Inverse analysis of the residual stress in laser-assisted milling

Abstract

In laser-assisted milling, higher temperature in shear zone softens the material potentially resulting in a shift of mean residual stress, which significantly affects the damage tolerance and fatigue performance of product. In order to guide the selection of laser and cutting parameters based on the preferred mean residual stress, inverse analysis is conducted by predicting residual stress based on guessed process parameters, which is defined as the forward problem, and applying iterative gradient search to find process parameters for next iteration, which is defined as the inverse problem. An analytical inverse analysis is therefore proposed for the mean residual stress in laser-assisted milling. The forward problem is solved by analytical prediction of mean residual stress after laser-assisted milling. The residual stress profile is predicted through the calculation of thermal stress, by treating laser beam as heat source, and plastic stress by first assuming pure elastic stress in loading process, then obtaining true stress with kinematic hardening followed by the stress relaxation. The variance-based recursive method is applied to solve inverse problem by updating process parameters to match the measured mean residual stress. Three cutting parameters including depth of cut, feed per tooth, and cutting speed, and two laser parameters including laser-tool distance and laser power, are updated with respected to the minimization of resulting residual stress and measurement in each iteration. Experimental measurements are referred on the laser-assisted milling of Ti–6Al–4 V and Si3N4. The percentage difference between experiments and predictions is less than 5% for both materials, and the selection is completed within 50 loops.

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Abbreviations

ρ :

Density

ξ :

Absorption ratio

α :

Thermal diffusivity

θ :

Rotation angle

ε p :

Peak strain

μ :

Friction coefficient

ϕ :

Shear angle

c p :

Specific heat

Cs :

Side cutting edge angle

d :

Grain size

d a :

Axial depth of milling

F c :

Cutting force

F t :

Tangential force

f z :

Feed per tooth

G s :

Shear modulus

G :

Gain coefficient

h :

Heat transfer coefficient

h p :

Plastic modulus

k AB :

Flow stress

K :

Thermal conductivity

K intensity :

Intensity distribution coefficient

K n :

Kalman gain matrix

L AB :

Shear length

L :

Laser-tool distance

P :

Laser power

P thrust :

Normal plowing force

P cut :

Cutting plowing force

P n :

Simulation covariance matrix

Q act :

Activation energy

R g :

Gas constant

R :

Error covariance matrix

R t :

Tool radius

r :

Radius of laser spot

r corner :

Corner edge radius

T laser :

Preheating temperature

T 0 :

Environment temperature

T m :

Melting temperature

t c :

Cutting depth

V f :

Feed rate

V r :

Cutting speed

w :

Cutting width

X drex :

Recrystallized volume fraction

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Correspondence to Yixuan Feng.

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Feng, Y., Hung, TP., Lu, YT. et al. Inverse analysis of the residual stress in laser-assisted milling. Int J Adv Manuf Technol 106, 2463–2475 (2020). https://doi.org/10.1007/s00170-019-04794-9

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Keywords

  • Residual stress
  • Inverse analysis
  • Laser-assisted milling
  • Ti–6Al–4V
  • Si3N4
  • Iterative gradient search