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Analytical modeling of residual stress in orthogonal cutting considering tool edge radius effect

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Abstract

Machining-induced residual stress is a leading cause of machining distortion. Many previous studies have been performed to model the relationship between various impact factors and machined residual stress, such as cutting parameters, lubrication, and cooling conditions etc. While few analytic studies examining the size effect of tool edge radius on residual stress have been performed. In order to better understanding the size effect of tool edge radius on machining-induced residual stress, thermomechanical coupling loading and unloading operations are applied to obtain the machining-induced residual stress on the basis of modeling mechanical loads and thermal loads for cutting with edge radiused cutters. Verification experimental results indicate that the proposed model is effective in judging and analyzing the characteristics of the residual stress profile beneath the machined surface in consideration of the tool edge radius effect. By case studies of Ti-6Al-4V turning those based on the proposed model, it was found that the value of surface residual stress increased with the tool edge radius changed from 0.01 mm to 0.03 mm, and the increased percentage of stresses in cutting and cutting width directions could be 132.6% and 191.1%, respectively. While the peak value of the compressive stress and the depth of the peak value decreased gradually, and the decreased percentages of the peak value of the compressive stress in cutting and cutting width directions are 77.8% and 88.6%. The decreased percentages of the depth of the peak value in cutting and cutting width directions are 47.6% and 63.5%.

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Abbreviations

R :

Resultant cutting force (N)

R c :

Measured cutting force in cutting direction (N)

R t :

Measured cutting force that perpendicular to the cutting direction (N)

S :

Shear force (N)

P :

Plowing force (N)

P c :

Plowing force in the cutting directions (N)

P t :

Plowing force perpendicular to the cutting directions (N)

F s :

Cutting force component along the shear plane (N)

F n :

Cutting force component perpendicular to the shear plane (N)

F c :

Cutting force component along the cutting direction (N)

F t :

Cutting force component perpendicular to the cutting direction (N)

F f :

Friction force (N)

N :

Cutting force component perpendicular to the chip contact surface (N)

φ :

Shear angle (in degree)

α :

Tool rake angle (in degree)

ξ :

Clearance angle of the tool (in degree)

μtc :

Friction coefficient of the tool-chip contact surface

μtw :

Friction coefficient of the tool-workpiece contact surface

η :

Friction angle between tool and workpiece (in degree)

β c :

Chip separation angle (in degree)

r :

Radius of cutting edge (μm)

w :

Contact width between the tool and workpiece (mm)

σ p :

Stress value of any point (xp, zp) below the shear plane (MPa)

σ s :

Stress value of any point (xs, zs) below the shear plane (MPa)

K :

Shear strength of the workpiece material (MPa)

q s :

Tangential load on the shear plane (MPa)

q n :

Normal load on the shear plane (MPa)

P s :

Tangential load along CD plane (MPa)

P n :

Normal load along CD plane (MPa)

DoC :

Depth of cut (mm)

σ mech :

Mechanical load of any point below the workpiece (MPa)

σ i,j, \( {\dot{\sigma}}_{i,j} \) :

Stress tensor and stress increment (MPa)

ε i,j, \( {\dot{\varepsilon}}_{i,j} \) :

Strain tensor and strain increment

Q shear :

Strength of the shear band heat source (J)

Q plough :

Strength of the plowing zone heat source (J)

k w,p :

Thermal conductivity of the workpiece material (W/(m°C))

a w,p :

Thermal diffusivity of the workpiece material (m2/s)

γ :

The proportion of cutting heat inflow to the workpiece

σ therm :

Thermal load of any point below the workpiece (MPa)

E w :

Young's modulus of the workpiece material (GPa)

v :

Poisson ratio of the workpiece material

Δσ i,j :

Stress unload increments (MPa)

Δε i,j :

Strain unload increments

v c :

Cutting speed (m/min)

f t :

Feed rate (mm/rev)

a e :

Width of cut (mm)

A, B, C, m, n :

Johnson-Cook constitutive parameters

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Funding

Financial support was from the Key Natural Science Project of Anhui Provincial Education Department (KJ2018A0021), Natural Science Foundation of Anhui Province (1908085QE230) and High-level talent fund of Anhui University.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Anhui University, Hefei, 230601, China

    Dong Yang

  2. Hefei Science and Technology College, Hefei, 231201, China

    Xiao Xiao

  3. School of Mechanical Engineering, Shandong University, Jinan, 250061, China

    Xiaoliang Liang

Authors
  1. Dong Yang
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  2. Xiao Xiao
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  3. Xiaoliang Liang
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Correspondence to Dong Yang.

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Yang, D., Xiao, X. & Liang, X. Analytical modeling of residual stress in orthogonal cutting considering tool edge radius effect. Int J Adv Manuf Technol 103, 2965–2976 (2019). https://doi.org/10.1007/s00170-019-03744-9

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