Bearing outer ring fault diagnosis test parameter setting optimization method

Abstract

The invention provides a bearing outer ring fault diagnosis test parameter setting optimization method, which comprises the following steps of: firstly, accurately acquiring structural parameters of a bearing by utilizing a measuring tool; secondly, testing and calculating the inherent frequency and the damping ratio of the bearing in the installed state through a modal experiment; selecting test working condition parameters according to the actual operation environment of the bearing, and calculating the fault characteristic frequency of the bearing; bearing fault simulation signal band-pass filtering processing is constructed; meanwhile, constructing a fault signal equivalent model; carrying out resonance demodulation analysis on the equivalent model, extracting an envelope spectrum and evaluating a fault diagnosis effect; and finally, circularly adjusting working condition parameters, iteratively optimizing the test working conditions, and selecting the working condition with the maximum fault characteristic frequency amplitude and the minimum noise interference as the optimal test condition. According to the invention, the accuracy and reliability of bearing outer ring fault detection are effectively improved, and powerful support is provided for fault diagnosis of mechanical equipment.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical equipment fault diagnosis, and in particular to a method for optimizing the setting of test parameters for bearing outer ring fault diagnosis. Background Art

[0002] Rolling bearings are core precision components supporting the operation of rotating machinery, and their operating status directly affects the efficiency and reliability of the equipment. Their structure consists of an outer ring, inner ring, rolling elements, and a cage, achieving low-friction load transfer through rolling contact. Especially when subjected to radial loads, the outer ring often becomes a high-incidence area for localized failures such as fatigue spalling and wear due to periodic stress concentration. According to statistics, approximately 30% of mechanical failures are caused by bearing failure, with outer ring failures accounting for a significant proportion. When a defect exists in the outer ring, the roller's periodic passage through the fault point triggers impact excitation, stimulating a vibration response modulated by the system's natural frequency, forming a high-frequency resonant signal characterized by the fault's passage frequency.

[0003] Hilbert resonance demodulation, which extracts fault characteristic frequencies through bandpass filtering and envelope spectrum analysis, has become a mainstream method for bearing fault diagnosis. For example, a rolling bearing fault detection method (Wu Jiande, Wang Ying, Lang Xun, et al. A Rolling Bearing Fault Detection Method [P]. Yunnan Province: CN202411533814.1, 2024-11-26) utilizes Hilbert demodulation to process the reconstructed signal and obtain an envelope spectrum, which is then used to determine the presence and location of a bearing fault. However, the current application of Hilbert resonance demodulation technology lacks quantitative analysis, resulting in a lack of theoretical guidance for the amplitude analysis of characteristic frequencies in the envelope spectrum. In engineering practice, there is a lack of quantitative understanding of the correspondence between system physical parameters and envelope amplitude spectrum distribution. As a result, the selection of sensor location, filtering range, and bearing speed in engineering testing often relies on experience, and improper selection can easily lead to missed faults.

[0004] In order to solve the above problems, the present invention provides a method for optimizing the setting of bearing outer ring fault diagnosis test parameters. The method has the following advantages: the present invention provides a clear theoretical analysis basis for the application of Hilbert resonance demodulation technology by constructing a fault signal equivalent model of the bearing outer ring fault vibration response; by repeatedly selecting test condition parameters, constructing a signal model, performing bandpass filtering and quantitatively analyzing the Hilbert resonance demodulation process, the present invention can find the optimal test condition, thereby guiding the reasonable selection of sensor position, filtering range and bearing speed in engineering testing, and improving the accuracy and reliability of diagnosis. Summary of the Invention

[0005] To address the challenges of existing technologies, this paper proposes a method for optimizing test parameters for bearing outer race fault diagnosis. This method aims to achieve high-precision detection of bearing outer race faults by constructing an equivalent fault signal model for the fault, combined with Hilbert resonance demodulation technology. This method also optimizes test parameters to improve the accuracy and reliability of mechanical equipment fault diagnosis.

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

[0007] A method for optimizing parameters of a bearing outer ring fault diagnosis test comprises the following steps:

[0008] a) Measure the structural parameters of the bearing, including the diameters of the inner and outer rings, the diameter of the rollers, and the number of rollers;

[0009] b) Test and calculate the natural frequency and damping ratio of the system with the bearing installed;

[0010] c) Select test operating parameters, including inner ring input speed frequency and load, and calculate the bearing fault characteristic frequency based on the bearing structural parameters and inner ring speed;

[0011] d) constructing a fault simulation signal of the bearing outer race fault vibration response;

[0012] e) performing bandpass filtering on the fault simulation signal, wherein the filtering parameters are selected according to the resonance peak determined in step b);

[0013] f) constructing an equivalent model of the fault signal, wherein the parameters of the equivalent model are selected based on the transfer function, fault passage frequency, and frequency multiplication in steps b) and c), and verifying the equivalent model by comparing it with the simulated signal after filtering in step e);

[0014] g) Quantitatively analyze the Hilbert resonance demodulation process of the fault signal equivalent model and obtain the demodulated envelope signal;

[0015] h) Circularly adjust the speed and load parameters, and repeat steps c) to step

[0016] g) Compare the fault feature clarity of the envelope spectrum under different working conditions and select the working condition with the largest fault frequency amplitude and the smallest noise interference as the optimal test condition.

