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Cutting Force Model in Micro-Dimple Pattern Process Using Two-Frequency Elliptical Vibration Texturing (TFEVT) Method

  • Rendi Kurniawan
  • Tae Jo KoEmail author
Regular Paper
  • 9 Downloads

Abstract

We herein propose a cutting force model in a micro-dimple pattern process using the two-frequency elliptical vibration texturing (TFEVT) method. The TFEVT method decreases the cutting force compared to the conventional texturing (CT) method owing to the intermittent cutting behavior. The cutting force model in the TFEVT method is formulated, in which the shear angle is assumed as a transient and the transient area of cut of the micro-dimple is determined. The transient area of cut of the micro-dimple can be determined by obtaining the starting and ending time of cutting, while the shear angle can be determined by Cerniway’s hypothesis. Finally, the cutting force model was compared with the experimental cutting force value. The comparison results show that the cutting force simulation is in agreement with the experimental cutting force value. The experimental results also show that the cutting force in the TFEVT method is lower than that in the CT method.

Keywords

Micro-dimple Cutting force model TFEVT Elliptical vibration 

List of symbols

\({\text{x}}\left( t \right)\)

Tool tip trajectory along x-axis (µm)

\({\text{y}}\left( t \right)\)

Tool tip trajectory along y-axis (µm)

\(V_{x} \left( t \right)\)

Tool tip velocity along x-axis (µm/s)

\(V_{y} \left( t \right)\)

Tool tip velocity along y-axis (µm/s)

\(a\)

Minor amplitude of elliptical locus (µm)

\(b\)

Major amplitude of elliptical locus (µm)

\(B\)

Amplitude of the sinusoidal wave (µm)

\(V_{f}\)

Nominal cutting speed (µm/s)

\(\phi\)

Phase difference of the elliptical locus (rad)

\(f_{h }\)

Ultrasonic vibration frequency (> 20 kHz) (Hz)

\(f_{l}\)

Low-vibration frequency (Hz)

\(t\)

Time (s)

\(\theta_{t} \left( t \right)\)

Velocity angle (rad)

Vt

Magnitude of the transient cutting velocity of the tool tip (µm/s)

\({\text{JC}}\left( {\text{t}} \right)\)

Transient Johnson–Cook shear stress model (MPa)

A, B, C, n, m

Material constant [A, B = (MPa); C, n, m = (dimensionless)]

\({\text{T}}\left( t \right)\)

Transient temperature (K)

Tr

Room temperature (K)

Tm

Melting temperature (K)

\(\varepsilon\)

Equivalent plastic strain (dimensionless)

\(\dot{\varepsilon }\)

Equivalent plastic strain rate (s−1)

\(\dot{\varepsilon }_{o}\)

Absolute plastic strain rate (s−1)

Cp

Specific heat of the workpiece (J/kg K)

ρ

Mass density of the workpiece (kg/m3)

K

Thermal conductivity (W/mK)

β

Generated energy fraction number (dimensionless)

RT

Non-dimensional thermal number (dimensionless)

\(\upalpha\left( t \right)\)

Transient rake angle (rad)

\(\alpha_{o}\)

Initial value of the negative rake angle (rad)

\(\beta \left( t \right)\)

Transient friction angle (rad)

\(\phi_{s} \left( t \right)\)

Hypothesized transient shear angle (rad)

\(\phi_{m} \left( t \right)\)

Merchant’s transient shear angle (rad)

\(TOC_{t} \left( t \right)\)

Transient thickness of cut (µm)

\(A_{t} \left( t \right)\)

Transient cutting area (µm2 = 10−12 m2)

\(F_{s} \left( t \right)\)

Transient shear force (N)

\(F_{r} \left( t \right)\)

Transient resultant cutting force (N)

\(F_{p} \left( t \right)\)

Transient principle cutting force (N)

\(F_{t} \left( t \right)\)

Transient thrust cutting force (N)

\(F_{{p_{rms} }} \left( t \right)\)

Root mean squared cutting forces Fp (N)

\(F_{{t_{rms} }} \left( t \right)\)

Root mean squared cutting forces Ft (N)

Notes

Acknowledgements

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant No. NRF-2017R1A2B2003932). Also this work was partially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1A4A1015581).

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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringYeungnam UniversityGyeongsan-siSouth Korea

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