A study on a deep-drawing process with two shaping states for a fuel-filter cup using combined simulation and experiment

Abstract

In this article, a deep-drawing process using a double-action hydraulic press is examined for its ability to machine the shaping deformation of a fuel-filter cup made from SPCC steel. Many researchers have studied the geometric, physical, and technological parameters of the deep-drawing process. However, most of those studies ignored the optimization parameters of the two shaping deformation states to ensure uniformity of thickness and the disappearance of wrinkling and tearing during machining. In this study, geometric and technological parameters (e.g. blank-holder force, die-shoulder radius, and radial clearance between punch and die) are optimized in both states. The deep-drawing process for a fuel-filter cup is simulated using ABAQUS software, and optimal parameters are determined by applying the Taguchi orthogonal array computation and combining it with an analysis of variance method. The numerical results are then verified with corresponding experiments. The obtained numerical and experimental results show that the die-shoulder radius is one of the most influential parameters affecting the shaping of the cup during the deep-drawing process. Moreover, the influences of technological parameters on the formability of sheet metal are finally analyzed and selected for designing and improving deep-drawing molds.

Keywords

Fuel-filter cup deep-drawing process optimal parameters double-action hydraulic press two shaping states

Introduction

Fuel-filter cups on cars and trucks are used to remove impurities from oil before returning it to the engine for lubrication and cooling. These cups are formed using a double-action hydraulic press with a deep-drawing process. Sometimes during this process, cups suffer wrinkling, tearing, and uneven thicknesses. To avoid these defects, fuel-filter cups are machined through two deformation states. Optimal parameters for the deep-drawing process are essential for improving cup quality. Padmanabhan et al.¹ sought to optimize sheet-metal forming using the finite element method (FEM) with the Taguchi orthogonal array. The die-shoulder radius, blank-holder force (BHF), and characteristic friction coefficient of a deep-drawn cup made of stainless steel were used to reduce production costs. Raju et al.² researched the influence of technological and geometric parameters of the deep-drawing process for cups made of sheet material AA6061. The Taguchi orthogonal array was used to determine the BHF, the shoulder radius of the die, and the nose radius of the punch. Singh et al.³ discovered the effectiveness of deep-drawing parameters (e.g. shoulder radius of die, nose radius of punch, coefficient of friction, and rate of deep drawing) based on the Gen algorithm with the cylindrical shaping process. Wifi and Mosallam⁴ researched the FEM-based assessment of performance for some non-conventional blank-holding techniques. A three-dimensional (3D) explicit-FEM was used to investigate the influence of various BHF on sheet-metal formability limits (viz. wrinkling and tearing). Aleksandrovic and Stefanovic⁵ used the BHF to control the friction on the blank holder during the deep-drawing process. Their cup was made of low-carbon steel sheet using three friction regimes (i.e. dry, oil, and polyethylene terephthalate foil). Reddy et al.⁶ and Gharib et al.⁷ developed optimizing coefficients for the deep-drawing process to determine BHF and minimize the drawing force. It was achieved without defects. Atrian and Fereshteh⁸ examined the effects of various deep-drawing process factors for steel and brass workpieces. FEMs were constructed and tested to show the tearing position on a cup. Sheng et al.⁹ studied the formation of tearing and wrinkling as two main failures in the deep-drawing process. Simulation and experimental models were built and compared to improve the process.

The proposed model has been successfully applied to two cone-drawing processes. Sherbiny et al.¹⁰ developed a FEM to simulate the deep-drawing processes for 3D sheet metal using ABAQUS/EXPLICIT FEM analysis software with appropriate material properties and boundary conditions. The development model of reverse elasticity prediction and distribution of thickness of the sheet metal were affected by the parameters of the deep-drawing process, including geometric and physical parameters. Nguyen et al.^11–15 performed FEM simulations to investigate the influence of technological and geometric parameters on the deformation of various products to improve the formability of materials.