[0017] Furthermore, step b) specifically includes:

[0018] Install the bearing in the mechanical system and install accelerometers at key locations. Use a data acquisition instrument to collect the vibration response signal measured by the accelerometer and the excitation signal applied by the hammer. Set the sampling frequency and sampling duration parameters to ensure that the collected signals accurately reflect the dynamic characteristics of the system.

[0019] The vibration response transfer function and coherence function of the system are measured using the hammer impact method;

[0020] Determine the natural frequency of the system based on the transfer function;

[0021] Calculates the damping ratio of a selected resonance peak using the half-power bandwidth method.

[0022] Furthermore, the damping ratio ζ is calculated as follows:

[0023]

[0024] Where f1 and f2 are the frequencies corresponding to the half-power point, f n is the natural frequency.

[0025] Furthermore, in step c), the outer race local fault frequency is calculated using the following formula:

[0026]

[0027] Where, f o is the outer ring fault passing frequency, Z is the number of rollers, d is the roller diameter, D is the bearing pitch diameter, α is the contact angle, f rps Enter the rotational frequency for the inner ring.

[0028] Furthermore, in step d), when constructing the fault simulation signal, the bearing assembly in the mechanical system is considered as a simplified multi-degree-of-freedom spring damping model. For a mechanical system with U degrees of freedom, the unit impulse response function of its vibration acceleration is expressed as:

[0029]

[0030] Where, is the system force F input to acceleration The unit impulse response of the output, U is the order of the system's degree of freedom, t represents time, the value of t is (0, +∞), m u is the modal mass of the u-th order, ζ u is the u-th order damping ratio, ω n,u is the u-th order undamped natural frequency of the system; ω d,u is the u-th order damped natural frequency; is the u-th order phase angle. When a local fault occurs in the outer ring, the excitation force of the mechanical system is a pulse sequence f(t) with equal intervals and amplitudes, which can be expressed as:

[0031]

[0032] Where i represents the order, t represents the time, C represents the amplitude of the pulse sequence, δ(.) represents the unit pulse function, τ represents the time interval, and τ = 1 / f o , fo is the outer race fault passing frequency;

[0033] The impact vibration signal caused by the bearing fault is expressed as the convolution of the pulse train and the unit impulse response Expressed as:

[0034]

[0035] Where U represents the order of freedom, K represents the number of impacts, and f n,u represents the u-th order undamped natural frequency, f d,u Indicates that the u-th order has a damped natural frequency, m u represents the modal mass of the uth order, and the vibration signal of the bearing fault is simulated using formula (5).

[0036] Furthermore, in step e), the upper and lower limits of the bandpass filtering are selected according to the center frequency of the selected resonance peak and the resonance peak interval. After the bandpass filtering, only the frequency cost of the impact vibration signal within the filtering interval is retained, and a limited number of spectral lines remain in its spectrum. The frequency domain expression is expressed as follows:

[0037]

[0038] Where U represents the order of the degree of freedom, is the system force F input to acceleration The output frequency response function, w represents the order of the spectrum line, w1 and w2 are the orders corresponding to the first and last spectrum lines respectively, j is a unit imaginary number, f o is the outer race fault passing frequency, f n,u represents the u-th order undamped natural frequency, ζ u is the u-th order damping ratio.

[0039] Furthermore, in step f), when constructing the fault simulation signal, the equivalent model of the fault signal is constructed by superimposing the harmonic signals. The equivalent model expression is:

[0040]

[0041] Where M is used to describe the total number of spectral lines, and its value is one less than the number of corresponding spectral lines. t represents time, and f o is the outer race fault passing frequency, f l is the frequency corresponding to the first spectral line from the left of the amplitude spectrum, ψ m is the phase corresponding to the m+1th spectral line, B m is the amplitude of the m+1th spectral line. The amplitude spectrum of B m =T m *C,T mis the amplitude of the m+1th spectral line obtained by mapping the transfer function, and C is the amplification factor caused by the rotation speed.

