Frequency Estimation in the Fault Detection of Rolling Element Bearing

w FIFTH INTERNATIONAL

CONGRESS

ON SOUND AND VIBRATION

DECEMBER 15-18, 1997 ADELAIDE, SOUTH AUSTRALIA

Frequency Estimation in the Fault Detection ;f Rolling Element Bearing Yu-Fang Wang

Peter J. Kootsookost MV Technology

CRASYS, Dept. of Systems Engineering, ANU, Canberra,

Ltd.

Unit 24, IDA Centre

ACT 0200

Pearse St., Dublin 2

AUSTRALIA.

IRELAND.

Abstract Faulty rolling element vibrations

bearings

which possess periodic envelope-autocorrelations.

envelope-autocorrelation

are the fault characteristic

paper, one of the improved

frequency

to remove the estimated frequency. and its harmonics

can be accurately

The main frequencies of this

frequency and its harmonics.

Notch Filtering Techniques

estimate the fault characteristic

1

under very low shaft speed and light load exhibit In this

with a designed filter is used to

and its harmonics.

The designed filter is used

With this technique, the fault characteristic frequency estimated.

Introduction The condition

tenance condition

costs,

monitoring

provide

monitoring

of rotating

a significant

machinery

improvement

can reduce operational

in plant economy,

and main-

especially

of rolling element bearings which are the most commonly

for the wearing

parts in rot sting machinery. A variety of bearing fault detection sional amplitude

parameters

techniques have been proposed.

The non dimen-

[1, 6], such as Crest factors(Cf ), Kurtosis value (Kv), and so

on, are reliable only in the presence of significant impulsiveness. Spectral

analysis of bearing vibration

in which the fault signals are not submerged

in background noise frequencies and other structural resonance frequencies is the useful diagnostic and fault detection technique. The cepstrum [1, 2], while it is seldom used on its own, is an invaluable complementary

technique to spectral analysis. It is also limited

tThis work was carried out while the author was at CRASys, Dept. of Systems Engineering, ANU, Canberra, ACT 0200, Australia. The authors wish to acknowledge the funding of the activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centres Program.

to use when strong background vibration

noise and other structural signals do not swamp the fault

signal.

Envelope

power

spectrum

noise level, but in complex

[4] is very useful in the presence

structures it also contains many other frequencies

frequencies. A moving window technique in the fault detection using this technique.

and side

of a ball bearing has been investi-

gated in [5], the signal to noise ratio of measured vibration improved

of a high background

signature of a ball bearing is

The algorithm is quite powerful in the early detection

of

flaws in a ball bearing system. Raw spectra or the demodulated pattern (“equal

frequency

defect frequency,

ones of a signal from defect bearings have an EFSD

spacing distribution” ) [7], the spacing of the main peak is the

and the features of multiple defects are the superposition

of these of

each defect. An impulse index based on the Haar transform, Haar transformed

and the phase-shift

data and the impulse index have been investigated

effect on both

in [8].

Most of these techniques are only available to the normal shaft speed. They are useful in laboratory

condition,

plants, especially

but will not be so effective in the harsh environment

when the speed is less than 100 RPM.

for the outer race fault, but not for the inner race fault and roller fault. fault is easily detected in comparison

of factory

Some of them may be useful The outer race

with the inner race fault and the roller fault [1, 4],

because the outer race is usually closer to the transducer. AR spectral estimation vibration

in low speed has been investigated

[9], it is very effective for

signal without high resonance frequencies and noise frequencies,

condition,

the vibration

resonance frequencies

signal from accelerometer

and noise frequencies,

may be weak, because the accelerometer

but in practical

usually contains some large peak high

the low fault characteristic

frequency

signal

is much more sensitive to the middle and high

frequencies. In this paper,

a frequency

estimation

technique

based on notch filtering proposed

by Quinn and Fernandes is used to estimate the fault characteristic harmonics

of the envelope-autocorrelation

frequency

and its

from the fault rolling element bearing under

the very low shaft speed and the light load.

The designed filter is used to remove the

estimated frequency.

z

Frequency

Estimation

Method

Frequency Estimation for Envelope-Autocorrelation

2.1

For periodical

envelope-autocorrelation

&(i)

from the fault rolling element bearing

under the very low shaft speed and the light load [14] can be expressed

NR Rzz(t) = p + ~

A~RCOS(jLW)t+

q&)+ n(t),

(1)

j=l where p is the mean value, W. is the fault characteristic bearing.

A~R and #&

frequency

of the rolling element

are the amplitude and the initial phase of j-th harmonic,

is the number of harmonics. cr2. This is a multi-harmonic

and ~R

n(t) is some zero-mean random noise sequence with variance frequency

estimation problem.

The maximum

likelihood frequency estimation &P =

[12] for the envelope-autocorrelation

m~axJR(U),

is (2)

where

T–1 (3)

t=l The maximization

2.2

of IR is computationally

intensive, particularly

if T is large.

Technique of Quinn and Fernandes in Frequency Estimation Quinn and Fernandes [11] have suggested a computationally

efficient and near statis-

tically efficient method for estimating frequency by estimating the parameters a and @ in the following

equation: l?,.(t)

subject

– pl?zz(t – 1) + Rzz(t – 2) = n(t) – cm(t – 1) + n(t – 2),

to a = ~. The estimated frequency

(4)

is found from

1 L@ = cos–l(–@. 2 The algorithm

proceeds as follows:

1. Set a = al = 2 cos(&)

where tii is some initial estimate of U. and set j = 1.

2. Filter the data to produce (t)j = ‘z.z(t)

~t,j + aj