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Multi-axis ball-end milling force prediction model considering the influence of cutting edge

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Abstract

Precise prediction of milling force is a crucial issue in multi-axis milling, which is important for evaluating the tool life and surface quality. In this paper, an improved force model for ball-end milling is proposed based on a novel uncut chip thickness (UCT) model as well as the consideration of edge effect and size effect. The computational model of UCT takes into account the influence of lead and tilt angles in ball-end milling. In addition, it utilizes a new discretization method of the uncut chip area that ensures the local cutting edge is perpendicular to the length of the elemental uncut chip area, making it more compatible with the classical oblique cutting model. For each elemental cutting edge, the force components are calculated through a purely analytical approach, considering the shear force, edge force, and size effect caused by cutting edge geometry in milling process. The proposed model is comprehensively validated with both FEM and multi-axis milling experiments for aluminum and titanium. The results indicate that the proposed model can predict the dynamic milling force under various cutting conditions in a good manner. Moreover, considering edge and size effects can further improve the prediction accuracy.

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Abbreviations

a p :

Depth of cut

f z :

Feed per tooth

R :

Tool radius

N :

Teeth number of the ball-end mill cutter

ψ ji :

Position angle of the element i of the jth cutting edge

κ :

Position angle between OPi and zT axis

κ s :

Starting angle of the axial contact angle

κ e :

Ending angle of the axial contact angle

κ m :

Boundary angle of the cutting area

dF t, dF r, dF a :

Tangential, radial, and axial components of cutting force

K tc, K rc, K ac :

Cutting force coefficients in tangential, radial, and axial directions

K te, K re, K ae :

Edge force coefficients in tangential, radial, and axial directions

θ :

Rotation angle of the spindle

i 0, i i :

Nominal helix angle and local helix angle

ϕ p :

Pitch angle between adjacent teeth

ϕ st, ϕ ex :

Cut-in angle and cut-out angle

φ i :

Lag angle of each cutting edge element

λ i s :

Edge inclination angle of the cutting edge element

α i n :

Normal rake angle of the cutting edge element

α i r :

Radial rake angle of the cutting edge element

dS :

Length of cutting edge element

db :

Chip width

h n :

Uncut chip thickness

α, γ :

Lead angle and tilt angle

τ i s :

Shear stress of the cutting edge element

ϕ i n :

Normal shear angle of the cutting edge element

β i n :

Normal friction angle of the cutting edge element

η i  c, η i  e, η i  s :

Chip flow angle, equivalent plane angle, and shear flow angle of the cutting edge element

V :

Cutting velocity

V c :

Chip flow velocity

ε, ̇ε, ̇ε 0, ̇ε m :

Shear strain, shear strain rate, reference shear strain rate, and maximum shear strain rate

T, T r, T m :

Material temperature, room temperature, and melting temperature

A, B, C, n, m :

Yield strength, hardening modulus, strain rate sensitivity coefficient, hardening exponent, and thermal softening index

ρ, c :

Material density and heat capacity

μ :

Taylor-Quinney coefficient

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Funding

This work was financially supported by the National Natural Science Foundation of China (52175482) and the Guangdong Major Project of Basic and Applied Basic Research (2021B0301030001).

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Authors and Affiliations

  1. Hubei Digital Manufacturing Key Laboratory, School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan, 430070, China

    Kejia Zhuang, Yan Yang, Chengjin Tian & Zhongmei Gao

  2. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Xing Dai & Jian Weng

  3. Institute of Machining Technology (ISF), TU Dortmund University, 44227, Dortmund, Germany

    Jian Weng

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  1. Kejia Zhuang
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Zhuang, K., Yang, Y., Dai, X. et al. Multi-axis ball-end milling force prediction model considering the influence of cutting edge. Int J Adv Manuf Technol 128, 357–371 (2023). https://doi.org/10.1007/s00170-023-11890-4

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