[0042] Furthermore, in step g), based on the theoretical framework of Hilbert transform, the Hilbert transform expression of the impact vibration signal is derived as follows:

[0043]

[0044] In the formula Represents the Hilbert transform of the vibration signal, M is used to describe the total number of spectral lines, the value is one less than the number of corresponding spectral lines, t represents time, B m is the amplitude of the m+1th spectral line, f o is the outer race fault passing frequency, f l is the frequency corresponding to the first spectral line from the left of the amplitude spectrum, ψ m is the phase corresponding to the m+1th spectral line;

[0045] Then, through Hilbert demodulation, the impact vibration signal is converted into its envelope signal, which is in the form of:

[0046]

[0047] Where B p , ψ p Represent the amplitude and phase of the pth spectral line, B q , ψ q represents the amplitude and phase of the qth spectral line.

[0048] Furthermore, in step c), the influence of noise is taken into consideration and the environmental noise of the test condition is measured to ensure the accuracy and reliability of the test results.

[0049] A system for implementing the method for optimizing the setting of test parameters for fault diagnosis of a bearing outer ring includes a drive motor, a transmission belt, a coupling, a shaft, a bearing seat, and an acceleration sensor; the coupling is installed between the drive motor and the bearing seat via the shaft, and the drive motor causes the bearing to run in the bearing seat via devices such as a transmission belt and a connecting bearing; the acceleration sensor is arranged on the bearing seat and the shaft neck; a force hammer is used to apply pulse excitation to the side of the bearing seat end cover, and a data acquisition instrument is used to collect the vibration response signal measured by the acceleration sensor and the excitation signal applied by the force hammer.

[0050] Compared with the existing technology, the beneficial effects of the present invention are:

[0051] Before a bearing failure actually occurs, numerical simulation dynamically replicates the vibration response characteristics of a bearing outer race failure. Combined with time-frequency domain analysis, this system determines optimal detection parameters and sensor placement, providing a theoretical basis for setting maintenance and inspection parameters. By developing a detection parameter configuration scheme based on resonance demodulation results, proactive guidance for bearing condition monitoring is achieved. This system can provide early warning of potential failures three to six operating cycles in advance, effectively preventing unexpected accidents. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 The present invention is a flow chart of an embodiment of a method for optimizing the setting of test parameters for a bearing outer ring fault diagnosis.

[0053] Figure 2 Schematic diagram of the bearing fault experimental platform and test environment in the embodiment.

[0054] Figure 3 is a transfer function diagram of the mechanical system where the bearing is located in the embodiment.

[0055] Figure 4 is a coherence function diagram of the mechanical system where the bearing is located in the embodiment.

[0056] Figure 5 3 is a time domain diagram of the bearing fault simulation signal after filtering in the embodiment.

[0057] Figure 6 3 is a frequency domain diagram of the bearing fault simulation signal after filtering in the embodiment.

[0058] Figure 7 is a time domain diagram of the equivalent model of the bearing fault signal in the embodiment.

[0059] Figure 8 is a time domain diagram of the envelope signal of the equivalent model in the embodiment.

[0060] Figure 9 : is the spectrum of the envelope signal of the equivalent model under the 300 rpm working condition in the embodiment.

[0061] Figure 10 : is the spectrum of the envelope signal of the equivalent model under the 600 rpm working condition in the embodiment.

[0062] Figure 11 : is the spectrum of the envelope signal of the equivalent model under the 900 rpm working condition in the embodiment.

[0063] Figure 12 : is the spectrum of the envelope signal of the equivalent model under the working condition of 1200 rpm in the embodiment.

[0064] Figure 13 : is the spectrum of the envelope signal of the equivalent model under the working condition of 1500 rpm in the embodiment. DETAILED DESCRIPTION

[0065] The present invention is described in detail below with reference to specific embodiments.

[0066] The system of the present embodiment of a method for optimizing the setting of bearing outer ring fault diagnosis test parameters includes a drive motor, a transmission belt, a coupling, a shaft, a bearing seat, an acceleration sensor, etc. Figure 2 As shown, the coupling is installed between the drive motor and the bearing seat through a shaft, and the drive motor causes the bearing to run in the bearing seat through a transmission belt, a connecting bearing and other devices; the acceleration sensor is arranged in key positions such as the bearing seat and the shaft neck;

[0067] Use a hammer to apply pulse excitation to the bearing seat, ensuring accurate direction and position, moderate and stable force, and ensuring repeatability and reliability of the excitation signal. Use a data acquisition instrument to collect the vibration response signal measured by the accelerometer and the excitation signal applied by the hammer. Set appropriate parameters such as sampling frequency and sampling duration to ensure that the collected signal accurately reflects the dynamic characteristics of the system.

[0068] like Figure 1 As shown, this embodiment proposes a method for optimizing the setting of bearing outer ring fault diagnosis test parameters, which is implemented by the following steps:

[0069] Step 1. Measure the structural parameters of the bearing.

[0070] First, use measuring tools such as micrometers, outside diameter gauges, and vernier calipers to measure the basic structural parameters of the bearing. Specific measurements include: inner and outer ring diameters, pitch diameter, roller diameter, number of rollers, and contact angle.

