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Research Papers

# Modeling of the Effect of Machining Parameters on Maximum Thickness of Cut in Ultrasonic Elliptical Vibration Cutting

[+] Author and Article Information
Chandra Nath, Ken Soon Neo

Department of Mechanical Engineering, National University of Singapore, 9, Engineering Drive 1, Singapore 117576

Mustafizur Rahman1

Department of Mechanical Engineering, National University of Singapore, 9, Engineering Drive 1, Singapore 117576mpemusta@nus.edu.sg

1

Corresponding author.

J. Manuf. Sci. Eng 133(1), 011007 (Jan 31, 2011) (8 pages) doi:10.1115/1.4003118 History: Received March 20, 2009; Revised November 20, 2010; Published January 31, 2011; Online January 31, 2011

## Abstract

In recent years, the ultrasonic elliptical vibration cutting (UEVC) technique has been found to be an efficient method for the ultraprecision machining of hard and brittle materials. During the machining at a given nominal depth of cut (DOC), the UEVC technique, because of its inherent mechanism, effectively reduces the thickness of cut (TOC) of the workpiece material through overlapping vibration cycles. For the ductile machining of hard and brittle materials, this TOC plays a critical role. However, the relationships between the nominal DOC, the TOC, and the relevant machining parameters have not yet been studied. In this study, the role playing machining parameters for the TOC are firstly investigated and then theoretical relations are developed for predicting the maximum TOC $(TOCm)$ with respect to the relevant machining parameters. It is found that four machining parameters, namely, workpiece cutting speed, tool vibration frequency, and tangential and thrust directional vibration amplitudes, influence the $TOCm$. If the speed ratio (ratio of the workpiece cutting speed to the maximum tool vibration speed in the tangential direction) is within a critical value 0.12837, then a reduced $TOCm$ can be obtained. It is also realized that if the $TOCm$ can be kept lower than the critical DOC $(DOCcr)$, then ductile finishing of brittle materials can be achieved. The above phenomenon has been substantiated by experimental findings while machining a hard and brittle material, sintered tungsten carbide. The findings suggest that the same concept can be applied for the ductile cutting of other hard and brittle materials.

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## Figures

Figure 1

Illustration of the UEVC principle

Figure 2

Effect of the nominal DOC on the finished surface generating in the UEVC method when (x1−x3)>0

Figure 3

Reduction of a given nominal DOC to a smaller TOCm value in the UEVC method: (a) at the critical and (b) within the critical conditions

Figure 4

Effect of speed ratio on cycle-overlap at various tangential directional vibration amplitudes a

Figure 5

Effect of speed ratio on the TOCm (condition: ap>b, where b=1.5 μm)

Figure 6

Effect of thrust vibration amplitude b of the tool on the TOCm at different Rs (condition: ap=4 μm and ap>b)

Figure 7

(a) Schematic of the UEVC experimental set up for facing experiments and (b) the set up with the Toshiba machine spindle

Figure 8

Nomarski photographs (500x) of the machined surfaces for various values of Rs and b at different locations ((i) 17.5 mm, (ii) 18.5 mm, and (iii) 19.5 mm) of the workpiece cutting region for the stated conditions in Table 3

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