Abstract
The parameter solving method for springback control mainly depends on theoretical models and numerical simulation. However, many assumptions are adopted in the theoretical model, which inevitably lead to prediction error in practical application. Therefore, for bending and straightening process, a difference iterative compensation method and secant iterative compensation method based on the implicit equation were proposed. In these methods, the deflection and curvature were taken as the control parameter of iterative compensation, and the convergence of deflection was also verified by theory. According to the proposed iterative compensation strategy, an automatic straightening equipment was developed. On this basis, the bending and straightening of shafts and stretch-bending experiments were carried out to demonstrate the efficiency and reliability of the proposed iterative compensation strategy. The results show that the iterative compensation methods can predict the next compensation value based on the springback value of each tests, so that the target value with the error of less than 2% can be obtained with 2–3 iterations. Moreover, the proposed methods are independent on the material properties and mechanical model, and has high convergence precision for the springback compensation problem.
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Abbreviations
- \( {\overline{\varepsilon}}_1 \),\( {\overline{\varepsilon}}_2 \) :
-
Equivalent strain
- \( {\overline{\varepsilon}}_1^e \),\( {\overline{\varepsilon}}_2^e \) :
-
Springback strain corresponds to \( {\overline{\varepsilon}}_1 \) and \( {\overline{\varepsilon}}_2 \)
- x :
-
Control parameter of iterative compensation
- f(x):
-
Relationship of the parameter before and after springback
- Δx :
-
The value of springback
- x p :
-
Target value of parameter after springback
- φ(x):
-
Implicit iterative function about x
- l t :
-
The length of the elastic region of shaft in bending
- l s :
-
The length of the plastic region of shaft in bending
- R :
-
Radius of shaft
- F :
-
Loading force
- M :
-
Bending moment
- y s :
-
Height from the elastic-plastic boundary point to the geometric center layer of shaft
- β :
-
Ratio of elastic region to plastic region
- K t :
-
Elastic limitation curvature
- M t :
-
Elastic limitation moment
- E :
-
Young’s modulus
- σ s :
-
Initial yield stress
- ε s :
-
Elastic limitation strain
- I z :
-
Moment of inertia of the central section respect to Z-axis.
- K :
-
Curvature of shaft under bending force F
- δ Σ :
-
Deflection before springback
- δ e :
-
Deflection of sprinback
References
Cui F (2002) Straightening theory and straightening machine. Metallurgical Industry Press, Beijing
Zhang Z, Yan Y, Yang H (2013) The straightening curature-radius model for the thin-walled tube and it’s validation. J Mech Eng 49(21):160–167
Ma GS, Tian YQ, Wang HL (2013) Study of load-deflection model of pressure straightening process for thick-walled steel pipe. J Netshape Form Eng 5(01):8–11
Chen ZX, Cheng H, Yang K (2007) A method of the calculation of straightening stroke for automatic precise pressure straightening. J East China Jiao tong U 02:127–130
Li J, Zou HJ, Xiong GL, Wang XM (2005) Research on theoretical model of press straightening process and its experiment (in Chinese). J Mech Strength 27(5):636–639
Lu H, Ling H, Leopold J, Zhang X, Guo C (2009) Improvement on straightness of metal bar based on straightening stroke-deflection model. Sci China Ser E 52(7):1866–1873
Zhao J, Song X, Cao H, Liu J (2014) Principle of multi-point bending one-off straightening process for longitudinally submerged arc welding pipes. J Mech Eng 50(2):92–97
Zhao J, Cao H, Zhan P, Ma R (2012) Pure bending equivalent principle for over-bend straightening and its experimental verification. J Mech Eng 48(8):28–33
Jiang S, He X, Yang D (2006) Straightening technology based on displacement control. J Comput Appl 30(9):2464–2466