[0071] These parameters form the basis for subsequent fault characteristic frequency calculation and model building. For example, for a cylindrical roller bearing model N205M, the key parameters are as follows: bearing pitch diameter 37.7 mm, roller radius 7.4 mm, contact angle 0°, and number of rollers 12. Measurement accuracy is crucial to ensure the accuracy of subsequent calculations.

[0072] Step 2. Test and calculate the natural frequency and damping ratio of the system with the bearing installed.

[0073] In order to accurately obtain the natural frequency and damping ratio of the system when the bearing is installed, a modal experiment is required. First, prepare high-precision accelerometers, force hammers, and data acquisition instruments to ensure that all equipment is calibrated. According to the structure and dynamic characteristics of the bearing system, accelerometers are reasonably arranged at key locations such as the bearing seat and shaft neck, and attention is paid to the installation method and position to avoid measurement errors. Use a force hammer to apply pulse excitation to the system. When striking, ensure that the direction and position are accurate, the force is moderate and stable, and the excitation signal is repeatable and reliable. Use the data acquisition instrument to collect the vibration response signal measured by the accelerometer and the excitation signal applied by the force hammer, set appropriate parameters such as sampling frequency and sampling duration, and ensure that the collected signal can accurately reflect the dynamic characteristics of the system.

[0074] After completing modal test data acquisition, the signals need to be processed to obtain the system's transfer function and coherence function. By analyzing the transfer function, the peak frequencies are found, which are the system's natural frequencies. In practice, the amplitude-frequency characteristic curve of the transfer function can be plotted to intuitively determine the peak frequencies.

[0075] like Figure 2 As shown, the bearing is installed in the bearing seat of the bearing fault diagnosis test system, and multiple sensors are installed. The vibration response transfer function and coherence function of the system are measured using the hammer tapping method. The natural frequency and damping ratio are calculated based on the transfer function. The specific steps are as follows:

[0076] Installation and tapping: Install the bearing on the bearing seat of the bearing fault diagnosis test system to ensure that it is firmly connected to the mechanical system. Use a hammer to tap the end cover of the bearing seat (near the fault-prone location) while collecting the vibration response signal through the acceleration sensor.

[0077] Data acquisition and analysis: Use a data acquisition card to record the vibration response signal, calculate and analyze the transfer function and coherence function of the bearing seat of the bearing fault diagnosis test system. The formula of the transfer function is:

[0078]

[0079] Where s is a complex variable, H(s), Y(s), and X(s) are the transfer function, the Laplace transform of the system output vibration signal, and the Laplace transform of the system input force signal, respectively. The interference function expression is:

[0080]

[0081] Where ω is the frequency, is the squared coherence function, G xy (ω) The cross power spectral density between the input signal and the output signal, G xx (ω), Gyy (ω) are the auto-power spectral density of the input signal and the auto-power spectral density of the output signal, respectively.

[0082] like Figure 3 and Figure 4 The reliability of the transfer function data is verified by analyzing the coherence function. The transfer function data within the frequency range where the coherence function value is close to 1 is considered reliable.

[0083] Damping ratio calculation: Use the half-power bandwidth method to analyze the selected resonance peak and accurately calculate the damping ratio of each order of the system. The half-power bandwidth method is a commonly used method to calculate the damping ratio. On the amplitude-frequency characteristic curve of the transfer function, find the peak amplitude. The difference between the two frequencies corresponding to the doublet is the half-power bandwidth, and the damping ratio ζ is calculated as follows:

[0084]

[0085] Where f1 and f2 are the frequencies corresponding to the half-power point, f n is the natural frequency.

[0086] For example, the center frequency of resonance peak A is 5216 Hz, the half-power bandwidth is about 160 Hz, and the damping ratio calculated by the half-power bandwidth method is 0.015; the center frequency of resonance peak B is 5700 Hz, the half-power bandwidth is about 220 Hz, and the damping ratio calculated by the half-power bandwidth method is 0.019.

[0087] Resonance Peak Analysis: Further analyze the transfer function spectrum and record the system's resonance peaks. When selecting resonance peaks, prioritize those with higher frequencies and larger damping coefficients. If multiple resonance peaks are found in the transfer function, such as Resonance Peak A and Resonance Peak B, prioritize Resonance Peak B, which has a natural frequency of 5700 Hz and a damping ratio of 0.019.

[0088] Step 3. Select the test operating parameters and calculate the bearing fault characteristic frequency.

[0089] According to the actual operating environment of the bearing, reasonably select the test condition parameters, such as the inner ring input speed frequency, load, etc. If necessary, measure the ambient noise of the test condition to ensure the accuracy and reliability of the test results. The specific steps are as follows:

[0090] Operating parameter selection: Initially set the inner ring input frequency to 300 rpm, increasing by a fixed value of 300 rpm each cycle, and the load to 50% of the rated load. If the ambient noise is high, use a sound level meter to measure and record the noise level.

