TALK TO TEQUIP PARTICIPANTS, IIT BOMBAY , December 2014
COMPONENT HEALTH MONITORING
BASED ON VIBRATION DATA
S K MAITI
G K DEVARAJULU CHAIR PROFESSOR
Department of Mechanical Engineering
INDIAN INSTITUTE OF TECHNOLOGY
BOMBAY
IMPORTANCE OF COMPONENT HEALTH
MONITORING
• HUMAN PATHOLOGICAL DATA – Health Status , ….. Treatment
• UNINTERRUPTED SERVICE - Power Sector, Transport,
Medical Services, …
• AVOID LOSS DUE TO DOWNTIME
• AVOID CATASTROPHIC ACCIDENT
TRADITIONAL METHODS - X-Ray, Ultrasonic, …
Railway tracks, Cross-country oil pipelines ..
ACCIDENTS & FAILURES ORIGINATING FROM
CRACK IN A COMPONENT
abduh137.files.wordpress.com
www.matcoinc.com
INACCESSIBLE COMPONENTS
http://www.dailykos.com/
(March, 2011)
http://www.underwaterconsultants.com/prosite/Ma
rine_Consultantsm___Construction_Inspection
http://bravenewclimate.com
/2011/03/12/japan-nuclear-earthquake/
INACCESSIBLE GEAR BOX SHAFT
ru.wikipedia.com
VIBRATION BASED METHODS – DATA
FOR CRACK DETECTION
• Advantages - Offers easy and quick data collection, Possible to
work with partial access of the component
• NATURAL FREQUENCY
Low frequency range (< 25kHz) [e.g. Cawley and Adams, 1978;
Cawley and Adams,
1979; Gudmondson, 1982; Papadopoulos and
Dimarogonas, 1987b; Rizos et al., 1990; Ostachowicz and Krawczuk, 1991;
Liang et al. 1991, 1992; Nandwana and Maiti, 1997a,b; Shifrin and Ruotolo,
1999; Chaudhari and Maiti, 2000a,b; Patil and Maiti, 2002a,b, 2003; Kim and
Stubbs, 2003; Murigendrappa and Maiti, 2004a,b; Mandava et al..,2007]
• High frequency - wave propagation range [e.g. Fromme and
Sayir, 2002; Cheong et al., 2004; Krawczuk et al. 2004; Karikera et al., 2007;
Masserey et al., 2006; Lu et al., 2008]
→
METHOD OF SOLUTION
• ANN [e.g., Luo and Hanagud, 1997; Marwala and Hunt, 1999; Yam et al.,
2003; Fang et al., 2005; etc]
• OPTIMISATION [e.g. Chinchalkar,2001; Krawczuk, 2002; Dado and
Shpli, 2003; Nahvi and Jabbari, 2005; Saridakis et al., 2008]
• ANALYTICAL MODELLING
[e.g.,
Cawley and Adams, 1978; Cawley
and Adams, 1979; Gudmondson, 1982; Papadopoulos and Dimarogonas, 1987b;
Rizos et al., 1990; Ostachowicz and Krawczuk, 1991; Liang et al. 1991, 1992;
Nandwana and Maiti, 1997a,b; Shifrin and Ruotolo, 1999; Chaudhari and Maiti,
2000a,b; Patil and Maiti, 2002a,b, 2003; Kim and Stubbs, 2003; Murigendrappa and
Maiti, 2004a,b; Mandava et al. , 2007]
The DD Project deals with analytical modelling &
crack detection
Crack Representation
Beam Vibration Modelling
CRACK MODELLING
LOCAL FLEXIBILITY - ROTATIONAL SPRING
[Cawley and Adams, 1991; Rizos et al., 1990; Loya et al., 2006, etc.]
y
y
x
a
z
z
h
Cross-section
b
MODELLING OF TRANSVERSE VIBRATION OF STRAIGHT BEAM
(No Crack, Euler-Bernoulli Formulation)
Long/slender beam → Length/depth > 11
y
Euler
A
z
Bernoulli
x
B
EQUATION OF TRANSVERSE
VIBRATION OF LONG BEAM

