Fault Detection for Rolling Element Bearings using Model-Based

Fault Detection for Rolling Element Bearings
using Model-Based Technique
ADVISOR : PROF. KENNETH A. LOPARO, PHD.
COMMITTEE MEMBERS: PROF. VIRA CHANKONG AND PROF. RICHARD KOLACINSKI
SORN SIMATRANG, EECS DEPTS.
26 JUNE 2015

Outline
o Motivation
o General Concepts of FDI
o Analytical Redundancy Methods
o The Work
o Mathematical Model
o Fault Frequencies
o Bearing Faults
o Formulate Fault
o Outer Race Fault (OR)
o Inner Race Fault (IR)
o Hammerstein – Wiener Model
o OR Data Preparation
o IR Data Preparation
o Observer Design
o Result and Diagnosis
o OR – IR , IR – OR Cases
o OR – Normal , Normal – OR Cases
o IR – Normal, Normal – IR Cases
o Future Work
o Question

Motivation: Why FDI on rolling element
bearing ?
o Other types of bearings may provide some better features but perform worse in some other
applications.
o The rolling element bearing optimizes weight, friction, cost, lifespan, and accuracy.
o Widely used in many applications.
o Unexpected damage before the estimated lifespan :
oImproper installation
oIncorrect handling
oContaminants
oMaterial wear
oLack of lubrication
oTough operating environments

FDI : General Concepts
o Fault : Undesired deviation from the usual condition.
o Occur in every part of the system from plants, sensors and actuators.
o Identify the location , type of the faults, occurrence.
o In general, based on the concept of redundancy.
o Hardware redundancy
o Analytical redundancy
Process
Input
Hardware Redundancy
Analytical Redundancy
FDI Algorithm
Diagnostic
Logic
Diagnostic
Logic
A set of
sensors
Extra set of
sensors
Output Alarm
Alarm

FDI : General Concepts
o Hardware redundancy : Compare a signal from various sources redundantly.
o More cost to install
o Analytical redundancy : Exploits a mathematical model, an estimation techniques.
o Reduce cost from implementations
o Requires a robustness to the systems uncertainties.
o Two main methods:
o The quantitative model-base methods:
o Require an explicit mathematical model
o Observer-based approaches
o The qualitative model-base methods :
o AI: pattern recognition, machine learning
Controller
Reconfiguration
Decision on FDI
Plant
Residual
Generation 1
Residual
Generation n
y
Residual 1
Residual n

FDIR: Analytical redundancy methods
oThree main processes.
o Generate residual via residual filters
o Normally, residuals are supposed to be zero
o Robust to the uncertainties, noises and disturbances
o Sensitive to the faults
o Each filter is sensitive to each specific fault
o Interpret residual : Statistical tool.
o Fault Occurrence
o Fault types
o Reconfiguration.
o Subsidize response from the faults
Controller
Reconfiguration
Decision on FDI
Plant
Residual
Generation 1
Residual
Generation n
y
Residual 1
Residual n

FDIR: Analytical redundancy methods
o Mathematical model.
o Newton’s law of motion
o Observation : system identification techniques.
o Noise.
o Noise frequencies cover the energy relating to the signature of
fault
o Residual is not zero under healthy conditions (Incorrect alarm)

FDIR: Noise Problem
o Two main approaches.
o Robust Residual Generation  Robust residual generators
o Observer-based methods
o Parity relation methods
o Kalman filter-based methods
o Robust Residual Evaluation Designing a robust hypothesis
testing algorithm.
o Decision making rule (Constant or Adaptive thresholds)

The work
o Focus on quantitative methods.
o Formulate FDI problem into a simple nonlinear model-based
framework.
o System identification (Hammerstein-Wiener Model)to generate a
residual
o Cross correlation diagnosis