[0091] Calculation of fault characteristic frequency: Based on the structural parameters of the bearing and the speed of the inner ring, calculate the local fault frequency of the outer ring. The calculation formula is:

[0092]

[0093] Where, f o is the outer ring fault passing frequency, Z is the number of rollers, d is the roller diameter, D is the bearing pitch diameter, α is the contact angle, f rps Enter the rotational frequency for the inner ring.

[0094] For example, for the above bearing, the number of rollers is 12, the roller diameter is 14.8 mm, the bearing pitch diameter is 37.7 mm, the contact angle is 0°, and the inner ring input speed is 600 rpm. Substituting the parameters into formula (11) yields the outer ring fault passing frequency of 48.22 Hz.

[0095] Step 4. Construct a fault simulation signal of the bearing outer race fault vibration response.

[0096] The bearing assembly in a mechanical system can be viewed as a simplified representation of a multi-degree-of-freedom spring-damper model, and its dynamic behavior can be approximately viewed as the linear superposition of several single-degree-of-freedom systems. When a bearing roller encounters a raceway defect, it triggers an impact excitation, and the signal captured by the sensor corresponds to the acceleration response under this impulse force excitation. In the case of low damping, for a mechanical system with U degrees of freedom, the unit impulse response function of its vibration acceleration can be approximately expressed as:

[0097]

[0098] Where, is the system force F input to acceleration The unit impulse response of the output, U is the order of the system's degree of freedom, and the value of t is (0, +∞), m u is the modal mass of the u-th order, ζ u is the u-th order damping ratio, ω n,u is the u-th order undamped natural frequency; ω d,u is the u-th order damped natural frequency; is the u-th order phase angle. When a local fault occurs in the outer ring, the excitation force of the mechanical system is a pulse sequence f(t) with equal intervals and amplitudes, which can be expressed as:

[0099]

[0100] Where i represents the order, t represents the time, C represents the amplitude of the pulse sequence, δ(.) represents the unit pulse function, τ represents the time interval, and τ = 1 / f o , f o is the outer race fault passing frequency. The impact vibration signal caused by the fault is the convolution of the pulse sequence and the unit impulse response. Expressed as:

[0101]

[0102] In the formula, K is the number of impacts, U is the order of the degree of freedom, K is the number of impacts, and f n,u represents the u-th order undamped natural frequency, f d,u Indicates that the u-th order has a damped natural frequency, m u In actual calculation, the vibration signal of bearing fault is simulated using formula (5).

[0103] In one embodiment, a fault simulation signal containing a second-order natural frequency is constructed. The pulse interval is the inverse of the fault passing frequency, i.e. 0.0207s. The order U is equal to 2, and the natural frequency f is n,1 Take 5216Hz, the natural frequency f n,2 Take 5700Hz, damping ratio ζ1 as 0.015, damping ratio ζ2 as 0.019, phase angle and All are set to 0, the sampling frequency is 25600, and the parameters are substituted into expression (14) to obtain the simulation signal when the outer race fault occurs.

[0104] Step 5. Band-pass filter the fault simulation signal.

[0105] The vibration signal collected by the accelerometer usually contains noise and other influencing factors. In order to improve the signal-to-noise ratio, the measured vibration acceleration response signal is first bandpass filtered. According to step 2, the effective transfer function is confirmed and the appropriate resonance peak is selected from it, with priority given to the resonance peak with a higher frequency and a larger damping coefficient. The upper and lower limits of the bandpass filter are selected based on the center frequency and resonance peak interval of the selected resonance peak. After bandpass filtering, only the frequency cost of the impact vibration signal within the filter interval is retained, and a limited number of spectral lines remain in its spectrum. The frequency domain expression can be expressed as:

[0106]

[0107] Where U represents the order of the degree of freedom, is the system force F input to acceleration The output frequency response function, w represents the order of the spectrum line, w1 and w2 are the orders corresponding to the first and last spectrum lines respectively, j is a unit imaginary number, f o is the outer race fault passing frequency, f n,u represents the u-th order undamped natural frequency.

[0108] As an example, in this embodiment, the filter parameters are selected as follows: based on the effective transfer function confirmed in step 2, the center frequency and the range of the resonance peak are selected as the upper and lower limits of the bandpass filter. For example, if the center frequency of resonance peak A is 5216 Hz and the bandwidth is approximately 600 Hz, the upper and lower limits of the filter are selected as 4900 Hz and 5500 Hz, respectively; if the center frequency of resonance peak B is 5700 Hz and the bandwidth is approximately 550 Hz, the upper and lower limits of the filter are selected as 5450 Hz and 6000 Hz, respectively.

