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Energy analysis of the extrusion process through a streamlined Gaussian die

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Abstract

Currently, the extrusion process with traditional conical die or elliptic die will cause the problems of high energy consumption and stress concentration. In order to address these problems, a novel streamline die characterized by the Gaussian function is designed first. The corresponding velocity field is constructed on the basis of the condition of equal flow per second. By using the newly constructed velocity field, the energy analysis of the extrusion is conducted, and the concrete internal work rate of plastic deformation, shearing work rate, and work rate of friction are obtained by a new method, called the feature-fitting substituting method. Then, the analytical expressions of extrusion force and stress state coefficient are obtained by the upper bound method. Simultaneously, the finite element (FE) simulation is conducted to verify the accuracy of the analytical expression of extrusion force and to disclose the advantages of the present die over the existing dies. The results show that the extrusion forces obtained from the present die match well with the simulation results, and the maximum deviation is no more than 1.73%. Above all, it is proved that the present Gaussian die can consume less energy and reduce the possibility of die loss evidently.

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Abbreviations

l :

The deformation zone length

R, R 0, R 1 :

The radius of the deformed workpiece and its boundary values on the inlet and outlet sections respectively

v z, v 0, v 1 :

The horizontal velocity of metal flow and its boundary values on the inlet and outlet sections

α :

The die semi-angle

\({\dot{\varepsilon}}_r,{\dot{\varepsilon}}_{\theta },{\dot{\varepsilon}}_z\) :

The strain rate components in the radial, circumference, and horizontal directions

\({\dot{\varepsilon}}_{Rz}\) :

The shear strain rate in the z-direction on the R-plane

v r, v θ, v z :

The velocity components in the radial, circumference, and horizontal directions

\({\dot{W}}_i,{\dot{W}}_s,{\dot{W}}_f\) :

The work rate of plastic deformation, shear energy rate, and work rate of friction

\(D\left({\dot{\varepsilon}}_{ij}\right)\) :

The specific plastic work rate

σ s, k :

The deformation resistance and the yield shear stress

\({\dot{\varepsilon}}_{eq}\) :

The equivalent strain rate

m, f :

The frictional factor and the friction coefficient

Δv t1, Δv t2 :

The velocity discontinuities on the inlet and outlet sections

Δv f :

The velocity discontinuity on the contact surface

\(J,{J}^{\ast },{J}_{\textrm{min}}^{\ast }\) :

The external energy rate, the calculated one, and its minimum value

σ e :

The extrusion stress

n σ :

The stress state coefficient

λ :

The extrusion ratio

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Acknowledgements

The authors also wish to acknowledge valuable suggestions from reviewers.

Funding

This research was supported by the National Natural Science Foundation of China (grant no. 52074187, U1960105, 52274388).

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Authors and Affiliations

  1. Shagang School of Iron and Steel, Soochow University, Suzhou, 215021, China

    Shun Hu Zhang, Yi Zhang & Xin Ying Liu

Authors
  1. Shun Hu Zhang
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  2. Yi Zhang
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  3. Xin Ying Liu
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Contributions

Shun Hu Zhang: responsible for investigation and writing—original draft.

Yi Zhang: responsible for theoretical derivation and experimental validation.

Xin Ying Liu: responsible for data curation, validation, and writing—review and editing.

Corresponding author

Correspondence to Shun Hu Zhang.

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The authors declare no competing interests.

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Highlights

• A novel streamline die for extrusion characterized by the gaussian function is designed.

• A new method called the feature-fitting substitution method is proposed to calculate the analytical extrusion force.

• The gaussian extrusion die can consume less energy and reduce the stress concentration of die.

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Zhang, S.H., Zhang, Y. & Liu, X.Y. Energy analysis of the extrusion process through a streamlined Gaussian die. Int J Adv Manuf Technol 127, 3715–3728 (2023). https://doi.org/10.1007/s00170-023-11757-8

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  • DOI: https://doi.org/10.1007/s00170-023-11757-8

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