Identification of transient modal parameters in rotary …...low-frequency oscillation parameters,"...

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


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


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


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


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


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


Sketch of operation algorithm

original

signal

frequency

&

damping ratio

HHT

filter LSE


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)


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


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.


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.


Kontakt

bime | Universität Bremen

Badgasteiner Straße 1

28359 Bremen

Dipl.-Ing. Linghan Li

Tel: +49 (421) 218 64806

E-Mail: [email protected]

Identification of transient modal parameters in rotary …...low-frequency oscillation parameters,"...

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