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Mathematical modelling, study and computer-aided design of flux-cored wire rolling in round gauges

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Abstract

The mathematical model of the stress–strain state during flux-cored wire rolling in round gauges has been developed. Simulation was based on dividing the deformation zone into elementary volumes and simultaneous solution of the plasticity condition for porous materials and power static equilibrium equation inside the elementary volume. A distinctive feature of this model is taking into account the porous medium strain in the deformation zone. The experiments have confirmed the validity of the mathematical model for predicting the powder density and the energy-power characteristics of the process. Based on the developed mathematical model, the criteria and conditions for optimization were formulated, and the algorithm was developed for the automated design of technology for flux-cored wire rolling in round gauges. As an example of the obtained solutions implementation, the calculation of sintered copper flux-cored wire rolling technology was given.

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Abbreviations

L pl :

Seal zone content

L lag :

Backward slip zone content

L adv :

Forward slip zone content

ab, cd :

Boundary sections of deformation zone

p x :

Standard surface stresses

d x :

Composition thickness along the deformation zone length

K R :

Number of elementary volumes when the deformation zone is broken along the rolling axis

f x :

Coefficient of external friction

L 0 :

Billet length before rolling

L 1 :

Billet length after rolling

S l1 :

Relative length of the forward slip zone on the driving working roll

σ x :

Standard axial stresses

α x :

Contact angle

τ x :

Shear contact stresses

\({\varepsilon }_{dx},{\varepsilon }_{lx}\) :

Deformation degree

\({\gamma }_{x}\) :

Density ratio

σ sxi :

Solid phase yield strength

ε ex :

Equivalent strain

∆ε exj :

Equivalent strain increment

σ 1 :

Front tension stress

i :

Serial number of axial rolling section

x :

Coordinate along the rolling axis

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Authors and Affiliations

  1. Automated Metal Forming Process and Machinery Department, Donbass State Engineering Academy, Akademichna 72, Kramatorsk, Donetsk Region, 84313, Ukraine

    Eduard P. Gribkov, Serhii O. Malyhin & Dmytro V. Merezhko

  2. Computer and information technology Department, Donbass State Engineering Academy, Akademichna 72, Kramatorsk, Donetsk Region, 84313, Ukraine

    Svetlana S. Hurkovskaya

  3. Handling systems and transport machines department, Donbass State Engineering Academy, Akademichna 72, Kramatorsk, Donetsk Region, 84313, Ukraine

    Elena V. Berezshnaya

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  1. Eduard P. Gribkov
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All authors participated in the design of this work and performed equally. All authors read and approved the final manuscript.

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Correspondence to Eduard P. Gribkov.

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Gribkov, E.P., Malyhin, S.O., Hurkovskaya, S.S. et al. Mathematical modelling, study and computer-aided design of flux-cored wire rolling in round gauges. Int J Adv Manuf Technol 119, 4249–4263 (2022). https://doi.org/10.1007/s00170-022-08662-x

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