[0109] Filtering: Use a digital filter to perform bandpass filtering on the signal. The filtered signal only retains the frequency components within the filter range, and a limited number of spectral lines remain in its spectrum. For resonance peak B, the filter bandwidth is 600Hz, and 12 high-amplitude spectral lines remain after filtering. The time domain and frequency domain diagrams of the simulated signal after filtering are as follows: Figure 5 and Figure 6 shown.

[0110] Step 6. Construct an equivalent model of the fault signal after bandpass filtering.

[0111] The filtered acceleration signal is recorded as According to the frequency domain expression, the main components of the signal are integer multiples of the fault characteristic frequency, forming an equally spaced harmonic superposition structure. Based on this, we can further construct an equivalent signal model of the bearing fault vibration signal after filtering. If there is an M+1 order frequency component in the signal, its mathematical expression can be characterized as a superposition of harmonic components, which can be expressed as:

[0112]

[0113] Where M is used to describe the total number of spectral lines, and its value corresponds to the number of spectral lines minus one, t represents time, and f o is the outer race fault passing frequency, f l is the frequency corresponding to the first spectral line from the left of the amplitude spectrum, ψ m is the phase corresponding to the m+1th spectral line, B m is the amplitude of the m+1th spectral line. The amplitude spectrum of B m =T m *C,T m is the amplitude of the m+1th spectral line obtained by mapping the transfer function, and C is the amplification factor caused by the rotation speed.

[0114] Calculate the frequency of the harmonic function in the equivalent model: calculate and count the frequency components of the fault passing frequency within the bandpass filter band. For example, if the bandpass filter range is 5450-6000Hz, the fault passing frequency f ois 48.22Hz, and there is an 11th-order frequency component in the signal, that is, M is equal to 10, and the minimum frequency multiplication f l It is 5497Hz.

[0115] Calculate the amplitude of the harmonic function in the equivalent model: Compare the frequency components of the harmonic function with the frequency of the transfer function. Find the closest frequency in the transfer function and record its index. Use the amplitude of the transfer function at the corresponding index as the amplitude B of the harmonic function. Determine the speed coefficient c based on the selected operating conditions. For example, for 600 rpm, c is 2. If the transfer function frequency interval is large, interpolation can be performed first.

[0116] Computational equivalent model: The sampling frequency is still 25600Hz, and the above parameters are substituted into expression (7) to obtain the equivalent model, whose time domain diagram is as follows: Figure 7 shown.

[0117] Step 7. Quantitatively analyze the Hilbert resonance demodulation process of the fault signal equivalent model and select the optimal test condition through iterative optimization. Specifically, compare the fault characteristics of the envelope spectrum under different conditions and select the condition with significant fault characteristic frequency amplitude and low noise interference as the optimal condition.

[0118] Based on the theoretical framework of Hilbert transform, the Hilbert transform expression of the impact vibration signal can be derived as follows:

[0119]

[0120] Then, through Hilbert demodulation, the impact vibration signal is converted into its envelope signal, which is in the form of:

[0121]

[0122] Where B p , ψ p Represent the amplitude and phase of the pth spectral line, B q , ψ q represents the amplitude and phase of the qth spectral line.

[0123] According to the above formula, the demodulated envelope square signal e 2 (t) There are only DC components and the first M-order fault through-frequency components. The amplitude of the m-th order fault through-frequency is Middle interval mf o The amplitudes of two spectral lines are multiplied by two and then vector summed. The absolute value of the vector summation result (i.e. the corresponding amplitude in the demodulated spectrum) is mainly affected by the interval mf in the amplitude spectrum. oTherefore, we can first obtain the amplitude of each order fault passing frequency component, then find the frequency component of the order with the most prominent amplitude, and then calculate the amplitude of the integer multiple of the fault passing frequency in the spectrum of the envelope square signal based on the amplitude of these frequency components. 2 (t), the envelope signal e(t) increases the high-order fault passing frequency components with an order greater than M, but the amplitude regularity of different spectral lines in its envelope spectrum |E(f)| and the spectrum of the envelope square signal E 2 Therefore, the estimated spectral distribution of the envelope square signal can be used to determine the approximate distribution of the envelope spectrum.

[0124] The specific calculation steps are as follows: First, based on the transfer function, the frequency components retained within the filter band (all of which are integer multiples of the fault characteristic frequency) are selected to construct a discrete signal array, which represents the analysis signal data. Then, a Hilbert transform is performed on the signal array to obtain the envelope signal of the original signal. Finally, a spectral analysis is performed on the obtained envelope signal. Spectral analysis can be performed directly on the envelope signal or after squaring the envelope signal and then performing spectral analysis. By observing the characteristic spectral components and amplitudes, the effectiveness of fault diagnosis under operating conditions is evaluated.

