Application of EMD in Fault Diagnosis of Motor Bearings

LI Xiao － quan，ZHANG Xing，XIE Yi － jing

(Missile College，Air Force Engineering University，Sanyuan 713800，China)

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 of various motor failures. Currently, the vibration signal analysis method is commonly used in bearing fault diagnosis [1 - 2]. This method requires the installation of a vibration sensor. Since the sensor is expensive and easy to damage, it limits the promotion of this method. The stator current signal analysis method is a non-invasive motor bearing fault detection method [3]. Compared with the bearing vibration signal analysis method, the stator current signal. It is easier to extract and the method is simpler and more practical.

Based on this, the Empirical Mode Decomposition (EMD) technology is applied below to decompose the single-phase power of the induction motor stator and successfully extract the fault characteristic quantities.

(2) The crest factor of the bearing vibration characteristic quantity correlates the peak value and the effective value of the vibration signal in real time with the ratio of the two. Therefore, there is no theoretical misjudgment when using it to detect and classify abnormal bearing sounds. and missed judgments.

(3) The difference between the peak value and the effective value of the bearing vibration characteristic quantity is related in real time to the peak value and the effective value of the vibration signal in the form of the difference between the two. Therefore, it can also effectively reflect the abnormal sound of the bearing vibration and solve the problem of difficult to display wave peaks. The non-digital bearing vibration meter of the factor can be considered as a substitute parameter for the crest factor to detect and control bearing vibration and abnormal sound.

1 EMD methods and basic theory

EMD [4] can decompose complex signals into a limited number of intrinsic mode functions (Intrinsic Mode Function, IMF), so that the instantaneous frequency defined by Hilbert transform is 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 different 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, that is, the signal is locally symmetrical about the time axis. The calculation process of extracting signal IMF is as follows

First, based on the maximum value point and minimum value point of the signal

Use cubic spline interpolation to find the average of its upper and lower envelopes

u = u1 (t) + u2 (t)

twenty one)

Then find the difference between X(t) and u

x = X(t) - u.------ ( 2)

Treat x as a new X(t) and repeat the above operations until x satisfies

Until the IMF condition, then let C1 = x, that is, divide the

The 1st component of departure.

Subtracting component c1 from the original signal, we get

X(t) - c1 = r1.------ (3)

Treat r1 as a new X(t) and process it according to the above process,

Each IMF signal is obtained in turn: c2, c3,..., until the local pole of r

When the value points are less than 2, the decomposition can be considered to be complete. At this time, r may be

1 DC or 1 trend.

After n decompositions, the original signal is decomposed into n eigenmodular functions

number and 1 residual quantity, that is

X(t) = Σ

n

i=1

ci + rn. ------(4)

2 Single-phase power spectrum analysis

Assume that the power supply of the motor is an ideal three-phase sinusoidal alternating current

pressure, and the structure of the motor itself is symmetrical. Normally functioning electricity

The motor phase current is an ideal sine wave. Taking phase A as an example, assume that the electric

The machine phase voltage and phase current are respectively

uA (t) = Um cos(ω1 t)

iA ( t) = Im cos( ω1 t - φf

{ ) ------(5)

In the formula: Um, Im are the phase current fundamental wave voltage and current amplitude respectively.

value; φf is the power factor angle of the motor.

Then the instantaneous power of phase A is

PA (t) = uA (t) iA (t) = 1

2 Um Im cos φ +

2 Um Im cos( 2ω1 t － φf ) 。------- ( 6)

When a bearing fails, its vibration characteristics will change significantly.

ation, causing vibration in the air gap of the motor, and the magnetic flux in the air gap is affected by

Modulation, modulation harmonics induce corresponding harmonics in the stator winding

wave current. Characteristics of bearing vibration frequency reflected in stator current

The frequency is [5]

fbng = | f1 ± nfv | ,------- (7)

fv is the vibration characteristic frequency when the bearing fails, which can be expressed as

In the formula: f1 is the power supply frequency; n = 1, 2, 3,…; fe is the external

Channel fault characteristic frequency; fi is the internal channel fault characteristic frequency; fb

is the characteristic frequency of steel ball failure; Z is the number of steel balls; fr is the motor rotation speed.

speed; Dw is the diameter of the steel ball; Dpw is the pitch circle diameter of the ball group; α is the joint

antenna.

