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Research Papers: Applications

Fractal Analysis for Vibrational Signals Created in a Ball-Screw Machine Operating in Short- and Long-Range Tribological Tests

[+] Author and Article Information
Min-Chi Chang

Department of Mechanical Engineering,
National Cheng Kung University,
Tainan City, 701, Taiwan, China

Jeng Luen Liou

Department of Aircraft Engineering,
Air Force Institute of Technology,
Kaohsiung, 820, Taiwan, China

Jeng-Haur Horng

Department of Power Mechanical Engineering and Centre of MEMS Design and Application,
Formosa University,
Yunlin, 63208, Taiwan, China

Yih Chyun Hwang

Hiwin Technologies Corp.,
No. 46, 37th Road,
Taichung Industrial Park,
Taichung, 40768, Taiwan, China

Jen Fin Lin

Department of Mechanical Engineering,
National Cheng Kung University,
Tainan City, 701, Taiwan, China
e-mail: jflin@mail.ncku.edu.tw

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received February 29, 2012; final manuscript received May 27, 2012; published online March 28, 2013. Assoc. Editor: Xiaolan Ai.

J. Tribol 135(3), 031101 (Mar 28, 2013) (11 pages) Paper No: TRIB-12-1031; doi: 10.1115/1.4023226 History: Received February 29, 2012; Revised May 27, 2012

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.

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Figures

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Fig. 1

Tilt-back ball screw machine and its control and cooling systems

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Fig. 2

Three kinds of sensor installed in the ball screw

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Fig. 3

Entire power spectrum of vibrational signals and the portion which is regressed well by a line with a negative slope

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Fig. 4

(a) Vibrational signals of the ball-screw machine acquired from a time period of 20 s; (b) the magnification of the vibrational signals associated with the forward movement

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Fig. 5

The values of (a) fractal dimension, and (b) topothesy for the vibrational signals acquired from the forward motion. A load of 60 kgf was applied in the gravitational direction.

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Fig. 6

The values of (a) fractal dimension, and (b) topothesy for the vibrational signals acquired from the forward motion. A load of 240 kgf was applied in the gravitational direction.

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Fig. 7

The value of (a) fractal dimension, and (b) topothesy for the vibrational signals obtained from the backward motion. A load of 60 kgf was applied.

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Fig. 8

The vibrational signals obtained for the nut’s inner surface with a mean surface roughness of (a) Ra = 0.20 μm, and (b) Ra = 0.16 μm

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Fig. 9

Variations of fractal dimension with time for (a) the forward movement, and (b) the backward movement

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Fig. 10

Variations of topothesy with time for (a) the forward movement, and (b) the backward movement

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Fig. 11

(a) Vibrational signals acquired in the axial direction, (b) the topothesies of the signals, and (c) the magnification of the vibrational signals in the time period with an unusual signal pattern

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Fig. 12

The results of the ball passing frequency predicted by Eq. (9) and the methods of time interval and fast Fourier transformation as a function of rotational speed

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Fig. 13

The number of ball-pass signal arising at different running time periods. The rotational speed is (a) 2100 rpm and (b) 3000 rpm.

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Fig. 14

The color changes in the grease collected at a time of (1) before running, (2) 55 min, (3) 12 h, (4) the end of this test (<26 h)

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Fig. 15

Variations of (a) fractal dimension Ds, and (b) topothesy G with time for the long-range durability test

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Fig. 16

Number distribution of G peaks obtained from the vibrational signals at the 9th hour

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Fig. 17

Variations of (a) G-skewness, and (b) Ds-skewness with time for the entire long-range durability test

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Fig. 18

Variations of the G parameters for friction torque and vibration signals in the long-range test time

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