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Formation mechanism and modeling of surface waviness in incremental sheet forming

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Abstract

Improving and controlling surface quality has always been a challenge for incremental sheet forming (ISF), whereas the generation mechanism of waviness surface is still unknown, which impedes the widely application of ISF in the industrial field. In this paper, the formation mechanism and the prediction of waviness are both investigated through experiments, numerical simulation, and theoretical analysis. Based on a verified finite element model, the waviness topography is predicted numerically for the first time, and its generation is attributed to the residual bending deformation through deformation history analysis. For more efficient engineering application, a theoretical model for waviness height is proposed based on the generation mechanism, using a modified strain function considering deformation modes. This work is favorable for the perfection of formation mechanism and control of surface quality in ISF.

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Abbreviations

BS:

Bending and stretching strain model

FE:

Finite element

FM:

Full model

ISF:

Incremental sheet forming

MBS:

Modified bending and stretching strain model

PM:

Partial model

TPISF:

Two-point incremental sheet forming

F, G, H, Q, M, and N :

Material coefficients of Hill48 yield function

F A, F B, F C :

Tangential forces per unit width in Regions A, B, and C, respectively

F dcf :

Tension force in friction experiment

F f :

Frictional force in friction experiment

F n :

Compressive force in friction experiment

H w :

Waviness height

K :

Material coefficient of Ludwik constitutive function

l :

Forming depth

L :

Width size of partial FE model

n :

Material hardening index of Ludwik constitutive function

r :

Distance to the spherical centre

R :

Tool radius

R z :

Surface roughness of maximum peak to valley height

sz :

Step size

t 0 :

Initial sheet thickness

V :

Feed rate in friction experiment

α :

Forming angle

α f :

Actual contacting angle

α t :

Actual forming angle after incremental forming

β :

Residual forming angle

σ 0 :

Yield stress

σ tan, σ cir, σ thi :

Normal stresses in tangential, circumferential, and thickness directions, respectively

σ Atan , σ Athi :

Tangential stress and thickness stress at Region A, respectively

σ Btan , σ Bthi :

Tangential stress and thickness stress at Region B, respectively

σ Bthi,r=R :

Contact stress along the thickness direction at Region B

σ xx, σ yy, σ zz :

Normal stresses along the X (rolling direction), Y (transverse direction), and Z (thickness direction) directions, respectively

\({\bar \sigma}\) :

Equivalent stress

φ :

Current forming angle

dϕ :

Increment of tangential length

dθ :

Increment of circumference width

ε B,BS, ε S,BS :

Bending strain and stretching strain in a bending and stretching strain model, respectively

ε B,MBS, ε S,MBS :

Bending strain and stretching strain in MBS, respectively

ε PMmax , ε FMmax :

Max principal strain of partial and full model at specific forming depth of l, respectively

ε p :

Predeformation strain

ε tan, ε cir, ε thi :

Normal strains in the tangential, circumference, and thickness directions, respectively

ε tan,BS :

Tangential strain evolution in BS

ε tan,MBS :

Tangential strain evolution in MBS

ε xx, ε yy, ε zz :

Normal strain along rolling direction, transverse direction and thickness direction, respectively

\({\bar \varepsilon}\) :

Equivalent strain

μ :

Friction coefficient

δ i :

Strain error

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Acknowledgements

The authors thank the support from the National Natural Science Foundation of China (Grant Nos. 51575028 and 51975328), and the Fundamental Research Funds for the Central Universities of China (Grant No. YWF-18-BJ-J-75). Also, the authors thank the suggestions of editors and reviewers.

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Beihang University, Beijing, 100083, China

    Kai Han, Xiaoqiang Li, Peng Xu, Yong Li & Dongsheng Li

  2. Beijing Institute of Aeronautical Materials, Beijing, 100095, China

    Kai Han

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

    Yanle Li

  4. Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, Jinan, 250061, China

    Yanle Li

  5. Materials Science Branch of Chinalco Research Institute, Chinalco Materials Application Research Institute Co., Ltd., Beijing, 102209, China

    Qing Li

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  1. Kai Han
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  2. Xiaoqiang Li
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  3. Yanle Li
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  4. Peng Xu
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  5. Yong Li
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  6. Qing Li
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Correspondence to Yanle Li.

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Han, K., Li, X., Li, Y. et al. Formation mechanism and modeling of surface waviness in incremental sheet forming. Front. Mech. Eng. 17, 23 (2022). https://doi.org/10.1007/s11465-022-0679-1

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  • DOI: https://doi.org/10.1007/s11465-022-0679-1

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