The Model
o 29 degrees of freedom nonlinear model.
o Time varying system.
o Developed by using Lagrange equation.
o The Matrix equation:
o 𝒒 58 ×1 =
0 29 ×29 𝐼 29 ×29
− 𝑀(𝑡) −1 𝐾(𝑡) 29 ×29
− 𝑀(𝑡) −1 𝐶(𝑡) 29 ×29 58 ×58
𝒒 58 ×1 +
0 29 ×1
− 𝑀(𝑡) −1 𝑁(𝑡, 𝑞) 29 ×1 58 ×1
o 𝒒 58 ×1 =
𝒒 29 ×1
𝒒 29 ×1 58 ×1
, 𝒒 58 ×1 =
𝒒 29 ×1
𝒒 29 ×1 58 ×1
Roter
Drive End
Fan End
Bearing Element
sinMotor Hou g
Mesurement Location
y
z
x

Fault Frequencies
•𝐹𝑇𝐹 =
𝑟𝑝𝑟
2
1 −
𝐵𝑑
𝑃𝑑
cos ∅
•𝐵𝑆 =
𝑃𝑑
2𝐵𝑑
(𝑟𝑝𝑠) 1 −
𝐵𝑑
𝑃𝑑
2
cos ∅ 2
•OR = N(FTF)
•𝐼𝑅 = 𝑁(𝑟𝑝𝑠 − 𝐹𝑇𝐹)
•Fundamental Train Frequency 𝐹𝑇𝐹
•Ball Spin 𝐵𝑆
•Outer Race 𝑂𝑅 frequency
•Inner Race 𝐼𝑅 frequency.
dB
( )dPitch Diameter P
(B )dBall Diameter
dP
( )Contact Angle 

( )Number of Balls N
Arthur C. Tinney, “The Analysis of Rolling Element Bearing, Vibration
Diagnostic Techniques”, Master’s Thesis, Ohio State University, 1973.

Bearing Faults
o Faults are from a wide range of factors from contaminants in raceway,
improper installation, and incorrect handling of a bearing.
o Leads to a train of impulse forces when every single bearing element passes
over the defective spot.
Figure from : Timken. 2015. Timken Bearing Damage Analysis with Lubrication Reference Guide. [ONLINE] Available at:
http://www.timken.com/en-us/Knowledge/ForMaintenanceProfessionals/Documents/Bearing-Damage-Analysis-
Reference-Guide.pdf. [Accessed 26 June 15].

Fault Types: Formulate Fault
o While a defected bearing run, impulse forces recur periodically with a
frequency depending on:
o Location of the fault on the bearing
o Geometry of bearing
o Relative speeds of the bearing components in respect to the shaft speed
o Two factors for modulating the amplitude of the impulse train:
oLoad distribution
oDistance between the fault point and the sensor
o In this research we assume that the outer race is stationary.

Fault Types: Outer Race Fault
o Outer raceway is always stationary.
o Fixed mechanical path.
o Sensor receive the same response periodically.
o No need to modulate the impulse train.
o Frequency depends on the rotational speed of the bearing element passing over the stationary
fault spot.
o 𝑥 𝑡 = 𝑎 𝑘=−∞
∞
𝛿 𝑡 − 𝑇𝑘

Fault Types: Ball Fault
o Defect is on the bearing rolling element.
o Defected ball might or might not hit both raceway or hit just one raceway or none or all.
o Frequency of the impulse train could be less than twice of the spin-ball frequency (BS).
o Variable distance between the sensor and the rotating fault.
o The load distribution profile affect the amplitude as well.
o Assuming the system is linear and the defective ball hit both raceway.
o 𝑥 𝑡 = 𝑎1 cos 𝜔𝑐 𝑡 + ∅1 + 𝑐1 𝑘=−∞
∞
𝛿 𝑡 − 2𝑇𝑘
o Load will affect the system output periodically in every single cycle.
o Effect for a uniform load distribution.
o 𝑥 𝑡 = 𝑏1 cos 𝜔𝑐 𝑡 + ∅1 + 𝑐1 ⋅ cos 𝜔𝑐 𝑡 + ∅2 + 𝑐2 𝑘=−∞
∞

