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Unified plastic limit analysis of the cap bottom generated by a dedicated cutting tool in orbital drilling

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Abstract

The mechanical analysis and deformation mechanism of cap formation in orbital drilling process plays a vital role in revealing the changing law of hole-making quality at the exit machining stage. The characteristics of cap formation, generated by a dedicated cutting tool, is proposed that aimed at orbital drilling process. Especially, the cap bottom is simplified as a simply supported circular plate under a partially uniform load based on the symmetrical feature of the geometrical morphology and force condition. Its corresponding unified plastic limit analysis is developed. Then the ultimate load, stress field, and plastic deformation at the bottom of the cap are derived from the unified yield criterion. Furthermore, in terms of the Tresca yield, Huber–von Mises, and twin-shear yield criteria, the solutions are obtained by numerical calculation method and compared them with each other. Finally, conclusions were made about the cap formation mechanism in the orbital drilling of holes from the unified plastic limit analysis perspective.

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Abbreviations

a*, b*, c*, d*, e* :

The diameter of zone 1, zone 2, zone 3, zone 4, and zone 5 of the cap geometry in cross-section view

f*, g*, α :

The thickness of the cap bottom, the whole cap, and the tilt angle of the thin ring on the periphery

l0, l1, l2, l3, l4 :

The length parameters of the front cutting edge

β0, β1, β2, β3, β4 :

The angle parameters of the front cutting edge

h0, hf0, hf1, hf2, hf3 :

The total thickness of cap and the thickness of the cap bottom at stage 1, stage 2, stage 3, and stage 4

hp0, hp1, hp2, hp3 :

The thickness of the cap periphery at stage 1, stage 2, stage 3, and stage 4

vfa, t:

The axial feeding rate and time

Fa0, Fr0, Ft0 :

The external forces in axial, radial, and tangential direction loaded on the cap bottom

Fa1, Fr1, Ft1 :

The external forces in axial, radial, and tangential direction loaded on the cap periphery

θ:

Polar angle

Oh, Ot :

The center of the hole to be machined and the center of tool

S1, S2 :

Any point on the cap bottom and cap periphery

a:

The radius of the plate

R, r:

The radius of any point in the plate and its dimensionless variable

Rp, rp :

The loading radius and its dimensionless variable

r0 :

The radius of the ring with the moments corresponding to the yield point B

rp0 :

The loading radius with the same value as the r0

P1 :

The plastic limit load

mr :

The dimensionless variable of the radial moment

mθ :

The dimensionless variable of the circumferential moment

M0 :

The ultimate bending moment

d1 :

The value of mr when r is equal to r0

b:

The unified strength theory parameter

a1, a2, b1, b2, c1, c2, c3 :

The integration coefficients in the moment fields of the plate

\( \dot{\mathrm{w}} \) :

The deflection rate in a circular plate

\( {\dot{\mathrm{w}}}_0 \) :

The deflection rate in the center of a circular plate

ci1, ci2 (i=1~6):

The integration coefficients in the velocity fields of the plate

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Funding

This research was supported by the National Key Research and Development Program of China (Grant No. 2016YFE0111400), the National Nature Science Foundation of China (Grant No. 51805476), and the Natural Science Foundation of Gansu Province, China (Grant No. 18JR3RA147).

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Authors and Affiliations

  1. School of Mechatronics Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Lan Zhou & Wei Li

  2. State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metals, Lanzhou University of Technology, Lanzhou, 730050, China

    Guosheng An & Wensheng Li

  3. State Key Laboratory of Fluid Power Transmission and Control, College of Mechanical Engineering, Zhejiang University, Hangzhou, 310027, China

    Haijin Wang

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  1. Lan Zhou
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  2. Guosheng An
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  4. Haijin Wang
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  5. Wei Li
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Lan Zhou and Guosheng An are the main authors and contribute in drafting the article, and Wensheng Li and Wei Li contribute in editing the article and act as supervisor for the Haijin Wang.

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Correspondence to Lan Zhou.

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Zhou, L., An, G., Li, W. et al. Unified plastic limit analysis of the cap bottom generated by a dedicated cutting tool in orbital drilling. Int J Adv Manuf Technol 115, 3301–3315 (2021). https://doi.org/10.1007/s00170-021-07354-2

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  • DOI: https://doi.org/10.1007/s00170-021-07354-2

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