Li J, Xiong GL (2007) Study on calculation method of press straightening stroke based on straightening process model. Key Eng Mater 63
Wang K, Wang B, Yang C (2011) Research on the multi-step straightening for the elevator guide rail. Proce Eng 16:459–466
Lu H, Xiong X (2016) Research on straightening process model based on iteration and self-learning. Ind Electron Appl
Kim SC, Chung SC Synthesis of the multi-step straightness control system for shaft straightening processes. Mechatronics 12(1):139–156
Yi JG, Wang ZH, Liu JT, Jiang HY (2007) Study on on-line intelligent measurement and control system of shaft parts' precision straightening machine. Int Con Electron Meas Ins IEEE 2:640–643
Liu JT, Yi JG, Jiang HY, Xing YZ, Wang L (2007) Study of control and measurement system for precision straightening machine. Int Symp Test Meas 1-75:261–5264
Zheng H, Han ZR, Chen J, Wang GD (2010) Experimental investigation on shaft straightening based on laser cladding, in Chinese. J Northeastern U 31(12):1729–1732
Świć A, Draczew A, Gola A (2016) Technology of heat treating-straightening of long shafts with low rigidity. Adv Sci Tech 10(31):207–214
Wang C, Yu G, Wang W, Zhao J (2018) Deflection detection and curve fitting in three-roll continuous straightening process for LSAW pipes. J Mater Process Technol 255:150–160
Cheng HS, Cao J, Xia ZC (2007) An accelerated springback compensation method. Int J Mech Sci 49(3):267–279
Zhang QF, Cai ZY, Zhang Y (2013) Springback compensation method for doubly curved plate in multi-point forming. Mater Design 47:377–385
Weiher J, Rietman B, Kose K (2004) Controlling springback with compensation strategies. AIP Con Proc
Karafillis AP, Boyce MC (1992) Tooling design in sheet metal forming using springback calculations. Int J Mech Sci 34(2):113–131
Karafillis AP, Boyce MC (1996) Tooling and binder design for sheet metal forming processes compensating springback error. Int J Mach Tool Manu 36(4):503–526
Wei G, Wagoner RH (2004) Die design method for sheet springback. Int J Mech Sci 46(7):1097–1113
Lingbeek R, Huétink J, Ohnimus S, Petzoldt M, Weiher J (2005) The development of a finite elements based springback compensation tool for sheet metal products. J Mater Process Tech 169(1):115–125
Nie X, Cheng A, Shen D, Zhong Z (2009) Springback calculation and compensation system based on rail member panel. J Mech Eng 45(7):194–198
Yang X, Ruan F (2011) A die design method for springback compensation based on displacement adjustment. Int J Mech Sci 53(5):399–406
Yang X, Ruan F (2012) Compensation direction for die-face adjustment based on springback compensation. J Jilin U (Eng Tech) 42(1):103–108
Cafuta G, Mole N, Štok B (2012) An enhanced displacement adjustment method: Springback and thinning compensation. Mater Design 40(3):476–487
Liao J, Xue X, Zhou C, Barlat F, Gracio JJ (2013) A springback compensation strategy and applications to bending cases[J]. Steel Res Int 84(5):463–472
Sun S, Liu Y, Li G (2013) The development of high strength steel stamping springback geometry compensation system based on CATIA. J Netshape Form Eng 5(2):1–5
Zhang Z, Wu J, Zang S, Wang M, Guo R, Guo S (2015) A new iterative method for springback control based on theory analysis and displacement adjustment. Int J Mech Sci 105:330–339
Zhang Z, Ma R, Wang C, Zhao J (2019) Research on springback control in stretch bending based on iterative compensation method. Math Probl Eng
Acknowledgements
The present work is financed by the Major projects of national science and technology (No. 2018ZX04007002-004-1), the National Natural Science Foundation of China (No. 52005431), the Natural Science Foundation of Hebei Province (No. E2020203086).
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Mu, Z., Ma, R., Zhao, J. et al. Research on iterative compensation method for springback control based on implicit equation. Int J Mater Form 14, 1097–1108 (2021). https://doi.org/10.1007/s12289-021-01625-9
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DOI: https://doi.org/10.1007/s12289-021-01625-9