[0125] This embodiment performs Hilbert transform on the equivalent signal and obtains its analytical signal according to the formula. By using the modulus value of the analytical signal, the envelope signal of the original signal is extracted, such as Figure 8 Compare the envelope spectrum of the equivalent model with the envelope spectrum of the transfer function and the simulated signal to check whether the amplitude assignment is reasonable. Analyze and record the spectrum characteristic components and amplitudes to evaluate the effect of fault diagnosis. Figure 10 is the spectrum of the envelope signal. It can be seen that the envelope signal only contains DC components and integer multiples of the fault characteristic frequency.

[0126] Step 8. Iterative optimization of the best test conditions.

[0127] Adjust the speed, load and other operating parameters cyclically, repeat steps 3 to 7, rebuild the model and perform demodulation analysis, compare the clarity of the fault characteristics of the envelope spectrum under different operating conditions, and select the operating condition with the largest fault frequency amplitude and the smallest noise interference in the envelope spectrum as the optimal one. The specific steps are as follows:

[0128] Working condition adjustment: Change the inner ring input speed frequency (for example, adjust from 300 rpm to 1500 rpm at a time) or load.

[0129] Model reconstruction and demodulation analysis: Reconstruct the equivalent model of the fault signal and perform demodulation analysis.

[0130] Optimization selection: Compare the envelope spectra under different working conditions and select the working condition with the largest fault frequency amplitude and the smallest noise interference as the optimal working condition. After multiple iterations, the spectrum of the envelope signal under different working conditions is obtained, such as Figures 9 to 13 It was found that when the inner ring input rotation frequency was 1200rpm and the load was 50% of the rated load, the amplitude of the fault characteristic frequency in the envelope spectrum was large and the number of spectral lines was large, and the anti-noise ability was strong. Therefore, this working condition was determined as the optimal test condition. Figure 11 : is the spectrum of the envelope signal of the equivalent model under the 900 rpm working condition in the embodiment. Figure 12 : is the spectrum of the envelope signal of the equivalent model under the working condition of 1200 rpm in the embodiment.

[0131] Through the above steps, the present invention can achieve efficient detection of bearing outer ring faults and determine the optimal test conditions, providing a reliable method for bearing fault diagnosis.

[0132] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, numerous modifications and variations are possible based on the contents of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the art can better understand and utilize the present invention.

Claims

1. A method for optimizing the setting of bearing outer ring fault diagnosis test parameters, characterized in that: The following steps are involved: a) Measure the structural parameters of the bearing, including the diameters of the inner and outer rings, the diameter of the rollers, and the number of rollers; b) Test and calculate the natural frequency and damping ratio of the system with the bearing installed; c) Select test operating parameters, including inner ring input speed frequency and load, and calculate the bearing fault characteristic frequency based on the bearing structural parameters and inner ring speed; d) constructing a fault simulation signal of the bearing outer race fault vibration response; e) performing bandpass filtering on the fault simulation signal, wherein the filtering parameters are selected according to the resonance peak determined in step b); f) constructing an equivalent model of the fault signal, wherein the parameters of the equivalent model are selected based on the transfer function, fault passage frequency, and frequency multiplication in steps b) and c), and verifying the equivalent model by comparing it with the simulated signal after filtering in step e); g) Quantitatively analyze the Hilbert resonance demodulation process of the fault signal equivalent model and obtain the demodulated envelope signal; h) Circularly adjust the speed and load parameters, and repeat steps c) to step g) Compare the fault feature clarity of the envelope spectrum under different working conditions and select the working condition with the largest fault frequency amplitude and the smallest noise interference as the optimal test condition.

2. A method for optimizing parameters for a bearing outer ring fault diagnosis test according to claim 1, characterized in that: Step b) specifically includes: Install the bearing in the mechanical system and install accelerometers at key locations. Use a data acquisition instrument to collect the vibration response signal measured by the accelerometer and the excitation signal applied by the hammer. Set the sampling frequency and sampling duration parameters to ensure that the collected signals accurately reflect the dynamic characteristics of the system. The vibration response transfer function and coherence function of the system are measured using the hammer impact method; Determine the natural frequency of the system based on the transfer function; Calculates the damping ratio of a selected resonance peak using the half-power bandwidth method.

3. The method for optimizing the setting of bearing outer ring fault diagnosis test parameters according to claim 2, characterized in that: The damping ratio ζ is calculated by the following formula: Where f1 and f2 are the frequencies corresponding to the half-power point, f n is the natural frequency.

4. The method for optimizing the setting of bearing outer ring fault diagnosis test parameters according to claim 1, characterized in that: In step c), the outer ring local fault frequency is calculated using the following formula: Where, f o is the outer ring fault passing frequency, Z is the number of rollers, d is the roller diameter, D is the bearing pitch diameter, α is the contact angle, f rps Enter the rotational frequency for the inner ring.

