identification of transient modal parameters in rotary …...low-frequency oscillation...
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bime | Bremen Institute for Mechanical Engineering | Bremen University
Identification of transient modal parameters
in rotary swaging process
07.12.2010 Bremen
Linghan Li
© bime Bremen University | L. Li | No. 2
Outline
Problem state and goal of this work
Experimental set up
Analysis with Fast Fourier Transform (FFT)
Proposed algorithm
Hilbert Huang Transform (HHT)
Least Square Error method (LSE)
Results and discussion
© bime Bremen University | L. Li | No. 3
Problem state and goal of this work
Goal of this work
To identify the time-varying structure parameters (frequency and
damping)
Proposed algorithm
Fast Fourier Transform (FFT)
Hilbert Huang Transform (HHT) & Least Square Error method (LSE)
Changes of
structure
parameters over
time
Machining with
non-stationary
processing forces
might lead to
© bime Bremen University | L. Li | No. 4
cylinder roller
spindle
die segment (forming tool)
Rotary swaging
Parameters
Material X5CrNi18-10
Spindle revolution (1/min) 2800
Blank diameter of wire(mm) 1.0, 1.3 and 1.5
Final diameter of wire(mm) 0.5
Deformation degree φ (-) 0.7, 1.0 and 1.1
rotary swaging
machinefeeding device base jaw
blank diameterfinal diameter
accelerometer
fixed on head
© bime Bremen University | L. Li | No. 5
FFT analysis and problem
FFT spectra
0 1 2 kHz 4
0.2
0.05
[-]
0.1
0FF
T a
mp
litu
de
frequency frequency
(a)
5
0
-2.5
-5
g
acce
lera
tio
n
0 0.01 0.02 0.03 s 0.05
time
closing frequency
(100Hz)
0 1 2 kHz 4
0.2
0.05
[-]
0.1
0FF
T a
mp
litu
de
(c)
0 1 2 kHz 4
0.2
0.05
[-]
0.1
0
(b)
0 1 2 kHz 4
0.2
0.05
[-]
0.1
0
(d)
idle state rotary swaging
15
0
-10
-15
g
5
-5
0 2 4 6 s 10time
acce
lera
tio
n
original signal
(a) idle state (φ = 0)
(c) φ = 1.0
(b) φ = 0.7
(d) φ = 1.1
© bime Bremen University | L. Li | No. 6
600 Hz 10000 4002000
0.05
0.1
[-]
0.2
frequency
Hilb
ert
am
plitu
de
marginal spectrum
IMF1; iteration 0 before
sifting
Hilbert Huang Transform
data intrinsic mode functions (IMFs)empirical mode decomposition
(EMD)
Hilb
ert
tran
sfo
rm
instantaneous
frequency
Hilbert
spectrum
marginal
spectrum
5
-2.5
[-]
0
-50 200 400 600 ms 1000
time
am
plitu
de
original signal
600 ms 10000 4002000
200
400
600
Hz
1000
-20
-15
-10
dB
0
time
insta
n. fr
eq
ue
ncy
Hilbert spectrum
IMF1
residue
© bime Bremen University | L. Li | No. 7
frequency
&
damping ratio
Least Square Error method
1( )T TP A A A B
Least Square algorithm
1
2
x(k) x(k+1) x(k+2)
px(k+1) x(k+2) x(k+3) =
p
x(k+L-3) x(k+L-2) x(k+L-1)
AP B
15
2
0
-1
[-]
am
plitu
de
-210 12
timems
0 0( ) sin( )tx t x e t
curve fitting process
a sampled time series
2.5
0.5
-0.5
[-]
am
plitu
de
-1.5
-2.50 0.02 0.04 0.06 s 0.1
time
windows size L
© bime Bremen University | L. Li | No. 8
Sketch of operation algorithm
original
signal
frequency
&
damping ratio
HHT
filter LSE
© bime Bremen University | L. Li | No. 9
marginal spectra
5
3
0
[-]
ma
rgin
al a
mp
.
2
1
01 2 kHz 4
frequency frequency
(a) (b)
(c) (d)5
3
0
[-]
ma
rgin
al a
mp
.
2
1
01 2 kHz 4
5
3
0
[-]
2
1
01 2 kHz 4
5
3
0
[-]
2
1
01 2 kHz 4
HHT analysis to define a filter
difference of area centroid
20
1
Hz
diff.
fr
eq
ue
ncy
10
02 3 4 5
frequency groups
40
6 [-] 8
area centroid of
2.frequency range
730
Hz
ce
ntr
e fre
qu
en
cy
720
700(a)
swaging state
750
710
(b) (c) (d)
(a) idle state (φ = 0) (b) φ = 0.7 (c) φ = 1.0 (d) φ = 1.1
filter2.frequency range
(500-1000Hz)
© bime Bremen University | L. Li | No. 10
Estimation of structure parameters
filtering
LSE
idle state rotary swaging
15
0
-10
-15
g
5
-5
0 2 4 6 s 10time
acce
lera
tio
n
original signal
900
700
Hz
fre
qu
en
cy
600
1.8
1
%
0.6
0.2
da
mp
ing
ra
tio
0 1 2 3 4 5 6 7 s 10
time
φ = 0.7φ = 1.0
φ = 1.1
estimation of structure parameters
8
0 1 2 3 4 5 6 7 s 108
© bime Bremen University | L. Li | No. 11
Summary
Dynamic behavior of machine is changed during the machining
operation.
HHT analysis is better suited for non-stationary series data.
The time-varying structure parameters (frequency and damping)
can be obtained using LSE method.
© bime Bremen University | L. Li | No. 12
Reference for proposed algorithm
HHT
N.E. Huang, Z. Shen, S.R. Long, et al., "The empirical mode decomposition and the
Hilbert spectrum for nonlinear and non-stationary time series analysis," Proceedings of
the Royal Society of London. Series A: Mathematical, Physical and Engineering
Sciences, vol. 454, pp. 903-995, 1998.
LSE
J.Z. Yang, C.W. Liu, W.G. Wu, "A hybrid method for the estimation of power system
low-frequency oscillation parameters," in Power and Energy Society General Meeting -
Conversion and Delivery of Electrical Energy in the 21st Century, 2008 IEEE, 2008, p.
1-1.
© bime Bremen University | L. Li | No. 13
Kontakt
bime | Universität Bremen
Badgasteiner Straße 1
28359 Bremen
Dipl.-Ing. Linghan Li
Tel: +49 (421) 218 64806
E-Mail: [email protected]