Design of ultrasonic elliptical vibration cutting system for tungsten heavy alloy

doi:10.1007/s11465-022-0715-1

Front. Mech. Eng.

2022, Vol. 17

Issue (4) : 59 https://doi.org/10.1007/s11465-022-0715-1

RESEARCH ARTICLE

Design of ultrasonic elliptical vibration cutting system for tungsten heavy alloy

Sen YIN, Yan BAO, Yanan PAN, Zhigang DONG, Zhuji JIN, Renke KANG(

)

Key Laboratory for Precision and Non-traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China

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Abstract

Nanoscale surface roughness of tungsten heavy alloy components is required in the nuclear industry and precision instruments. In this study, a high-performance ultrasonic elliptical vibration cutting (UEVC) system is developed to solve the precision machining problem of tungsten heavy alloy. A new design method of stepped bending vibration horn based on Timoshenko’s theory is first proposed, and its design process is greatly simplified. The arrangement and working principle of piezoelectric transducers on the ultrasonic vibrator using the fifth resonant mode of bending are analyzed to realize the dual-bending vibration modes. A cutting tool is installed at the end of the ultrasonic vibration unit to output the ultrasonic elliptical vibration locus, which is verified by finite element method. The vibration unit can display different three-degree-of-freedom (3-DOF) UEVC characteristics by adjusting the corresponding position of the unit and workpiece. A dual-channel ultrasonic power supply is developed to excite the ultrasonic vibration unit, which makes the UEVC system present the resonant frequency of 41 kHz and the maximum amplitude of 14.2 μm. Different microtopography and surface roughness are obtained by the cutting experiments of tungsten heavy alloy hemispherical workpiece with the UEVC system, which validates the proposed design’s technical capability and provides optimization basis for further improving the machining quality of the curved surface components of tungsten heavy alloy.

Keywords tungsten heavy alloy ultrasonic elliptical vibration cutting Timoshenko’s theory resonant mode of bending finite element method

Corresponding Author(s): Renke KANG

Just Accepted Date: 23 June 2022 Issue Date: 11 January 2023

Cite this article:

Sen YIN,Yan BAO,Yanan PAN, et al. Design of ultrasonic elliptical vibration cutting system for tungsten heavy alloy[J]. Front. Mech. Eng., 2022, 17(4): 59.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-022-0715-1
https://academic.hep.com.cn/fme/EN/Y2022/V17/I4/59

Fig.1 Ultrasonic elliptical vibration cutting process: (a) non cutting, (b) beginning of cutting, (c) cutting, and (d) end of cutting.

Fig.2 Effect of (a) amplitude and (b) phase difference on elliptical vibration locus.

Fig.3 Design scheme of ultrasonic elliptical vibration cutting system.

Tab.1 Design conditions of ultrasonic vibration unit

Fig.4 Curves of bending resonant of the constant cross section bending vibration horn.

Fig.5 Modal analysis of the horn: (a) vibration contour of horn A, (b) vibration vector of horn A, (c) vibration contour of horn B, (d) vibration vector of horn B, (e) vibration contour of horn C, and (f) vibration vector of horn C.

Fig.6 Realization of dual-bending resonant modes.

Tab.2 Geometric dimension parameters of the corrected vibrator in Fig. 6

Fig.7 Modal analysis of the ultrasonic vibration unit: (a) vibration contour of bending vibration A, (b) vibration vector of bending vibration A, (c) vibration contour of bending vibration B, and (d) vibration vector of bending vibration B.

Fig.8 Results of harmonic response and transient dynamic analyses: (a) frequency-domain vibration outputs, (b) time-domain vibration outputs, and (c) vibration locus of one vibration period in the X?Z plane.

Fig.9 Frequency tracking algorithm and ultrasonic power supply: (a) fuzzy PID frequency automatic tracking algorithm and (b) self-developed dual-channel ultrasonic power supply.

Fig.10 Results of the impedance analysis: (a) ultrasonic elliptical vibration unit, (b) 1st PZTs, and (c) 2nd PZTs. PZT: piezoelectric transducer.

Fig.11 Scheme of the protective shell and clamping mode of ultrasonic vibration unit: (a) design scheme and (b) entity. PZT: piezoelectric transducer.

Fig.12 Principle and results of amplitude measurement: (a) principle of amplitude measurement, (b) time-domain vibration outputs along the X and Z directions; elliptical vibration locus at phase differences of (c) 90°, (d) 60°, (e) 30°, and (f) 0°.

Fig.13 Effect of voltage values on two amplitudes.

Fig.14 Computational model of 3-degree-of-freedom ultrasonic elliptical vibration cutting characteristics: (a) application of ultrasonic elliptical vibration unit in the face cutting, (b) computational model on the plane formed by cutting depth and feed directions, (c) computational model on the plane formed by cutting depth and cutting directions, and (d) projection of elliptical vibration locus.

Fig.15 Comparison between (a) 2-DOF UEVC and (b) 3-DOF UEVC. DOF: degree-of-freedom, UEVC: ultrasonic elliptical vibration cutting.

Tab.3 Mechanical properties of tungsten heavy alloy

Tab.4 Cutting experiments parameters

Fig.16 Cutting experiments of hemispherical workpiece: (a) setup of cutting experiments and (b) computational model of hemispherical workpiece processing.

Fig.17 Comparison of tungsten heavy alloy hemispherical workpiece in UEVC and CC: (a) machined hemispherical workpiece and (b) Ra at different α_t values. UEVC: ultrasonic elliptical vibration cutting, CC: common cutting.

Fig.18 Comparison of 3D surface topography and cutting residual height curve at different α_t values: (a) α_t = 105°, (b) α_t = 90°, (c) α_t = 60° and (d) α_t = 15°.

Abbreviations
CC	Common cutting
DOF	Degree-of-freedom
FEM	Finite element method
PID	Proportional–integral–derivative
PZT	Piezoelectric transducer
UEVC	Ultrasonic elliptical vibration cutting
UEVTH	Ultrasonic elliptical vibration tool holder
Variables
A	Sectional area of rod
A₁, A₂	Amplitude along the Z and X directions, respectively
A_p	Sectional area of the PZT
C₁	Static capacitance
C₂	Dynamic capacitance
d	Diameter
D	Displacement
E	Young’s modulus
E_h	Young’s modulus of the horn
E_p	Young’s modulus of the PZT
f	Resonant frequency
F	Shear force
G	Shear modulus
G_p	Shear modulus of the PZT
K	Equivalent elastic modulus coefficient
G_e	Effective shear modulus
G_eh	Effective shear modulus of the horn
G_ep	Effective shear modulus of PZT
I	Moment of inertia
l	Length of the uniform rod
l_p	Thickness of a single PZT
l_v	Length of the vibrator that should be shortened
L₁	Dynamic inductance
L₀	Inductive load
M	Bending moment
R₁	Dynamic resistance
Ra	Surface roughness
Z_e	Equivalent impedance
$ω$	Angular frequency
ρ	Density
ρ_h	Density of the horn
ρ_p	Density of the PZT
γ	Poisson’s ratio
γ_h	Poisson’s ratio of the horn
γ_p	Poisson’s ratio of the PZT
?φ	Phase difference between the dual-bending vibration
α_t	Angle between the vibrator axis and feed direction
β_t	Angle between A₁ and feed direction
ξ	Rotational angle

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