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Springback behavior and control strategy for dimensional accuracy of hydroformed tubular parts

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Abstract

Hydroformed tubular parts have been widely used in a variety of applications requiring high strength and high dimensional accuracy. However, the essence and strategy for controlling dimensional accuracy of the parts have not been given an in-depth investigation. In this paper, a strategy for compensating the springback of hydroformed tubular parts is proposed to improve their dimensional accuracy. It is believed that the parts have the highest dimensional accuracy when the expansion amount of die cavity is exactly equal to the springback of tubular part by controlling the internal pressure. The theoretical calculation formula of target pressure is firstly derived under the assumption of axisymmetric plane strain without considering the influence of clamping force. The proposed control strategy was then implemented experimentally to validate its feasibility. It is shown that the diameters of SAPH440 tubular parts increase linearly with increasing internal pressure from 60 to 240 MPa. After unloading and removing the tubular parts from die cavity, a certain springback will occur on the parts. When the internal pressure reaches the target pressure of 150 MPa, the diameter of final part is exactly equal to the target value. Moreover, due to the inevitable effect of clamping force in experiments, the target pressure in the experiment is lower than that from theoretical prediction. Finally, it is further proved by repeated experiments that the diameter deviation of tubular parts can be controlled accurately within range of [-0.05 mm, + 0.05 mm]. These results provide theoretical basis and technical support for precision manufacturing of key components for automobile and aerospace.

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Abbreviations

d 0 :

Initial diameter of tube blank

t 0 :

Initial thickness of tube blank

t :

Thickness of tubular part

r :

Radius of tubular part

D :

Diameter of tubular parts (die cavity) under pressurization

D 0 :

Design value of the diameter of die cavity (design value of the diameter of final hydroformed tubular parts)

D 1 :

Diameter of final hydroformed tubular parts

∆D′:

Expansion amount of die cavity

∆D :

Springback of tubular parts

p :

Internal pressure

p′:

Contact pressure between the outer surface of tube blank and the surface of the die cavity

p cr :

Calibration pressure. When \(p={p}_{cr}\), the tube blank is just attached to the die cavity, and the die has no elastic deformation.

\({p}_{cr}^{\mathrm{^{\prime}}}\) :

Target pressure, \({p}_{cr}^{^{\prime}}>{p}_{cr}\). When \(p={p}_{cr}^{^{\prime}}\), the diameter expansion amount of die cavity is equal to the springback of tubular parts.

K :

Strength coefficient of tube blank

n :

Strain hardening exponent of tube blank

σ s, σ b :

Yield strength and tensile strength of tube blank

\({\sigma }_{si}^{\mathrm{^{\prime}}}\) :

Flow stress of tube blank

η max :

Ultimate expansion ratio of tube blank

σ se :

Yield strength of die material

\({\sigma }_{se}^{\mathrm{^{\prime}}}\) :

Flow stress of die material in elastic stage

σ θ, σ r :

Circumferential and radial stresses of tube blank

σ θ d, σ zd, σ rd :

Circumferential, axial and radial stresses of die

C :

Integration constant

r i, r e :

Inside radius and outside radius of tube blank

R :

Radius of die

R i, R e :

Inside radius and outside radius of die if it is equivalent to a thick-walled cylinder

u r :

Elastic displacement of die cavity in radial direction

E :

Elasticity modulus of tube blank

E e :

Elasticity modulus of die material

μ :

Poisson's ratio of die material

∆ε i :

Springback strain of tubular parts after unloading

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Acknowledgements

The authors wish to express their gratitude to the funding supports from the China Postdoctoral Science Foundation (No. 2020M670907), the foundation of National Key Laboratory for Precision Hot Processing of Metals, Harbin Institute of Technology (JCKYS2021603C002), the National Natural Science Foundation of China (No. 51805357), and the Heilongjiang Postdoctoral Fund (No. LBH-Z20017).

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Authors and Affiliations

  1. National Key Laboratory for Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin, 150001, China

    Xiao-Lei Cui, Cong Han, Jiuqiang He & Shijian Yuan

  2. School of Materials Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China

    Xiao-Lei Cui, Cong Han, Jiuqiang He & Wangcheng Xu

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  1. Xiao-Lei Cui
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Cui, XL., Han, C., He, J. et al. Springback behavior and control strategy for dimensional accuracy of hydroformed tubular parts. Int J Mater Form 16, 15 (2023). https://doi.org/10.1007/s12289-023-01736-5

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