5. The method for optimizing the setting of bearing outer ring fault diagnosis test parameters according to claim 1, characterized in that: In step d), when constructing the fault simulation signal, the bearing assembly in the mechanical system is considered as a simplified multi-degree-of-freedom spring damping model. For a mechanical system with U degrees of freedom, the unit impulse response function of its vibration acceleration is expressed as: Where, is the system force F input to acceleration The unit impulse response of the output, U is the order of the system's degree of freedom, t represents time, the value of t is (0, +∞), m u is the modal mass of the u-th order, ζ u is the u-th order damping ratio, ω n,u is the u-th order undamped natural frequency of the system; ω d,u is the u-th order damped natural frequency; is the u-th order phase angle; when a local fault occurs in the outer ring, the excitation force of the mechanical system is a pulse sequence f(t) with equal intervals and amplitudes, which can be expressed as: Where i represents the order, t represents the time, C represents the amplitude of the pulse sequence, δ(.) represents the unit pulse function, τ represents the time interval, and τ = 1 / f o , f o is the outer race fault passing frequency; The impact vibration signal caused by the bearing fault is expressed as the convolution of the pulse train and the unit impulse response Expressed as: Where U represents the order of freedom, K represents the number of impacts, and f n,u represents the u-th order undamped natural frequency, f d,u Indicates that the u-th order has a damped natural frequency, m u represents the modal mass of the uth order, and the vibration signal of the bearing fault is simulated using formula (5).

6. The method for optimizing the setting of bearing outer ring fault diagnosis test parameters according to claim 1, characterized in that: In step e), the upper and lower limits of the bandpass filtering are selected based on the center frequency of the selected resonance peak and the resonance peak interval. After the bandpass filtering, only the frequency cost within the filtering interval of the impact vibration signal is retained, and a limited number of spectral lines remain in its spectrum. The frequency domain expression is expressed as follows: Where U represents the order of the degree of freedom, is the system force F input to acceleration The output frequency response function, w represents the order of the spectrum line, w1 and w2 are the orders corresponding to the first and last spectrum lines respectively, j is a unit imaginary number, f o is the outer race fault passing frequency, f n,u represents the u-th order undamped natural frequency, ζ u is the u-th order damping ratio.

7. The method for optimizing the setting of bearing outer ring fault diagnosis test parameters according to claim 1, characterized in that: In step f), when constructing the fault simulation signal, the equivalent model of the fault signal is constructed by superposition of harmonic signals. The equivalent model expression is: Where M is used to describe the total number of spectral lines, and its value is one less than the number of corresponding spectral lines. t represents time, and f o is the outer race fault passing frequency, f l is the frequency corresponding to the first spectral line from the left of the amplitude spectrum, ψ m is the phase corresponding to the m+1th spectral line, B m is the amplitude of the m+1th spectral line; The amplitude spectrum of B m =T m *C,T m is the amplitude of the m+1th spectral line obtained by mapping the transfer function, and C is the amplification factor caused by the rotation speed.

8. The method for optimizing the setting of bearing outer ring fault diagnosis test parameters according to claim 1, characterized in that: In step g), based on the theoretical framework of Hilbert transform, the Hilbert transform pair expression of the impact vibration signal is derived as follows: In the formula Represents the Hilbert transform of the vibration signal, M is used to describe the total number of spectral lines, the value is one less than the number of corresponding spectral lines, t represents time, B m is the amplitude of the m+1th spectral line, f o is the outer race fault passing frequency, f l is the frequency corresponding to the first spectral line from the left of the amplitude spectrum, ψ m is the phase corresponding to the m+1th spectral line; Then, through Hilbert demodulation, the impact vibration signal is converted into its envelope signal, which is in the form of: Where B p , ψ p Represent the amplitude and phase of the pth spectral line, B q , ψ q represents the amplitude and phase of the qth spectral line.

9. The method for optimizing the setting of bearing outer ring fault diagnosis test parameters according to claim 1, characterized in that: In step c), the influence of noise is taken into consideration and the ambient noise of the test conditions is measured to ensure the accuracy and reliability of the test results.

10. A system for implementing the above-mentioned method for optimizing the setting of test parameters for a bearing outer ring fault diagnosis test, characterized in that: It includes a drive motor, a transmission belt, a coupling, a shaft, a bearing seat, and an acceleration sensor; the coupling is installed between the drive motor and the bearing seat through the shaft, and the drive motor enables the bearing to run in the bearing seat through devices such as a transmission belt and a connecting bearing; the acceleration sensor is arranged on the bearing seat and the shaft neck; a force hammer is used to apply pulse excitation to the side of the bearing seat end cover, and the vibration response signal measured by the acceleration sensor and the excitation signal applied by the force hammer are collected by a data acquisition instrument.

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