In this study, FEM and experimental models are constructed for the deep-drawing process of a fuel-filter cup. Numerical simulations using the Taguchi orthogonal computation and analysis of variance (ANOVA) methods are used to determine the optimal parameters. Then, the optimal geometric and technological parameters are applied to ensure uniformity of thickness without the tearing and wrinkling phenomena. Numerical and experimental results show that cup defects are significantly reduced with the proposed method.

Geometric model and material of the fuel-filter cup

Geometric model

The fuel-filter cup is usually used in cars to filter out dregs and rust in fuel and create clean fuel for engines. The shape and size of fuel-filter cups are shown in Figure 1. The shaped surface is required to be absent wrinkling, tearing, or scratching. The normal thickness of the fuel-filter cup is 0.6 mm, and the variation of thickness should not exceed 0.1 mm with the deep-drawing process. The 3D model of the cup is used to design a deep-drawing mold using ABAQUS software. In Figure 1, $d_{3}$ is the diameter of the outer rim of the cup, $d_{2}$ is the inner diameter, $d_{1}$ is the bottom diameter, $r$ is the bottom radius, $h_{1}$ is the height of the curved bottom, $h_{2}$ is the depth, and $t$ is the thickness.

Figure 1.

The size and shape for 3D model of fuel-filter cup.

Material

The fuel-filter cup is made from SPCC sheet steel (JIS G3141), having a thickness of 0.6 mm. The mechanical properties of the steel (i.e. directional tensile strength and material response curve) are used in the FEM simulation, as shown in Table 1. The flow-stress curve of SPCC sheet steel is defined with equation (1)

\bar{σ} = K . {(ε_{eq}^{pl})}^{n}

(1)

where K is the plasticity coefficient, $n$ is the hardening exponent, $\bar{σ}$ is the stress value, and $ε_{eq}^{pl}$ is the deformation value.

Table 1.

Properties of the SPCC sheet steel (JIS G3141).¹⁵

Properties	Values
Materials	SPCC
Rolling direction	0°	45°	90°
Yield stress (MPa)	166	173	175
Anisotropic coefficient $(r)$	1.78	1.64	1.93
Plasticity coefficient $K$ (MPa)	422	436	441
Hardening exponent $n$ value	0.274	0.290	0.293
Density ( $ρ$ , kg/mm³)	7.8e-06
Elastic modulus ( $E$ , kN/mm²)	210
Poisson ratio $(μ)$	0.3

Deep-drawing process of the double-action hydraulic press

FEM model

In this study, the deep-drawing process of shaping the fuel-filter cup is simulated with ABAQUS software.¹⁶ The 3D FEM model for the deep-drawing process is shown in Figure 2, wherein the punch is fixed, and a blank holder and die are moved in the vertical direction to achieve the size of the shaped cup via two deformation states. Rigid models are used to analyze the punch, blank holder, and die, and their displacements are represented with reference points. The blank is modeled using deformable elements and a shell model of S4R-reduced integration.

Figure 2.

The 3D model of FEM in ABAQUS software.

To express the anisotropic behavior of the material, elastic and plastic deformations of SPCC sheet steel were simulated based on the Hill’48 productivity criteria.¹⁷ The Hill’48 classic-yield surface function is the most prominent and frequently used yield function to account for the plastic anisotropy of steel materials, mainly because of its simple handling in manual and numerical calculations. It is a simple extension of the isotropic von Mises function, which can be expressed in terms of rectangular Cartesian stress components, as used in equation (2)

\begin{matrix} {(f (σ))}^{2} & = F {(σ_{yy} - σ_{zz})}^{2} + G {(σ_{zz} - σ_{xx})}^{2} \\ + H {(σ_{xx} - σ_{yy})}^{2} + 2 L {(σ_{yz})}^{2} \\ + 2 M {(σ_{zx})}^{2} + 2 N {(σ_{xy})}^{2} \end{matrix}