Fault Types: Inner Race Fault
o Not stationary.
o Distance between the fault spot and the sensor is a function of time.
o Impulse train is periodic with the inner ring frequency (and the shaft speed).
o 𝑥 𝑡 = 𝑎2 cos 𝜔𝑠 𝑡 + 𝜃1 + 𝑐1 𝑘=−∞
∞
𝛿 𝑡 − 𝑇𝑘
o Assuming uniform distribution.
o 𝑥 𝑡 = 𝑏2 cos 𝜔𝑐 𝑡 + 𝜃1 + 𝑐1 ⋅ cos 𝜔𝑠 𝑡 + 𝜃2 + 𝑐2 𝑘=−∞
∞

Fault Types: Inner Race Fault
At 1800 RPM, 𝐼𝑅 = 𝑁 𝑟𝑝𝑠 − 𝐹𝑇𝐹 = 162.469 rounds per second which is
0.0062 seconds.

Hammerstein – Wiener Model
o Network of a static nonlinear block with a dynamic linear block.
o Captures the nonlinearities by nonlinear functions at the input and output of the linear system
block.
o Allows us to exploit the linear systems theories on nonlinear system.
Linear Model (B/F)
Output Nonlinearity
(h)
Input
Nonlinearity
(f)
x(t)w(t) y(t)u(t)

System Identification : OR Data
Preparation
o In order to gain an acceptable identified model i.e. 70 %  Filter  Truncate the data.
Outer race fault vibration signal has a period 0.0093 seconds
Truncated signals to one period length
(0.0093 seconds)
The selected signal with length 0.0093
seconds
Perform
Hammerstein
– Wiener
Identification

System Identification : IR Data
Preparation
Variety of amplitudes: Each interval has 3 lobes recurring periodically.

Preparation
Determining the representative IR data by averaging.
38 period-like elements with length 38 X 0.0062 = 0.2356 sec
Truncate into 38
pieces
Truncated signals with various amplitudes
but same length (0.0062 sec)
Perform pointwise averaging
all the truncated signals
The average signal with length 0.0062 sec
Perform
Hammerstein
– Wiener
Identification

Preparation

Observer Design: Schematic
o 𝑓 ⋅ 𝐼𝑅 and 𝑓 ⋅ 𝑂𝑅 : Restricted to be a
static monotonic piecewise linear function.
o Exploit the linearity of the linear
component: Linear system theories.
o 𝑢𝐼𝑅 and 𝑢 𝑂𝑅 are the impulse train
corresponding with IR frequency and OR
frequency.
o Residual of the IR and OR observer are
obtained from 𝑦 − 𝑦𝐼𝑅 and 𝑦 − 𝑦 𝑂𝑅
respectively.
ˆ
IR IRz z
ˆ
IRz IRz 1
( )IRg 
( )IRg
IRL
Plant
IR Linear System
OR Linear System
ORL
ORzˆ
ORz
ˆ
OR ORz z

 
1
( )ORg 
( )ORg
u
( )IRf
( )ORf




y
y
y
y
y
ˆ
IRz
ˆ
ORz ÔRy ÔRy
ÔRy
ÔRy y
ÎRyÎRy
ÎRy
ÎRy y
y
IRu
ORu

Results and Diagnosis
o Based on the cross-correlation between the residual 𝑦 − 𝑦𝐼𝑅 and 𝑦 − 𝑦 𝑂𝑅 with its
corresponding impulse train.
o For example : 𝑦 − 𝑦𝐼𝑅 is corresponding with 𝑢𝐼𝑅.
o 𝑦 − 𝑦𝐼𝑅 is corresponding to the IR impulse train when IR fault occurs and also true for the OR
case.
o 𝑦 − 𝑦𝐼𝑅 is not corresponding to the IR impulse train when OR fault occurs.
o 𝑦 − 𝑦 𝑂𝑅 is not corresponding to the OR impulse train when IR fault occurs.
o Two main components of residual:
o The series of impulse responses. (correspond well with the impulse train)
o The discrepancies between the output of the observer model and the real output (𝑦)

Observer Residual: When IR Fault Occurs
Residual from IR Observer Residual from OR Observer

Observer Residual: When OR Fault Occurs

Results and Diagnosis: Conclusions
o Residual from the specific observer model match with its own impulse train input when the
fault that corresponds with the observer model occurs.
o Rotational machine output (𝑦) reflects the characteristics of the fault corresponding to the
specific observer model.
o By analyzing the cross-correlation between the residual and the impulse train input, we are
able to detect the abnormality.

