In this work, the random vibration characteristics of a beaded rope under a concentrated load are investigated. A stochastic model describing the sawing force of a single diamond-beaded rope was established, based on the principle of volume invariability. The governing equations of the beaded rope were obtained using Hamilton's principle. Theoretical expressions were derived to calculate the response power spectral density (PSD), load-response cross-PSD and the mean square value of the beaded rope lateral displacement, for a beaded rope subject to a concentrated load. The influence of the parameters on the random vibration characteristics of a beaded rope was analyzed, including the effects of the linear speed of the beaded rope, the tension of the beaded rope, and the location of the concentrated load. Numerical examples are given. Results show that as the tension of the beaded rope increases, the PSD and mean square value of the rope displacement are reduced. However, as the linear velocity of the beaded rope increases, the PSD and mean square value of the rope displacement are also increased. During movement of the diamond-beaded rope, the mean square value of the transverse displacement fluctuates predominantly, because of the time-varying impact force caused by the diamond beads.

Issue Section:
Research Papers
Keywords:
Machine dynamics, Random vibration
Topics:
Diamonds, Ropes, Stress, Displacement, Random vibration, Tension

References

1.
Ataei
,
M.
,
Mikaiel
,
R.
,
Sereshki
,
F.
, and
Ghaysari
,
N.
,
2012
, “
Predicting the Production Rate of Diamond Wire Saw Using Statistical Analysis
,”
Arabian J. Geosci.
,
6
(
5
), pp.
1289
–
1295
.
Google Scholar
Crossref
Search ADS
 
2.
Tönshoff
,
H. K.
, and
Hillmann-Apmann
,
H.
,
2002
, “
Diamond Tools for Wire Sawing Metal Components
,”
Diamond Relat. Mater.
,
11
(
6
), pp.
742
–
748
.
Google Scholar
Crossref
Search ADS
 
3.
Turchetta
,
S.
,
Polini
,
W.
,
Gelfusa
,
G.
, and
Venafro
,
E.
,
2014
, “
A New Sawing Machine by Diamond Wire
,”
Int. J. Adv. Manuf. Technol.
,
70
(
1
), pp.
73
–
78
.
Google Scholar
Crossref
Search ADS
 
4.
Swope
,
R. D.
, and
Ames
,
W. F.
,
1963
, “
Vibrations of a Moving Thread Line
,”
J. Franklin Inst.
,
275
(
1
), pp.
36
–
55
.
Google Scholar
Crossref
Search ADS
 
5.
Rao
,
G. V.
,
1992
, “
Linear Dynamics and Active Control of an Elastically Supported Travelling String
,”
Comput. Struct.
,
43
(
6
), pp.
1041
–
1049
.
Google Scholar
Crossref
Search ADS
 
6.
Wickert
,
J. A.
, and
Mote
,
C. D.
,
1990
, “
Classical Vibration Analysis of Axially Moving Continua
,”
ASME J. Appl. Mech.
,
57
(
3
), pp.
738
–
744
.
Google Scholar
Crossref
Search ADS
 
7.
Wickert
,
J. A.
, and
Mote
,
C. D.
,
1991
, “
Traveling Load Response of an Axially Moving String
,”
J. Sound Vib.
,
149
(
2
), pp.
267
–
284
.
Google Scholar
Crossref
Search ADS
 
8.
Wei
,
S. B.
, and
Kao
,
I.
,
2000
, “
Vibration Analysis of Wire and Frequency Response in the Modern Wire Saw Manufacturing Process
,”
J. Sound Vib.
,
231
(
5
), pp.
1383
–
1395
.
Google Scholar
Crossref
Search ADS
 
9.
Xu
,
L. X.
,
Yang
,
Y. H.
,
Chang
,
Z. Y.
, and
Liu
,
J. P.
,
2011
, “
Modal Analysis on Lateral Vibration of Axially Moving Roller Chain Coupled With Lumped Mass
,”
J. Cent. South Univ. Technol.
,
18
(
1
), pp.
108
–
115
.
Google Scholar
Crossref
Search ADS
 
10.
Chen
,
L. Q.
,
2005
, “
Analysis and Control of Lateral Vibrations of Axially Moving String
,”
ASME Appl. Mech. Rev.
,
58
(
2
), pp.
91
–
116
.
Google Scholar
Crossref
Search ADS
 
11.
Ulsoy
,
A. G.
, and
Mote
,
C. D.
,
1982
, “
Vibration of Wide Band Saw Blades
,”
J. Eng. Ind.
,
104
(
1
), pp.
71
–
78
.
Google Scholar
Crossref
Search ADS
 
12.
Khorasany
,
R. M. H.
,
Panah
,
A. M.
, and
Hutton
,
S. G.
,
2012
, “
Vibration Characteristics of Guided Circular Saws: Experimental and Numerical Analyses
,”
ASME J. Vib. Acoust.
,
134
(
6
), p.
061004
.
Google Scholar
Crossref
Search ADS
 
13.
Darabi
,
M. A.
,
Kazemirad
,
S.
, and
Ghayesh
,
M. H.
,
2012
, “
Free Vibrations of Beam-Mass-Spring Systems: Analytical Analysis With Numerical Confirmation
,”
Acta Mech. Sin.
,
28
(
2
), pp.
468
–
481
.
Google Scholar
Crossref
Search ADS
 
14.
Foda
,
M. A.
,
2012
, “
Vibration Control and Suppression of an Axially Moving String
,”
JVC/J. Vib. Control
,
18
(
1
), pp.
58
–
75
.
Google Scholar
Crossref
Search ADS
 