Let the phase A current be

In the formula: Im, Ibm1n, Ibm2n are the fundamental frequency component, f1 - nfv component, respectively.

The amplitude of f1 + nfv component current; φf, φ1n, φ2n are the fundamental frequency division respectively

quantity, f1 - nfv component, f1 + nfv component current lags behind the voltage

phase angle.

At this time, the instantaneous power of phase A is

Comparing the instantaneous power of phase A before and after the fault, it can be seen that after the fault

The single-phase instantaneous power signal contains richer information. and

Compared with the single-phase instantaneous power during normal operation, the single-phase power after a fault

In addition to the DC component and the 2-octave frequency component, the instantaneous power also contains

2f1 ± nfv and nfv components, which can be used as diagnostic bearings

Fault characteristic quantity. Filter out the DC component, and the remaining nfv component is far away from the 2f1 ± nfv and 2f1 components, which can be decomposed through EMD and solved

This eliminates the shortcoming that f1 ± nfv and f1 are too close to each other in the stator current. Therefore

Bearing failure can be determined by detecting the nfv component.

3 Simulation verification

Assume the diameter of the steel ball Dw = 7. 94 mm, ball group pitch circle diameter

Dpw = 39. 04 mm, shaft speed 150 r/min, simulated SKF -

6205 If the bearing steel ball fails, the rotation frequency of the bearing inner ring is 29. 25

Hz( n = 1) [6], according to the fault frequency, let: Im = 10, Ibm11 =

Ibm21 = 0. 4, fv = 29． 25, φf = φ1n = φ2n = π/4, take

The sampling frequency is 1000 Hz and 1024 data are sampled. Then the current signal

It can be expressed as (Phase A as an example) [7]

iaf = 10cos( 100t - π/4) + 0． 4cos(70．75t－

π/4) + 0． 4cos(129．25t-π/4).------- (13)

Phase A fault current and instantaneous power signal are shown in Figure 1.

According to the EMD decomposition method, the DC component in the signal PAf (t) is filtered out,

Then perform EMD decomposition on the filtered single-phase power spectrum to simulate

The true result is shown in Figure 2.

In Figure 2, IMF1 is the IMF component of the three components with frequencies 2f1, 2f1 + fv, and 2f1 - fv superimposed together. Since these 3 components

The frequencies are close to each other, making it difficult for EMD to separate them. IMF2 is needed

The fv component to be extracted has a frequency far away from other components, as shown in Figure 1, Figure

2 It is known that the 2sf component is accurately separated by EMD. To avoid endpoints

Effect, 0 is selected in Figure 3. 1～1． 1 s as the analysis object

Let’s study it. As you can see from the figure, its frequency is about 14. 6 Hz,

The amplitude is 88. IMF3 is the residual component, which has no impact on the results.

Therefore, the next step of decomposition is not carried out, and the separated IMF2 component can be

as a criterion for failure. The simulation results also show that: even when the bearing

In case of minor faults, the fault characteristic components can still be accurately improved.

Pick.

4 Conclusion

When the motor bearing fails, the single-phase power spectrum ratio is fixed

The sub-current spectrum contains richer fault information. By analyzing the single-phase

The power spectrum was decomposed by EMD and the fv fault characteristics were successfully extracted.

quantity, solving the problem that the fault characteristic quantity in the stator current is consistent with the fundamental frequency

A difficult problem that is too close to be broken down. Since the current signal is smaller than the vibration signal

It is easier to collect and has low cost, so this method is widely used in bearing fault diagnosis.

has good application prospects.