Cross-Correlation: Impulse Train itself
cross-correlation of 𝑢 𝑂𝑅 cross-correlation of 𝑢𝐼𝑅

Cross-Correlation: When IR Fault Occurs
Residual from IR Observer V.S. IR Impulse Train Residual from OR Observer V.S. OR Impulse Train

Cross-Correlation: When OR Fault Occurs

Results and Diagnosis: Conclusions
o The cross-correlation consists of the two main components.
o The pyramid profile : Constructed by the cross-correlation between the impulse train and the
residuals that are corresponding with the impulse train. (Impulse Response)
o The spikes (at the base of the pyramid profile) : Due to the impulse train and the residuals that
are not corresponding with the impulse train. (Transient response , Discrepancies between
HWM model and the original data)
o By considering these cross-correlation results, we are able to interpret what fault type occurs
and when it occurs in the data timeline.

OR – IR Case
OR fault : 0.000985 - 0.2 seconds , IR fault 0.2 – 0.4 seconds.

OR – IR Case : Residual

OR – IR Case : Cross-Correlation

IR – OR Case
IR fault : 0.001000 - 0.2 seconds , OR fault 0.2 – 0.4 seconds.

IR – OR Case : Residual

IR – OR Case : Cross-Correlation

OR – NORMAL Case
OR fault : 0.003 - 0.2 seconds , Normal: 0.2 - 0.4 seconds.

OR – NORMAL Case: Residual

OR – NORMAL Case: Cross-Correlation

NORMAL –OR Case
Normal : 0 - 0.2 seconds , OR fault : 0.2 - 0.4 seconds.

NORMAL –OR Case: Residual

NORMAL –OR Case: Cross-Correlation

IR – NORMAL Case
IR fault : 0.001 - 0.2 seconds , Normal : 0.2 - 0.4 seconds.

IR – NORMAL Case : Residual

IR – NORMAL Case : Cross-Correlation

NORMAR – IR Case
Normal : 0 - 0.2 seconds , IR fault : 0.2 - 0.4 seconds.

NORMAL – IR Case : Residual

NORMAL – IR Case :Cross-Correlation

Future Work
o Proof of convergence for the reduced system.
o Reduced system is similar to the conventional observer design scheme except the input and output
nonlinearity added
o Choosing nonlinearity components to be a simple monotonic piecewise linear function
o Systematic design procedures.
o System identification technique does not allow a real-time fault detection.
o Acquire the data to determine the system model first
o Numerical error: Nearly unobservable  Huge Feedback gain  Round-off errors.
o Optimal data length : Enough information but not too long to avoid a complicated result
systems.

Future Work
o Ball fault.
o Not only the defective spot might or might not hit the raceways but also which raceways the defective
spot might hit
o Solution : Implementing more observer models for each case as follows:
 The case when the defective spot hits one time in one rotation.
 Hits the inner raceway
 Hits the outer raceway
The case when the defective spot hits twice in one rotation.
 Hits the inner raceway and the outer raceway

Future Work
 The defective spot hits three times in one rotation.
 Hits the inner raceway and outer raceway
 The defective spot does not hit in one rotation.
 Mixed between the previous cases , it is governed by a random process that describes how the
fault will jump between the previous cases.
o Categorize more and different cases , Choose the different ways to obtain the observer model
for each case.
o Data from the real experiment.

Question
Picture from Wiki Common

Fault Detection for Rolling Element Bearings using Model-Based

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