(2)

where x, y, and z are the rolling direction (RD), transverse direction, and normal direction, respectively. F, G, H, and N are the current state parameters of anisotropy obtained by different material tests. They are defined by equation (3)

{\begin{matrix} F = \frac{1}{2 R_{22}^{2}} + \frac{1}{2 R_{33}^{2}} - \frac{1}{2 R_{11}^{2}} \\ G = \frac{1}{2 R_{11}^{2}} + \frac{1}{2 R_{33}^{2}} - \frac{1}{2 R_{22}^{2}} \\ H = \frac{1}{2 R_{11}^{2}} + \frac{1}{2 R_{22}^{2}} - \frac{1}{2 R_{33}^{2}} \\ L = \frac{3}{2 R_{23}^{2}}, M = \frac{3}{2 R_{13}^{2}}, N = \frac{3}{2 R_{12}^{2}} \end{matrix}

(3)

where $R_{11}$ , $R_{22}$ , $R_{33}$ , $R_{12}$ , $R_{13}$ , and $R_{23}$ are anisotropic yield-stress ratios. For plane-stress cases, only four yield-stress ratios are needed. Here, we assume that the RD is a user-defined reference yield stress. Thus, $R_{11} = 1$ and $R_{22}$ , $R_{33}$ , $R_{12}$ are defined as 1.0143, 1.2026, and 1.0068, respectively, following equation (4). This equation is imported into the material model to investigate the tearing phenomenon via FEM simulation

{\begin{matrix} R_{22} = \sqrt{\frac{r_{90} (r_{0} + 1)}{r_{0} (r_{90} + 1)}} \\ R_{33} = \sqrt{\frac{r_{90} (r_{0} + 1)}{(r_{0} + r_{90})}} \\ R_{12} = \sqrt{\frac{3 (r_{0} + 1) r_{90}}{(2 r_{45} + 1) (r_{0} + r_{90})}} \end{matrix}

(4)

Parameter determination for deep-drawing process

The deep-drawing mold-design parameters are classified into two categories. The first category refers to the geometrical parameters used to design the mold. The second refers to the physical and technological parameters used during the deep-drawing process.

Design geometric-parameter determination of the fuel-filter cup molds

To design fuel-filter cup molds, geometrical parameters should be recognized, as shown in Figure 3, where $r_{d}$ is the die-shoulder radius, $r_{p}$ is the punch-nose radius, $t$ is the blank thickness, and $w_{c}$ is the radial clearance between punch and die. Figure 4 presents the deep-drawing model for two continuous deformation states on the double-action hydraulic press. The geometric parameters of molds can be referenced in Table 2.

Figure 3.

General geometric parameters of the cup molds.

Figure 4.

Deformation state model on the double-action hydraulic press machine.

Table 2.

Quoted parameters.¹⁰

Die-shoulder radius $(r_{d})$	$r_{d} = (6 - 10) t$	For first draw
Punch nose radius $(r_{p})$	$r_{p} = (3 - 4) t$	For $6.3 \leq d_{p} < 100 mm$
	$r_{p} = (4 - 5) t$	For $100 \leq d_{p} < 200 mm$
	$r_{p} = (5 - 7) t$	For $200 mm \leq d_{p}$
Radial clearance $(w_{c})$	$w_{c} = (1.75 - 2.25) t$	For steel, deep drawing

Before starting the deep-drawing process, the size and shape of the workpiece must be identified for mold design. From the requirements of cup shape and size, as shown in Figure 1, the diameter of the blank is determined. To calculate the blank diameter, the entire symmetrical part of the cup must be divided into different individual symmetry axis components. Then, its surface areas are calculated. The diameter of the original blank can be determined using equations (5) and (6)¹⁸

A_{z} = π [\frac{d_{1}^{2}}{2} + 2 r h_{1} + d_{2} (h_{2} - h_{1}) + \frac{d_{3}^{2}}{4}]

(5)

