Design of ultrasonic elliptical vibration cutting system for tungsten heavy alloy

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.

Graphical abstract

Keywords

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

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Nomenclature

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
Ap	Sectional area of the PZT
C1	Static capacitance
C2	Dynamic capacitance
d	Diameter
D	Displacement
E	Young’s modulus
Eh	Young’s modulus of the horn
Ep	Young’s modulus of the PZT
f	Resonant frequency
F	Shear force
G	Shear modulus
Gp	Shear modulus of the PZT
K	Equivalent elastic modulus coefficient
Ge	Effective shear modulus
Geh	Effective shear modulus of the horn
Gep	Effective shear modulus of PZT
I	Moment of inertia
l	Length of the uniform rod
lp	Thickness of a single PZT
lv	Length of the vibrator that should be shortened
L1	Dynamic inductance
L0	Inductive load
M	Bending moment
R1	Dynamic resistance
Ra	Surface roughness
Ze	Equivalent impedance
\omega	Angular frequency
ρ	Density
ρh	Density of the horn
ρp	Density of the PZT
γ	Poisson’s ratio
γh	Poisson’s ratio of the horn
γp	Poisson’s ratio of the PZT
∆φ	Phase difference between the dual-bending vibration
αt	Angle between the vibrator axis and feed direction
βt	Angle between A1 and feed direction
ξ	Rotational angle

Acknowledgements

The authors are grateful to the financial support from the National Natural Science Foundation of China (Grant No. U20A20291), the Xingliao Talent Program of Liaoning Province, China (Grant No. XLYC1907183), and the Fundamental Research Funds for the Central Universities, China (Grant No. DUT22ZD201).

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