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Abstract: Taking the single － phase power spectrum as the research object，the fault frequency fv is picked up in single － phase power spectrum by using EMD． The simulation results show that this method is highly sensitive and clear，successfully solving the problem of which fault component frequency of motor bearing is too close to basic wave to be separated in stator current． It is feasible to apply in fault diagnosis of motor bearings．
Key words: motor bearing; power spectrum; EMD; fault diagnosis
The probability of motor bearing failure is about 40%, accounting for the largest proportion among various motor faults. At present, the commonly used method in bearing fault diagnosis is vibration signal analysis, which requires the installation of vibration sensors. Due to the high cost and easy damage of the sensors, the promotion of this method is limited. The stator current signal analysis method is a non-invasive method for detecting motor bearing faults. Compared to the bearing vibration signal analysis method, the stator current signal is easier to extract, and the method is more simple and practical.
Based on this, the following text applies Empirical Mode Decomposition (EMD) technology to decompose the single-phase power of the induction motor stator and successfully extract fault feature quantities.
1. EMD Method and Basic Theory
EMD can decompose complex signals into finite intrinsic mode functions (IMF), thus making the Instantaneous phase and frequency defined by Hilbert transform meaningful. The IMF has the following characteristics:
(1) In the entire data sequence, the number of extreme points and zero crossing points should be equal, or at most differ by 1. (2) At any point on the signal, the average value of the envelope defined by the local maximum and local minimum is zero, indicating that the signal is locally symmetric about the time axis.
The calculation process for extracting signal IMF is as follows.
First, according to the maximum and minimum points of the signal X (t), the average value of its upper envelope and lower envelope is obtained by using cubic Spline interpolation
Then calculate the difference between X (t) and u
x=X (t) - u. (2)
Regard x as the new X (t) and repeat the above operation until x meets the IMF conditions, where C1=x is the first component separated from the original signal.
Subtracting component c1 from the original signal yields
X (t) - c1=r1. (3)
Treat r1 as a new X (t) and follow the above process to obtain each IMF signal in sequence: c2, c3,... until the local extreme points of r are less than 2, which can be considered as the end of decomposition. At this time, r may be a direct flow or a trend.
After n factorizations, the original signal is decomposed into the sum of n eigenmode functions and 1 residual, i.e
2. Single-phase power spectrum analysis
Assuming that the power supply of the motor is an ideal three-phase sinusoidal AC voltage, and that the structure of the motor itself is symmetrical. The phase current of a normally operating motor is an ideal sine wave. Taking phase A as an example, let the phase voltage and phase current of the motor be
In the formula, Um and Im are the amplitude of the fundamental voltage and current of the phase current, respectively; φ F is the power factor angle of the motor.
Then the instantaneous power of phase A is
When a bearing malfunctions, its vibration characteristics will significantly change, causing vibration in the motor air gap. The magnetic flux in the air gap is modulated, and the modulated harmonics induce corresponding harmonic currents in the stator winding. The characteristic frequency reflected by the bearing vibration frequency in the stator current is
Fbng=| f1 ± nfv |, (7)
Fv is the characteristic frequency of vibration during bearing failure, which can be expressed as
In the formula: f1 is the frequency of the power supply; N=1, 2, 3; Fe is the characteristic frequency of external channel faults; Fi is the characteristic frequency of internal channel faults; Fb is the characteristic frequency of steel ball faults; Z is the number of steel balls; Fr is the motor speed; Dw is the diameter of the steel ball; Dpw is the diameter of the pitch circle of the ball group; α is the contact angle.
Set the A-phase current as
In the formula: Im, Ibm1n, Ibm2n are the amplitudes of the fundamental frequency component, f1 nfv component, and f1+nfv component currents, respectively; φ F, φ 1n, φ 2n represents the phase angle of the fundamental frequency component, f1 nfv component, and f1+nfv component where the current lags behind the voltage.
At this point, the instantaneous power of phase A is
Comparing the instantaneous power of phase A before and after the fault, it can be seen that the single-phase instantaneous power signal after the fault contains more abundant information. Compared with the single-phase instantaneous power during normal operation, the single-phase instantaneous power after a fault not only contains the DC component and 2-fold frequency component, but also contains 2f1 ± nfv and nfv components, which can be used as fault characteristic quantities for diagnosing bearings. By filtering out the DC component, the remaining nfv component is far away from the 2f1 ± nfv and 2f1 components, which can be decomposed through EMD, solving the problem of f1 ± nfv and f1 being too close in the stator current. Therefore, bearing failure can be determined by detecting the nfv component.
3 Simulation verification
Assuming the diameter of the steel ball Dw=7.94 mm, the pitch diameter of the ball group Dpw=39.04 mm, and the shaft speed of 150 r/min, simulating the SKF-6205 bearing steel ball failure, the rotation frequency of the bearing inner ring is 29.25 Hz (n=1) [6]. Based on the fault frequency, let: Im=10, Ibm11=Ibm21=0.4, fv=29.25, φ F= φ 1n= φ 2n=π/4, with a sampling frequency of 1000 Hz and 1024 data samples, the current signal can be represented as (A phase as an example)
The A-phase fault current and instantaneous power signal are shown in Figure 1. The DC component in the signal PAf (t) is filtered out using the EMD decomposition method, and then the filtered single-phase power spectrum is decomposed by EMD. The simulation results are shown in Figure 2.
Figure 1 A-phase Fault Current and Instantaneous Power Signal
Figure 2 Decomposition diagram of single-phase power EMD
IMF1 in Figure 2 is the IMF component composed of three components with frequencies of 2f1, 2f1+fv, and 2f1-fv. Due to the close frequency of these three components, it is difficult for EMD to separate them. IMF2 is the fv component that needs to be extracted, with its frequency far away from other components. As shown in Figures 1 and 2, the 2sf component is accurately separated through EMD. To avoid endpoint effects, 0.1-1.1 s was selected as the analysis object in Figure 3. From the figure, it can be seen that its frequency is approximately 14.6 Hz and its amplitude is 88. IMF3 is a residual component, and since it has no impact on the results, no further decomposition was performed. The separated IMF2 component can be used as a criterion for faults. The simulation results also indicate that even in the event of minor bearing faults, the fault feature components can still be accurately extracted.
Figure 3 Fault feature component fv
4 Conclusion
When the motor bearing malfunctions, the single-phase power spectrum contains more abundant fault information than the stator current spectrum. By EMD decomposition of the single-phase power spectrum, the fv fault feature quantity was successfully extracted, solving the problem of the fault feature quantity in the stator current being close to the fundamental frequency and cannot be decomposed. Due to the fact that current signals are easier to collect than vibration signals and have lower costs, this method has good application prospects in bearing fault diagnosis.
More about KYOCM Self-aligning Ball Bearing:
Self-aligning ball bearings have two rows of balls, a common sphered raceway in the outer ring and two deep uninterrupted raceway grooves in the inner ring. They are available open or sealed. The bearings are insensitive to angular misalignment of the shaft relative to the housing, which can be caused, for example, by shaft deflection.
2023-07-03