D = 1.13 \sqrt{A_{z}}

(6)

where $A_{z}$ is the surface area (Figure 1), and $D$ is the diameter of the original blank. During the drawing process, a cylindrical cup requires identification via drawing steps by determining the proportion, $β$ , between the diameters of the original blank to the diameter of the drawn part, as shown in equations (7)–(10)¹⁸

β = \frac{Blank - \emptyset D}{Punch - \emptyset d}

(7)

β = \frac{D}{d} with one drawing

(8)

β_{1} = \frac{D}{d_{f}} for the first drawing

(9)

β_{n} = \frac{d_{n - 1}}{d_{n}} for the next drawing

(10)

The total deep-drawing factor is calculated using the ratio between the diameters of the original blank and the final diameter of the deep-drawing process, as shown as equation (11)

β_{tot} = \frac{Initial - \emptyset D}{Final - \emptyset d}

(11)

With several deep-drawing steps, the total draw factor becomes a product of the individual draw ratios of equation (12)

β_{tot} = β_{1} \cdot β_{2} \cdot \dots \cdot β_{n}

(12)

The maximum height can be achieved from the size of the original blank using an approximate calculation, where the thickness of the drawing cup equals the thickness of the blank, and the radius of curvature of the punch can be ignored. The height of the filter cup for the first deformation state can be defined with equation (13)¹⁹

h_{f} = \frac{D^{2} - d_{f}^{2}}{4 d_{f}}

(13)

where $h_{f}$ is the height of the cup in the first deformed state, $D$ is blank diameter, and $d_{f}$ is the mean diameter of the cup in the first deformed state. The height of the cup at the nth drawing step is calculated as equation (14)

h_{n} = \frac{t (D^{2} - d_{n}^{2})}{4 d_{n} t_{n}}

(14)

Obviously, $d_{n}$ is the mean diameter of the deformed state after $n$ -redraw and $t_{n}$ is the thickness of the wall then, while $t$ is the original thickness of the blank.

Physical and technological parameter determination

To determine the physical and technological parameters used in the deep-drawing process, Figure 5 can be used, where $(A)$ is the friction area between the sheet-metal blank/holder and sheet-metal blank die. $(B)$ is the friction area between the sheet-metal blank and die radius, and $(C)$ is the friction area between the sheet-metal blank and punch edges. $(F_{tot})$ is the deep-drawing force, and $(F_{BH})$ is the BHF.²⁰ When the punch moves deeper, heavy friction occurs at the corner radius of the cup, causing tearing (see area C in Figure 5). Friction in the field of plastic deformation is normally explained by the contact relationship of sheet metal with the blank holder and die-shoulder radius (see areas $A$ and $B$ in Figure 5). In this study, we assume that the coefficient of friction between the punch and the blank is $μ_{p} = 0.25$ , that between the blank holder and the blank is $μ_{h} = 0.125 - 0.2$ , and that between the die and blank is $μ_{d} = 0.125 - 0.2$ .²⁰

Figure 5.

Friction areas when deep drawing a cup.

With deep drawing, tearing defects are caused by uncontrolled deep forces (equation (15)) that cannot be transmitted to the bottom of the cup²⁰

F_{tot} \leq aUTS π d_{p} t

(15)

where $a$ , $UTS$ , $d_{p},$ and $t$ are the correction factor for steel from 1:05 to 1:55, the tensile strength of the sheet metal (MPa), the diameter of the punch (mm), and the sheet-metal thickness (mm), respectively. The BHF $(F_{BH})$ is determined using experimental and simulation processes when wrinkling and tearing occurs (equation (16)). Figure 6 shows the limit of the BHF²¹

F_{BH - Wrinking} < F_{BH} < F_{BH - Tearing}

(16)

Figure 6.

Work domain of blank-holder force in deep drawing.