2
x
2
  y
 y
 EI 2   A 2  0
dt
 x 
2
2
MODELLING OF TRANSVERSE VIBRATION OF
STRAIGHT BEAM WITH CRACK
y
a
z
b
Z1
Z2
Numerical study
Error
β → less than 1.0%
a → less than 1.0%
[Cawley and Adams, 1979; Liang et al., 1991; Dimarogonas, 1996; Nandwana and Maiti, 1997]
Dimensionless Kt = K = f(λ,β)= F(ω,β)
= F1(ω,β)/ F2(ω), No Crack F2(ω)=0
K
Numerical study
Error
β → less than 1.0%
a → less than 1.0%
β
λ = λmeas
Zero Setting or Datum Setting
theor
meas
DISCONTINUOUS SUPPORTS
In-situ Application
http://deepakvenkat.com
BEAMS ON MULTIPLE SUPPORTS AND
MULTI-STEP BEAMS
[Nandwana, 1997]
Z1
Experiment
Error
β → 16%
a → 15%
Z1
Z3
Z2
Z2
Z4
Zs
FUKUSHIMA DAIICHI UNIT 1
http://www.dailykos.com/
FLYOVER GEOMETRY
www.matcoinc.com
Various test beam geometries. (a) Taper beam. (b) One side
taper beam. (c) Two segment beam. (d) Uniform-taper-uniform
three segment beam [Chaudhuri, 2000].
Error
β → 3.5%
a → 19%
DEFORMABLE & DISCONTINUOUS SUPPORT
http://mirror-au-nsw1.gallery.hd.org
pipeline-with-smarttape-straingauge
http://smartec.ch/HTMLFiles/SNAM_Rete_Gas__Gas_pipeline_monitoring.htm
=L1/L
EI2
EI1
h2
h1
l1
Kf
Kf
L
(b)
)
(a)
L
(d)
)
(c)
L2
L
(e)
EI
Numerical study - Error
h
(f)
Ks
L
Kf
L
β → 4.4%
a → 4.7%
Sample MTech or Dual Degree
Project
NEW ISSUES
Short Beams/Shafts
www.universalgears.com
Configurations
with Initial Crack,
Prediction of Growth
LIFE CALCULATION
P
t
Fatigue Crack Growth
Rate Measurement
Experiment
a
L
TIMOSHENKO OR SHORT BEAM
z
TIMOSHENKO OR SHORT BEAM (Contd.)
EI
 4 Z  x, t 
x
EI
4
 A
 4  x, t 
x
4
 2 Z  x, t 
 A
t 2
4
4
E   Z  x, t    2 I   Z  x, t 

  I 1 

0


2
2
4
 k G  x dt
 k G  t
 2  x, t 
t 2
4
4
2


x
,
t

  x, t 




E

I


  I 1 

0


2 2
4
 k G  x dt
 k G  t
ϕ
ψ
[Lele and Maiti, JSV, 2002 ]
ψ
SHORT BEAM WITH CRACK
• Formulation
- First Time
• Crack Representation - Rotational Spring
• Crack Detection - With good accuracy
CRACK GROWTH DETECTION
• Specimens - Aluminium
• Crack - Electro Discharge Wire-Cut Machining
• Frequencies - Measured by Accelerometer
• Crack Growth - 1% to 20% of Initial Crack Size.
Good Accuracy
→
[Lele and Maiti, 2002]
Material: Aluminium
CONCLUDING REMARKS
• FORMULATION FOR BEAMS OF DIFFERENT
GEOMETRY AND SUPPORT CONDITIONS GIVEN
TO ENABLE CRACK DTECTION
• BOTH LONG AND SHORT BEAMS CONSIDERED
• SMALL CRACK GROWTH
• SOME RESULTS
DETECTED
EXPERIMENTALLY VERIFIED