shock response signal model to characterize the fault characteristics and modulation mechanism; perform envelope demodulation on the shock response through Hilbert transform, and separate the spectral cluster characteristics formed by the coupling action of modulation parameters and time-varying shocks in the demodulation spectrum; Fault diagnosis module, which is used to perform numerical simulation on the excitation force-vibration response-envelope signal of the bearing with unequal intervals and amplitude modulation, reveal the bearing fault characteristics; compare the vibration acceleration data of the bearing to be diagnosed with the envelope spectrum characteristics of the simulation signal to obtain the fault diagnosis result of the bearing to be diagnosed.

9. A computer device, characterized in that, The device includes a processor and a memory. The memory is used to store instructions or computer programs. The processor is used to execute the instructions or computer programs in the memory so that the device executes the steps of the method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, Instructions are stored in the computer-readable storage medium. When the instructions run on the device, the device executes the steps of the method according to any one of claims 1-7.

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