Numerical simulation and experimental results

Numerical simulation

In this study, a FEM simulation was conducted and verified using a Hyundai design fuel-filter cup and the general parameters shown in Figure 1. $d_{1} = 34 mm, d_{2} = 108 mm, d_{3} = 120 mm, h_{1} = 15 mm, h_{2} = 160 mm, r = 100 mm, and t = 0.6 mm$ . By substituting these values into equations (6)–(8), we obtain $β_{tot} = 2.78$ . Thus, the number of drawing strokes can be divided into three drawing periods for the conventional forming method. However, the double-action hydraulic press was used. Thus, the change of drawing force, BHF, drawing speed, and punching stroke was very convenient and accurate. However, the mold was designed and machined for the deep-drawing process using two states of continuous deformation. The deformed states can be used to calculate diameters and height as equations (8)–(13) as $2.78 = β_{tot} = β_{1} \cdot β_{2} < 2.1 \cdot 1.35, d_{f} = 144, d_{s} = 108 mm (before mentioned)$ with $β_{2} = 144 mm / 108 mm = 1.33$ , and $h_{f} = 118 mm$ .

Based on calculated technological, geometric, and physical parameters, the preliminary data sheet of the deep-drawing mold used to determine the region of the BHF by means of FEM simulation and experiment is expressed in Table 3.

Table 3.

Geometric, technological, and physical parameters of the deep-drawing mold.

Parameters	Values
Blank diameter $(D)$	302 mm
Blank thickness $(t)$	0.6 mm
Diameter of the first punch $(d_{f})$	144 mm
Shoulder radius of the first die $(r_{df})$	3 mm
Nose radius of the first punch $(r_{pf})$	5 mm
Diameter of the first die $(D_{f})$	146 mm
Diameter of the second punch $(d_{s})$	108 mm
Shoulder radius of the second die $(r_{ds})$	3 mm
Diameter of the second die $(D_{s})$	109.8 mm
Radial clearance between the first punch and die $(w_{f})$	1.0 mm
Radial clearance between the second punch and die $(w_{s})$	0.9 mm
Cup height of the first deep drawing $(h_{f})$	118 mm
Cup height of the second drawing $(h_{s})$	160 mm
Friction coefficient of punch and blank $(μ_{p})$	0.25
Friction coefficient of blank holder and blank $(μ_{h})$	0.125
Friction coefficient of die and blank $(μ_{d})$	0.125

By using the FEM to simulate as the setting parameters, Figures 7 and 8 depict the deformed shapes of wrinkling and tearing phenomena when changing the BHF $(F_{BH})$ . Based on FEM simulation results and the limited region of the BHF to prevent wrinkling, tearing on the cup, the BHF should be smaller than forming force $(F_{BH} < F_{tot})$ . For the first deformed state, when the BHFs are 9 and 13 tons, then the wrinkling and tearing will occur (Figure 7(a) and (b)), respectively. Figure 8 shows the BHFs as wrinkling and tearing occurrence are 6 and 10 tons for the second deformed state, respectively. So, BHF must be arranged between wrinkling and tearing value to avoid that phenomenon.

Figure 7.

Limited domain of blank-holder force (F_BH) between wrinkling and tearing occurrence in the FE simulation in the first deformed state: (a) F_BH = 9 tons (wrinkling) and (b) F_BH = 13 tons (tearing).

Figure 8.

Limited domain of blank-holder force $(F_{BH})$ between wrinkling and tearing in the FE simulation in the second deformed state: (a) F_BH = 6 tons (wrinkling) and (b) F_BH = 10 tons (tearing).

Experimental results

The deep-drawing process of the fuel-filter cup was performed on the double-action hydraulic press at the maximum load capacity of 50 tons. Market oils were used as lubricant.¹⁹ The experimental setup is shown in Figure 9. To confirm the accuracy of FEM results, corresponding experiments were conducted, as shown in Figure 10. The results showed good agreement between numerical simulation and experimental results.

Figure 9.

The double-action hydraulic press and deep-drawing mold.

