In the present study, the vibrational and frictional torque signals acquired from the forward-backward movements of a commercial ball-screw system were considered via mono fractal analysis. The short-range tests were carried out in order to investigate the effects of operating conditions, a nut's inner surface roughness and the applied pretension (preload) on the fractal dimension (Ds) and topothesy (G). The long-range test was conducted to observe the variations of vibrational and frictional torque signals and thus the fractal parameters acquired from the ball-screw operations under the condition of no fresh grease supply during the testing process. The effects of the ball-screw rotational speed and pretension on the G parameter of vibrations were greater than the Ds parameter. In the backward movement, the highest G value always occurred at the highest rotational speed (3000 rpm in this study). The Ds parameter generated in the forward movement by the nut's inner surface before polishing produced a value greater than that by the nut with a polished surface. The G parameter related to vibrational amplitudes showed a value before polishing greater than that after polishing. The unusual vibrational signals are assumed to be related to ball passing behavior. Their experimental frequency was verified to be consistent with the frequency predicted by the ball pass theory. An increase in the rotational speed can bring a significant increase in the number of ball-pass signals. The G parameter and its skewness data, defined for the number distribution function of the G peaks, showed values that in general increased with the test time if the fresh grease was not supplied during the long-range test.

References

References
1.
Meng
,
H. C.
, and
Ludema
,
K. C.
,
1995
, “
Wear Models and Predictive Equations: Their Form and Content
,”
Wear
,
181–183
, pp.
443
457
.10.1016/0043-1648(95)90158-2
2.
Williams
,
J. A.
,
1999
, “
Wear Modelling: Analytical, Computational and Mapping: A Continuum Mechanics Approach
,”
Wear
,
225–229
, pp.
1
17
.10.1016/S0043-1648(99)00060-5
3.
Mandelbort
,
B.
,
1982
,
The Fractal Geometry of Nature
,
W. H. Freeman
,
New York
.
4.
Zhou
,
G.
,
Leu
,
M.
, and
Blackmore
,
D.
,
1995
, “
Fractal Geometry Modeling With Applications in Surface Characterisation and Wear Prediction
,”
Int. J. Machine Tools Manuf.
,
35
(
2
), pp.
203
209
.10.1016/0890-6955(94)P2374-O
5.
Logan
,
D.
, and
Mathew
,
J.
,
1996
, “
Using the Correlation Dimension For Vibration Fault Diagnosis of Rolling Element Bearing—I. Basic Concepts
,”
Mech. Syst. Signal Process.
,
10
, pp.
241
250
.10.1006/mssp.1996.0018
6.
Logan
,
D.
, and
Mathew
,
J.
,
1996
, “
Using the Correlation Dimension For Vibration Fault Diagnosis of Rolling Element Bearing—I. Selection of Experimental Parameters
,”
Mech. Syst. Signal Process.
,
10
, pp.
251
264
.10.1006/mssp.1996.0019
7.
He
,
Z. J.
,
Zhao
,
J. Y.
,
Me
,
Y. B.
, and
Meng
,
Q. F.
,
1996
, “Wavelet Transform and Multi-Resolution Signal Decomposition for Machinery Monitoring and Diagnosis, in Proceedings of the 1996 IEEE International Conference on Industry Technology, Shanghai, China, Vol. 1, pp.
724
727
.
8.
Jiang
,
J. D.
,
Chen
,
J.
, and
Qu
,
L. S.
,
1999
, “
The Application of Correlation Dimension in Gear Box Condition Monitoring
,”
J. Sound Vib.
,
223
, pp.
529
541
.10.1006/jsvi.1998.2161
9.
Xia
,
Y.
,
Zhang
,
Z. R.
,
Chen
,
W. C.
, and
Liu
,
X. J.
,
2001
, “
Application of Fractal Dimension to Vibration Diagnosis of IC Engines
,”
J. Vibr. Meas. Diag.
,
21
, pp.
209
213
. Available at: http://zdcs.nuaa.edu.cn
10.
Purkait
,
P.
, and
Chakravorti
,
S.
,
2003
, “
Impulse Fault Classification in Transformers by Fractal Analysis
,”
IEEE Trans. Dielec. Electr. Insulation
,
10
, pp.
109
116
.10.1109/TDEI.2003.1176571
11.
Wong
,
K. L.
,
2004
, “
Application of Very-High-Frequency (VHF) Method to Ceramic Insulators
,”
IEEE Trans. Dielectrics Electrical Insul.
,
11
, pp.
1057
1063
.10.1109/TDEI.2004.1387829
12.
Zhu
,
H.
,
Ge
,
S.
,
Cao
,
X.
, and
Tang
,
W.
,
2007
, “
The Changes of Fractal Dimensions of Frictional Signals in the Running-In Wear Process
,”
Wear
,
263
, pp.
1502
1507
.10.1016/j.wear.2007.02.011
13.
Loutrids
,
S. J.
,
2008
, “
Self-Similarity in Vibration Time Series: Application to Gear Fault Diagnostics
,”
J. Vibr. Acoust.
,
130
, p.
031004
.10.1115/1.2827449
14.
Chester
,
S.
,
Wen
,
H. Y.
,
Lundin
,
M.
, and
Kasper
,
G.
,
1989
, “
Fractal-Based Characterization of Surface Texture
,”
Appl. Surf. Sci.
,
40
, pp.
185
192
.10.1016/0169-4332(89)90001-9
15.
Nogues
,
J.
,
Costa
,
J. L.
, and
Rao
,
K. V.
,
1992
, “
Fractal Dimension of Thin Film Surfaces of Gold
,”
Physica A
,
182
, pp.
532
541
.10.1016/0378-4371(92)90019-M
16.
Mandelbrot
,
B.
,
Passoja
,
D.
, and
Paullay
,
A.
,
1984
, “
Fractal Character of Fracture Surface of Metals
,”
Nature
,
308
, p.
721
.10.1038/308721a0
17.
Dubuc
,
B.
,
Quiniou
,
J. F.
,
Roques-Carmes
,
C.
,
Tricot
,
C.
,
Zucker
,
S. W.
,
1989
, “
Evaluating the Fractal Dimension of Profiles
,”
Phys. Rev. A
,
39
, pp.
1500
1512
.10.1103/PhysRevA.39.1500
18.
Mandelbrot
,
B. B.
,
1982
,
The Fractal Geometry of Nature
,
W. H. Freeman
,
New York
.
19.
Papoulis
,
A.
,
1965
,
Probability, Random Variables and Stochastic Process
,
McGraw-Hill
,
New York
.
20.
Berry
,
M. V.
, and
Berman
,
D. H.
,
1980
, “
On the Weieratrass-Mandelbrot Fractal Function
,”
Proc. R. Soc. London, Ser. A
,
A370
, pp.
459
484
.10.1098/rspa.1980.0044
21.
Yan
,
W.
, and
Komvopoulos
,
K.
,
1998
, “
Contact Analysis of Elastic-Plastic Fractal Surfaces
,”
J. Appl. Phys.
,
84
, pp.
3617
3624
.10.1063/1.368536
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