A comparative study on the effects of boundary

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Nov 20, 2018 - Xiaoxiang Li1. & Meng Chen1. & Liang Li1 ..... Cui XH, Li JJ, Mo JH, Xiao SJ, Du EH, Zhao J (2011) Numerical simulation of electromagnetic ...
The International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-018-3098-z

ORIGINAL ARTICLE

A comparative study on the effects of boundary constraints on electromagnetic sheet forming Ning Liu 1 & Zhipeng Lai 1 & Quanliang Cao 1 & Xiaotao Han 1 & Yujie Huang 1 & Xiaoxiang Li 1 & Meng Chen 1 & Liang Li 1 Received: 19 July 2018 / Accepted: 20 November 2018 # Springer-Verlag London Ltd., part of Springer Nature 2018

Abstract This paper investigates the effect of boundary constraints on the plastic deformation behavior of a ∅458 circular sheet metal in an electromagnetic forming process. Both experiments and simulations were conducted on a flat spiral coil system. In the experiments, two different boundary conditions were imposed on the workpiece flange by utilizing a blank holder with and without a draw bead to control the draw-in of the flange. Both the final profile and thickness distribution of the workpiece are sensitive to the boundary constraint, due to the varied draw-in material flow. Furthermore, according to the morphology characteristic of the deformation profile, three typical deformation stages can be recognized, where the thickness reduction at the sheet center only occurs in the first and third stages. This work provides a better understanding of the deformation behavior in the electromagnetic sheet-forming process under varied boundary constraints, which is fundamental for the further development of this process. Keywords Electromagnetic sheet forming . Constraint condition . Deformation behavior . Draw-in

1 Introduction In recent years, lightweight material use has become a general trend in various industries due to increasing demands for energy conservation and emission reduction. Aluminum alloys, a type of lightweight material, have long been used in the aerospace, automotive, and electronic fields due to its characteristics of high strength and low density [1]. Unfortunately, the low formability of aluminum alloys at room temperature limits their application to some extent. Electromagnetic forming (EMF), a high-velocity forming process used to shape metallic workpieces with pulsed magnetic pressure, has been recognized as a powerful enabler process for the forming of aluminum alloys due to its advantages of improved formability, actively controlled spring-back, and suppressed wrinkling [2, 3]. Therefore, this technology has been used for forming sheet [4, 5] and tube [6, 7] metal parts for a long time. Over the past few decades, various coil designs and process variations of EMF have been proposed in the field of sheet metal forming. Takatsu et al. [8] performed a sheet-bulging

* Liang Li [email protected] 1

Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, Hubei, China

process using a flat spiral coil and investigated the involved dynamic deformation via both experiments and simulation. They found that nonuniform magnetic pressure leads to an uneven plastic deformation process. To produce a more uniform magnetic pressure by altering the coil configuration, Kamal and Daehn [9] proposed an innovative coil design, namely, a uniform pressure actuator. Compared to a conventional spiral coil, this uniform-pressure coil has the advantages of producing a more uniform magnetic pressure, high-energy efficiency, and mechanical robustness, encouraging applications of this coil for forming, embossing, and welding [10–12]. Considering the processing method, Shang and Daehn [13] proposed a new process called electromagneticassisted sheet metal forming and found that the process is useful for extending the forming capability of the conventional process by improving the forming limit [14], reducing the springback [15], and altering the strain distribution [16]. In addition, some scholars investigated the effect of the processing parameters on electromagnetic sheet metal bulging and analyzed the dynamic deformation behavior during the forming process [17, 18]. While most existing EMF processes allegedly provide a stretching deformation mode, some recent work has highlighted the effect of the material flow of the sheet flange (draw-in) on sheet metal deep drawing. Lai et al. [19, 20] proposed to increase the forming depth by enhancing the draw-in using a

Int J Adv Manuf Technol

dual-coil system and successfully manufactured a deep drawing cup of AA1060-H24 with a drawing ratio of 3.25. Cui et al. [21] combined a radial magnetic pressure with traditional stamping and increased the depth of a cylinder by 31% after applying the forming process three times. By using the electromagnetic pulse-assisted incremental drawing method, Fang et al. [22] increased the drawing depth by 21.8%, 36.7%, and 141.6% under different conditions. Ma et al. [23] investigated the influence of the blank-holder force and lubricant on the sheet dome height and strain distribution. Lai et al. [24] developed a lightweight EMF process to shape a ∅1378-mm sheet metal part using a one-time forming process. Their results showed that the drawing deformation mode plays an important role in the electromagnetic sheet-forming process. However, the mechanism of the effect of the draw-in on the deformation behavior of a large sheet and the dynamic forming process of the workpiece requires further investigation. Accordingly, to better understand the mechanism of this effect, this paper presents a detailed study on the effect of boundary constraints on the deformation behavior of a ∅458 circular sheet workpiece. The experiments were carried out based on a flat spiral coil system, and two constraint conditions were imposed on the sheet flange to induce different amounts of draw-in material flow. The underlying mechanism of the effect of the draw-in on the electromagnetic sheetforming process was revealed by simulations.

2 Experiment 2.1 Experimental setup Figure 1 shows the assembly of the experimental setup, which consists of a forming coil, blank holders, and a die. A circular sheet metal workpiece is placed on top of the die and beneath the coil. The initial gap between the coil and workpiece is 10 mm. The workpiece is made from annealed aluminum alloy AA1060 with a thickness of 1.5 mm and a diameter of 458 mm. The central 398-mm diameter region of the workpiece is not clamped. Figure 2 shows the detailed structural Fig. 1 Assembly of the experimental setup

dimensions of the forming coil. The forming coil has one layer with 60 turn windings, and the inner and outer radii of the coil are 30 and 145 mm, respectively. The cross-section of the copper conductor is 1.5 × 16 mm. A high-strength material (Zylon) is used to improve the structural strength of the coil. Figure 3a shows photos of the die and the blank holders. The detailed dimensions of the draw bead and the draw groove are shown in Fig. 3b. In the experiments, the draw bead is used to restrict the material flow of the sheet flange. The capacitor bank system used in the experiments contains two capacitors, each of 160 μF, and the maximum discharge energy is 100 kJ, with a discharge voltage of 25 kV.