Figure 10.

Typical wrinkling (a) and tearing (b) occurrence on the surface of the fuel-filter cup.

Parameter optimization

To improve the formability of the product, the deep-drawing process of the first deformation stage was performed as shown in Figure 11(a). During this stage, wrinkling at the top of the cup and uneven thicknesses occurred. Therefore, the measurement of 10 points on the wall angle of the cup was adopted, as shown in Table 4. Figure 11(b) shows experiments and corresponding FEM simulation results along the cross-section. The average thickness distribution from the FEM simulation was near the average thickness obtained from the corresponding experimental result. The difference between the average measured results on the FEM and experiment was lower than 1.6%. From the comparison data of the FEM and the corresponding experimental results, an optimal process is needed to obtain the uneven thickness values of the cup wall after deep drawing in the first deformation stage to prevent tearing during the second stage.

Figure 11.

The location of the filter cup thickness at the first stage with original design by (a) experiment and (b) simulation.

Table 4.

Comparison between experimental results and FEM predictions for wall thickness.

Thickness measurement points (mm)	Experiment	FEM
1	0.814	0.8067
2	0.703	0.7261
3	0.638	0.6578
4	0.575	0.6040
5	0.549	0.5585
6	0.508	0.5260
7	0.511	0.5172
8	0.568	0.5626
9	0.581	0.5802
10	0.582	0.5818
Average	0.6029	0.6121

FEM: finite element method.

There are various parameters effected during wrinkling and tearing, such as BHF, radial clearance between die and punch, die/punch shoulder radius, and so on. If those conditions change, the stress and strain of the cup will also change, leading to changing thickness of the sheet and the ductile fracture forming-limit diagram failure criterion (FLDCRT) in the FEM simulation. Thus, in the current study, the influence of the BHF (F_BH), die-shoulder radius (r_d), and radial clearance between die and punch (w_c) on the formability of product was evaluated. The BHF was determined using the limitations between wrinkling and tearing. Table 5 lists the levels of the selected parameters. Using the Taguchi method²² and an orthogonal array, L9 was used for experimental design planning. Using the Taguchi orthogonal algorithm reduced the number of experimental designs from 27 to 9 cases, as shown in Table 6. Table 7 and Figure 12 present the measured thickness results of 10 points along the wall angle of the product via FEM simulation, according to the Taguchi orthogonal algorithm (i.e. L9).

Table 5.

The selected parameters and their level of simulation in the first deformation stage.

Factor	Level
	1	2	3
A (F_BH) (kN)	100	110	120
B (r_df) (mm)	4	5	6
C (w_f) (mm)	1	1.1	1.2

Table 6.

L9 orthogonal array for FE simulations.

Case	Factor
	A (F_BH)(kN)	B (r_df)(mm)	C (w_f)(mm)
1	1 (100)	1 (4)	1 (1.0)
2	1 (100)	2 (5)	2 (1.1)
3	1 (100)	3 (6)	3 (1.2)
4	2 (110)	1 (4)	2 (1.1)
5	2 (110)	2 (5)	3 (1.2)
6	2 (110)	3 (6)	1 (1.0)
7	3 (120)	1 (4)	3 (1.2)
8	3 (120)	2 (5)	1 (1.0)
9	3 (120)	3 (6)	2 (1.1)

FEM: finite element.

Table 7.

The results of the distribution of wall thickness in FE simulation.

