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Research on the tool tip trajectory deflection control and cutting characteristics of elliptical vibration cutting based on guided wave transmission

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Abstract

Chip and surface roughness (Ra) are the two main problems in ultra-precision machining. In the current research on elliptical vibration cutting (EVC), little is known about the impact of high-frequency tool tip ellipse trajectory deflection on the quality of cutting surfaces. In this paper, effective control of the tool tip ellipse trajectory deflection is achieved by adjusting phase difference. We also explain how tool tip ellipse trajectory changes affect chip and surface roughness. Firstly, an EVC device is optimized to obtain orthogonal vibration output of the tool tip based on the guided wave transmission technique. Secondly, we establish an elliptical trajectory deflection control model of the tool tip. Analysis of the control model shows that (1) when the tool tip amplitude and phase difference are simultaneously adjusted, the tool tip trajectory can be controlled at an angle of deflection with the same elliptical shape; (2) when only phase difference is adjusted, control of the tool tip trajectory is achieved at an angle of deflection with a different elliptical shape. At a phase difference below 90°, elliptical trajectory of the tool tip is considered positive, while at an angle exceeding 90°, the reverse is true. Analysis of cutting characteristics of the tool tip ellipse trajectory deflection controlled by phase difference adjustments and finite element simulation indicate that as the phase difference increases, the continuity of the chip and Ra first becomes better then poorer due to friction force reversal effect. At a phase difference of 60°, elliptical trajectory of the tool tip is positive with an appropriate dynamic plunging angle for optimized quality of the cutting surface. Overall, test results of our cutting experiment are consistent with theoretical reports demonstrating the feasibility and effectiveness of the current work.

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Abbreviations

Z :

Logarithm of impedance mode

δ :

Impedance phase

f :

Frequency

P 1 :

Tool tip ellipse trajectory in the oxy plane

P 2 :

Tool tip ellipse trajectory after deflection in the oxy plane

\( {P}_1^{\prime } \) :

Tool tip ellipse trajectory in the o1x1y1 plane

\( {P}_2^{\prime } \) :

Tool tip ellipse trajectory after deflection in the o1x1y1 plane

η :

Deflection angle

a :

Tool tip amplitude after deflection in x direction

b :

Tool tip amplitude after deflection in y direction

m :

Tool tip amplitude in x direction

n :

Tool tip amplitude in y direction

t :

Time

θ :

Phase difference

v :

Cutting speed

x(t):

Displacement of tool tip ellipse trajectory in x direction

y(t):

Displacement of tool tip ellipse trajectory in y direction

x′(t):

Displacement in x direction after the tool tip ellipse trajectory deflects

y′(t):

Displacement in y direction after the tool tip ellipse trajectory deflects

β :

Phase difference after deflection

R th1 :

Residual heights of the phase difference at 30°

R th2 :

Residual heights of the phase difference at 60°

R th3 :

Residual heights of the phase difference at 150°

γ 1 :

Dynamic plunging angles of the tool rake face with phase difference at 30°

γ 2 :

Dynamic plunging angles of the tool rake face with phase difference at 60°

γ 3 :

Dynamic plunging angles of the tool rake face with phase difference at 150°

Ra:

Surface roughness

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Funding

This work was supported by the Natural Science Foundation of Fujian Province (project number: 2017J01700) and the Science and Technology Key Project of Fujian Province (project number: 2017H0025). The authors would also like to thank Prof. Qihui Wu for his contribution to the improvement of the language.

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Authors and Affiliations

  1. School of Mechanical and Energy Engineering, Jimei University, Xiamen, 361021, Fujian Province, China

    Yu’an Jiang, Jun Pi, Yuzhou Zhang, Tao Jiang, Guang Yang & Zhihuang Shen

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  1. Yu’an Jiang
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  2. Jun Pi
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Correspondence to Jun Pi.

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Jiang, Y., Pi, J., Zhang, Y. et al. Research on the tool tip trajectory deflection control and cutting characteristics of elliptical vibration cutting based on guided wave transmission. Int J Adv Manuf Technol 108, 3101–3117 (2020). https://doi.org/10.1007/s00170-020-05552-y

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