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A hybrid model for force prediction in orthogonal cutting with chamfered tools considering size and edge effect

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Abstract

Researches on the modeling of machining difficult-to-cut metals are important for optimization of the processing parameters, in which the force modeling is essential due to its significant influence on the performance of tools and the quality of parts. A semi-analytical method for force prediction in orthogonal cutting with chamfered tools considering both edge and size effect is proposed in this paper. The plastic deformation in the shear band was investigated using a parallel shear zone model and unequal division shear zone model. The influence of size effect on cutting force was discussed and a simplified expression of improvement factor is introduced to describe the sharp increase of shear stress under the condition of low feed rate. Simulations of orthogonal cutting with different chamfer lengths are conducted to analyze the variation of cutting force with respect to chamfer length, which reveals that the influence of chamfer length on cutting force is determined by the ratio of chamfer length to uncut chip thickness. A modified function considering the trend of material flow condition is proposed, which treats the total cutting force as a combination of cutting forces caused by chamfered edge and rake face. The calibration of constants in the proposed method is achieved using particle swarm optimization (PSO), a meta-heuristic algorithm for complicated non-linear models. The experiments show that the method works well on both fitting and predicting modules in orthogonal cutting of AISI 304 using cemented carbide tools with 15° chamfer angle or 25° chamfer angle.

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Abbreviations

α, β, ϕ :

Rake angle, friction angle, shear angle

f :

Feed rate

w :

Depth of cut

f0, p :

Constants in empirical friction model

V, Vc, Vs :

Cutting velocity, chip flow velocity, shear velocity

γ, \( \dot{\gamma} \),\( {\dot{\gamma}}_0 \) :

Shear strain, shear strain rate and the reference strain rate

A, B, C, n, m :

Parameters in Johnson-Cook’s equation

T, Tr, Tm :

The temperature in the shear band, room temperature, melting temperature

η :

The portion of the deformation energy as the generation of heat in the shear band

ΔT :

The temperature rise due to plastic deformation in the parallel shear zone model

m chip :

The mass of chip formation per second

ψ :

The percentage of the heat in shear zone transferred into workpiece

t :

Uncut chip thickness (UCT)

ρ, c, λ :

The density, specific heat, thermal conductivity of workpiece material

R T :

A dimensionless parameter in parallel shear zone model

k :

The unequal ratio in unequal division shear zone model

q :

The constant characterizing the non-uniform distribution of the tangential velocity in the deformation zone in unequal division shear zone model.

h :

The thickness of the shear band

μ :

Taylor-Quinney coefficient

τ s :

Shear stress calculated using Johnson-Cook’s law

τ ss :

Improved shear stress considering size effect

α t :

Empirical parameter

G :

Shear modulus of the workpiece material

b :

The magnitude of the Burgers vector

\( \overline{r} \) :

Nye factor

u :

Exponential factor

z :

Constant in the introduced function of size effect

Kt, Kf :

Cutting force coefficients in cutting speed direction, feed rate direction

Ft, Ff :

Cutting force components in cutting speed direction, feed rate direction

F s :

Shear force

S :

Introduced factor in this paper considering the material flow state.

x, y :

Constants in S

r :

The ratio of chamfer length to UCT

L, θ :

Chamfer length, chamfer angle

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Funding

This work is partially supported by the National Natural Science Foundation of China (51705385), China Scholarship Council (201906950051), and The Fundamental Research Funds for the Central Universities (2019-YB-019).

Author information

Authors and Affiliations

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

    Jian Weng, Kejia Zhuang & Han Ding

  2. Division of Production and Materials Engineering, Lund University, 22100, Lund, Sweden

    Jian Weng & Jinming Zhou

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

    Han Ding

Authors
  1. Jian Weng
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  2. Kejia Zhuang
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Correspondence to Kejia Zhuang.

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Appendix

Appendix

The distribution of strain and strain rate in the shear zone is considered uniform in a plane parallel to a primary shear plane, which means there is only shear deformation in the primary deformation zone. The function of shear strain and strain rate can be expressed as

$$ \gamma =\left\{\begin{array}{ll}\frac{{\dot{\gamma}}_m{z}_e^q}{\left(q+1\right)V\sin \phi {(kh)}^q}& {z}_e\in \left[0, kh\right)\\ {}-\frac{{\overset{.}{\gamma}}_m{\left(h-{z}_e\right)}^q}{\left(q+1\right)V\sin \phi {\left(1-k\right)}^q{h}^q}+\frac{\cos \alpha }{\cos \left(\phi -\alpha \right)\sin \phi }& {z}_e\in \left[ kh,h\right]\end{array}\right. $$
(30)
$$ \dot{\gamma}=\left\{\begin{array}{cc}\frac{{\dot{\gamma}}_m}{(kh)^q}{z}_e^q& {z}_e\in \left[0, kh\right)\\ {}\frac{{\dot{\gamma}}_m{\left(h-{z}_e\right)}^q}{{\left(1-k\right)}^q{h}^q}& {z}_e\in \left[ kh,h\right]\end{array}\right. $$
(31)

where ze is the distance from the lower boundary to the calculated plane. The total thickness of the shear band is always considered half of UCT [29]. \( {\dot{\gamma}}_m \) is the maximum of shear stress in the shear band, happens on the main shear plane, and can be determined as

$$ {\dot{\gamma}}_m=\frac{\left(q+1\right)V\cos \alpha }{h\cos \left(\phi -\alpha \right)} $$
(32)

The unequal division ratio k can be expressed as [36].

$$ k=\frac{\cos \phi \cos \left(\phi -\alpha \right)}{\cos \alpha } $$
(33)

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Weng, J., Zhuang, K., Zhou, J. et al. A hybrid model for force prediction in orthogonal cutting with chamfered tools considering size and edge effect. Int J Adv Manuf Technol 110, 1367–1384 (2020). https://doi.org/10.1007/s00170-020-05943-1

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