15.
Li
,
X. Y.
, and
Chen
,
L. Q.
,
2008
, “
Modal Analysis of Coupled Vibration of Belt Drive Systems
,”
Appl. Math. Mech.
,
29
(
1
), pp.
9
–
13
.
Google Scholar
Crossref
Search ADS
 
16.
Ding
,
H.
, and
Zu
,
J. w.
,
2013
, “
Effect of One-Way Clutch on the Nonlinear Vibration of Belt-Drive Systems With a Continuous Belt Model
,”
J. Sound Vib.
,
332
(
24
), pp.
6472
–
6487
.
Google Scholar
Crossref
Search ADS
 
17.
Beikmann
,
R. S.
,
Perkins
,
N. C.
, and
Ulsoy
,
A. G.
,
1996
, “
Free Vibration of Serpentine Belt Drive Systems
,”
ASME J. Vib. Acoust.
,
118
(
3
), pp.
406
–
413
.
Google Scholar
Crossref
Search ADS
 
18.
Wu
,
J. M.
,
Wang
,
Z. M.
,
Wu
,
Q. M.
, and
Wang
,
Y.
,
2009
, “
Transverse Vibration Characteristics of a Paper Web With Multi-Roller Supports
,”
J. Low Freq. Noise, Vib. Act. Control
,
28
(
2
), pp.
133
–
144
.
Google Scholar
Crossref
Search ADS
 
19.
Kulachenko
,
A.
,
Gradin
,
P.
, and
Koivurova
,
H.
,
2007
, “
Modeling the Dynamical Behaviour of a Paper Web Part I
,”
Comput. Struct.
,
85
(
1
), pp.
131
–
147
.
Google Scholar
Crossref
Search ADS
 
20.
Kulachenko
,
A.
,
Gradin
,
P.
, and
Koivurova
,
H.
,
2007
, “
Modeling the Dynamical Behaviour of a Paper Web Part II
,”
Comput. Struct.
,
85
(
3–4
), pp.
148
–
157
.
Google Scholar
Crossref
Search ADS
 
21.
Chen
,
J. P.
,
Wang
,
S. Z.
, and
Wu
,
W. Y.
,
2008
, “
Transverse Vibration of a Longitudinally Moving Soft Thin Fabric
,”
Int. J. Nonlinear Sci. Numer. Simul.
,
9
(
1
), pp.
75
–
80
.
Google Scholar
Crossref
Search ADS
 
22.
Varello
,
A.
, and
Carrera
,
E.
,
2014
, “
Free Vibration Response of Thin and Thick Nonhomogeneous Shells by Refined One-Dimensional Analysis
,”
ASME J. Vib. Acoust.
,
136
(
6
), p.
061001
.
Google Scholar
Crossref
Search ADS
 
23.
Marynowski
,
K.
,
2010
, “
Free Vibration Analysis of the Axially Moving Levy-Type Viscoelastic Plate
,”
Eur. J. Mech. A/Solids
,
29
(
5
), pp.
879
–
886
.
Google Scholar
Crossref
Search ADS
 
24.
Ghayesh
,
M. H.
,
Amabili
,
M.
, and
Païdoussis
,
M. P.
,
2013
, “
Nonlinear Dynamics of Axially Moving Plates
,”
J. Sound Vib.
,
332
(
2
), pp.
391
–
406
.
Google Scholar
Crossref
Search ADS
 
25.
Li
,
W. M.
, and
Hong
,
J. Z.
,
2012
, “
Research on the Iterative Method for Model Updating Based on the Frequency Response Function
,”
Acta Mech. Sin.
,
28
(
2
), pp.
450
–
457
.
Google Scholar
Crossref
Search ADS
 
26.
Elishakoff
,
I.
, and
Santoro
,
R.
,
2014
, “
Random Vibration of a Point-Driven Two-Span Beam on an Elastic Foundation
,”
Arch. Appl. Mech.
,
84
(
3
), pp.
355
–
374
.
Google Scholar
Crossref
Search ADS
 
27.
Dong
,
X. J.
,
Peng
,
Z. K.
,
Zhang
,
W. M.
,
Meng
,
G.
, and
Chu
,
F. L.
,
2013
, “
Parametric Characteristic of the Random Vibration Response of Nonlinear Systems
,”
Acta Mech. Sin.
,
29
(
2
), pp.
267
–
283
.
Google Scholar
Crossref
Search ADS
 
28.
Huang
,
G. Q.
,
Huang
,
H.
,
Guo
,
H.
, and
Xu
,
X. P.
,
2009
, “
Influences of Sawing Parameters on Forces and Energy in Wire Sawing of Granite
,”
J. Mech. Eng.
,
45
(
3
), pp.
234
–
239
.
Google Scholar
Crossref
Search ADS
 
29.
Malkin
,
S.
,
1989
,
Grinding Technology: Theory and Applications of Machining With Abrasives
,
SEM
,
New York
.
30.
Polini
,
W.
, and
Turchetta
,
S.
,
2004
, “
Force and Specific Energy in Stone Cutting by Diamond Mill
,”
Int. J. Mach. Tools Manuf.
,
44
(
11
), pp.
1189
–
1196
.
Google Scholar
Crossref
Search ADS
 
31.
Lutes
,
L. D.
, and
Sarkani
,
S.
,
2004
,
Random Vibrations Analysis of Structural and Mechanical Systems
,
Elsevier
,
Amsterdam
.
Copyright © 2016 by ASME
You do not currently have access to this content.