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Spatial variable curvature metallic tube bending springback numerical approximation prediction and compensation method considering cross-section distortion defect

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Abstract

With the advantages of continuous bending, small bending diameter, and variable curvature, the spatial variable curvature (SVC) bent metallic tube (MT) is widely used in the aeronautics industry. Due to the complex characteristics of its central axis, SVC MT bending is prohibitive in terms of modeling and analysis, which results in a rather high calculation complexity. The springback is the primary detection that directly affects the axial forming accuracy. To achieve higher forming accuracy, this paper provides a numerical approximation springback prediction and compensation method considering cross-section distortion for SVC MT. The curvature and torsion mapping function of MT central axis before and after springback is constructed. According to the characteristics of different SVC MT, the differential equations in the SVC springback prediction model are solved by using three numerical approximation methods. The springback compensation method is subsequently obtained by inverse operation of the mapping relationship. To verify the feasibility of the proposed method, a 00Cr17Ni14Mo2 tube is bent with a multi-roll bender into the spiral shape. The results of the three springback numerical approximation methods and the numerical simulation result are compared. It illustrates that the Runge–Kutta method owns the highest prediction accuracy, so that we choose the Runge–Kutta method for bending compensation. The result indicates that the position deviation of each node is less than 1.4% along with the average position deviation of 0.80% after springback compensation.

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Abbreviations

\(n(s)\) :

Unit normal vector

\(a(s)\) :

Unit tangent vector

\(b(s)\) :

Unit binormal vector

\(\kappa (s)\) :

Curvature of the spatial free curve

\(\tau (s)\) :

Torsion of the spatial free curve

\(\rho\) :

Curvature radius

\(\varphi\) :

Torsion angle

\({\lambda }_{b}\) :

Curvature radius mapping relationship function

\({\lambda }_{b}^{-1}\) :

Curvature radius mapping relationship inverse function

\({\lambda }_{t}\) :

Twist angle mapping relationship function

\({\lambda }_{t}^{-1}\) :

Twist angle mapping relationship inverse function

\({\sigma }_{e}\) :

Bending tangential tension compression stress in the elastic region

\({\tau }_{e}\) :

Torsion circumferential shear stress in the elastic region

\({\sigma }_{p}\) :

Bending tangential tension compression stress in the plastic region

\({\tau }_{p}\) :

Torsion circumferential shear stress in the plastic region

\({M}_{e}\) :

Bending moment of the elastic region on the cross-section

\({M}_{p}\) :

Bending moment of the plastic region on the cross-section

\({T}_{e}\) :

Torque of the elastic region on the cross-section

\({T}_{p}\) :

Torque of the plastic region on the cross-section

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Funding

This work has been funded by the Joint Funds of the National Natural Science Foundation of China (U20A20287), the National Natural Science Foundation of China (51905476), and the Key R&D Program of Zhejiang Province (2019C05SAB51751).

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Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 31,000, China

    Zili Wang, Lemiao Qiu, Shuyou Zhang, Dingyu Fang & Le Wang

  2. Zhejiang Province Key Laboratory of Aerospace Metal Tube Forming Technology and Equipment, King-Mazon Co., Ltd., Lishui, 32,000, China

    Zili Wang, Yaochen Lin & Shuyou Zhang

  3. College of Mechanical Engineering, Yangzhou University, Yangzhou, 225,127, China

    Ci He

Authors
  1. Zili Wang
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  2. Yaochen Lin
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  3. Lemiao Qiu
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  4. Shuyou Zhang
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  7. Le Wang
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Correspondence to Lemiao Qiu.

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Wang, Z., Lin, Y., Qiu, L. et al. Spatial variable curvature metallic tube bending springback numerical approximation prediction and compensation method considering cross-section distortion defect. Int J Adv Manuf Technol 118, 1811–1827 (2022). https://doi.org/10.1007/s00170-021-08051-w

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