2.2 Experimental conditions Two boundary constraints were imposed on the workpiece flange in the experiments. The experiments were performed under a 10.24-kJ energy, and the detailed experimental conditions are listed in Table 1.

2.3 Experiment measurements The discharge current flowing through the coil was measured by a Rogowski coil and then used as the excitation for the simulation model to calculate the produced electromagnetic force and sheet deformation. The profiles of the deformed workpiece were measured by a three-dimensional scanner. The thickness distribution along the radial direction was measured with an interval of 5 mm using a Vernier caliper to evaluate the thickness reduction of the workpiece. The drawin of the sheet flange was determined by measuring four evenly distributed diameters around the circumference.

3 Numerical model To better understand the dynamic process, an electromagneticmechanical-coupled numerical model was established via LSDYNA.

Int J Adv Manuf Technol Fig. 2 Detailed structure of the forming coil

3.1 Flowchart of the simulation model Figure 4 shows a flowchart of the electromagneticmechanical-coupled model. When the electromagnetic model has been executed, the calculated Lorentz force will be imported into the mechanical model. Then, the mechanical model will calculate the sheet deformation and return the new geometric parameters of the workpiece to calculate the electromagnetic field in the next electromagnetic step by updating the boundary element matrices. In this manner, the coupling of the two fields is achieved.

avoids the nondivergence problem caused by air mesh distortion. In the electromagnetic model, the current is considered uniform in the circuit. This is useful to save computational time in cases with relatively low-frequency currents. Figure 5 shows the excitation discharge current in the electromagnetic model, which was measured in Exp. 1. The equiva1 , and the result is lent frequency is simply calculated as 4T approximately equal to 0.5 kHz, where T is the time when the current reaches its peak value. The frequency satisfies the condition of the low-frequency approximation mentioned above. Table 2 lists the detailed parameters used in the electromagnetic model.

3.2 Electromagnetic model 3.3 Mechanical model The electromagnetic model is realized by using a hybrid of the finite element method (FEM) and boundary element method (BEM). Therefore, the model does not require air meshes. This strategy saves time by not computing air meshes and

Figure 6 shows the mechanical model. In the model, the coil and die are considered a rigid body. The workpiece is regarded as an isotropic-plasticity body with rate effects

Fig. 3 Die and blank-holders: a photos of the die and the blank holders; b detailed dimensions of the draw groove and draw bead

Int J Adv Manuf Technol Table 1

Experimental conditions

Experiment

Blank holder

Blank holder force

Discharge voltage

Exp. 1

With draw bead

100 kN

10 kV

Exp. 2

Without draw bead

5 kN

10 kV

Exp. 1: A large blank holder force acting on the blank holder with a draw bead to restrict the material flow in the sheet flange. The corresponding simulation is defined as Sim. 1. Exp. 2: For comparison, sheet forming was performed using a blank holder without a draw bead and a small blank holder force. On the one hand, a flat blank holder and a small blank holder force can allow sufficient material flow in the sheet flange. On the other hand, the blank holder force can prevent wrinkling in the deformation process. The corresponding simulation is defined as Sim. 2.

Fig. 5 Coil current measured in the experiment

defined as surface-to-surface contacts, and the workpiece is defined as the master surface; other forming tools are defined as slave surfaces. The friction coefficients of the contact interfaces are 0.15. The detailed parameters used in the mechanical model are shown in Table 3.

that use the power law hardening rule. The quasi-static stress-strain curve of AA1060 is obtained in the material storage of LS-DYNA, and the expression is described by: σqs ¼ 125:3*ε0:25

ð1Þ

where σqs is the quasi-static stress and ε is the plastic strain. To reflect the influence of a high-strain rate on the mechanical properties of the sheet metal workpiece, the Cowper-Symonds constitutive model was used to solve for the sheet deformation [25],   • m  εp ð2Þ σ ¼ σqs 1 þ P

4 Results and discussion 4.1 Deformation morphology 4.1.1 Deformation profile Figure 7 compares the deformed sheets under two boundary constraints. Figure7a presents the formed workpiece from Exp. 1, and Fig. 7b presents the formed workpiece from Exp. 2. To observe the profiles of the workpiece more clearly, the workpieces were cut in half along a path across the center. The dome heights of the workpieces formed in Exp. 1 and Exp. 2 are 88 and 95 mm, respectively, where the introduction of the draw-bead induces a 7.4% lower dome height. Figure 8 further compares the deformation profiles of the two formed workpieces. Both the simulation results and

where σqs is the quasi-static stress in Eq. (1), εp • is the plastic strain rate, and P and m are 6500 s−1 and 0.25 for aluminum, respectively. To simplify the simulation model using a blank holder with a draw bead, the nodes of the elements in the sheet flange are defined as fixed constraints. The coil and the workpiece are modeled using eight-node hexahedral solid elements, and the blank holder and die are modeled using shell elements. The contacts between the workpiece and the forming tools are Fig. 4 Flowchart of the implemented algorithm

Establish the electromagnetic model and the mechanical model via LS-DYNA

EM Model

T=t0+Ƹt

Recalculate boundary element matrices

Lorentz force

Yes No End

T