Measured thickness (mm)at locations	Taguchi L9
	L1	L2	L3	L4	L5	L6	L7	L8	L9
1	0.8126	0.8100	0.8187	0.8307	0.8046	0.8046	0.8143	0.8067	0.8144
2	0.7097	0.7255	0.7422	0.7272	0.7184	0.7184	0.7221	0.7261	0.7380
3	0.6433	0.6578	0.6696	0.6468	0.6571	0.6571	0.6375	0.6578	0.6689
4	0.5892	0.6090	0.6120	0.5858	0.6128	0.6128	0.5754	0.6040	0.6157
5	0.5503	0.5692	0.5694	0.5471	0.5688	0.5688	0.5440	0.5585	0.5807
6	0.5245	0.5349	0.5391	0.5064	0.5311	0.5311	0.5077	0.5260	0.5460
7	0.5096	0.5242	0.5284	0.5083	0.5158	0.5158	0.5045	0.5172	0.5259
8	0.5640	0.5643	0.5626	0.5642	0.5621	0.5621	0.5630	0.5626	0.5592
9	0.5814	0.5814	0.5815	0.5811	0.5799	0.5799	0.5801	0.5802	0.5815
10	0.5836	0.5834	0.5841	0.5827	0.5815	0.5815	0.5819	0.5818	0.5833
Average	0.6068	0.6160	0.6208	0.6080	0.6132	0.6132	0.6030	0.6121	0.6214

FEM: finite element.

Figure 12.

Thickness distribution of wall angle from FEM simulation.

From the wall-angle thickness measurements of the FEM (Table 7 and Figure 12), the thinness position occurred at point 7, where the cup thickness was 0.5045 mm, 15.92% thinner than the original (case no. 7). Otherwise, case no. 3 of the FEM simulation had the smallest thickness (0.5284 mm), 11.93% thinner. Thus, case L3 (A1B3C3) with BHF (F_BH₁) = 100 kN, die-shoulder radius (r_df) = 6 mm, and radial clearance between die and punch (w_f) = 1.2 mm were chosen for the first deformation stage.

In the fuel-filter cup deep-drawing process, thin variations in the wall-angle and tearing often occurred during the second deformation stage. The Taguchi orthogonal array was carried out via simulation for each case based on the levels of the selected parameters (Table 8). The FEM simulation results are shown in Table 9, indicating the FLDCRT of the final shape. If FLDCRT > 1, a fracture will occur. According to the Taguchi method, the bigger the FLDCRT, the better the formability of the final product. Then, the signal-to-noise ratio is determined with equation (17). As shown in Table 9, The phenomenon of ductile fracturing during simulation occurred for cases 1, 4, 7, and 8, where the FLDCRT value was greater than one unit

η_{i} (dB) = - 10 lo g_{10} (FLDCR T^{2})

(17)

Table 8.

The selected parameters and their level of simulation in the second stage.

Factor	Level
	1	2	3
D (F_BH₂) (kN)	70	80	90
E (r_ds) (mm)	4	5	6
F (w_s) (mm)	1	1.1	1.2

Table 9.

Simulation results by Taguchi orthogonal array.

Case	Column number and factor assignment			FLDCRT
	D $(F_{BH 2})$ (kN)	E $(r_{ds})$ (mm)	F $(w_{s})$ (mm)	Value	$η_{i}$ (dB)
1	1 (70)	1 (4)	1 (1.0)	1.172	−1.3786
2	1 (70)	2 (5)	2 (1.1)	0.7966	1.9752
3	1 (70)	3 (6)	3 (1.2)	0.7616	2.3655
4	2 (80)	1 (4)	2 (1.1)	1.062	−0.5225
5	2 (80)	2 (5)	3 (1.2)	0.9077	0.8412
6	2 (80)	3 (6)	1 (1.0)	0.8288	1.6310
7	3 (90)	1 (4)	3 (1.2)	2.116	−6.5103
8	3 (90)	2 (5)	1 (1.0)	1.307	−2.3255
9	3 (90)	3 (6)	2 (1.1)	0.8606	1.3040

FLDCRT: forming-limit diagram failure criterion.

As part of the Taguchi method,²¹ ANOVA was used to describe the relationship between the parameters and the observed values of the FLDCRT. Table 10 summarizes the calculated results of equations (18) and (19)

3 {(m_{j 1} - m)}^{2} + 3 {(m_{j 2} - m)}^{2} + 3 {(m_{j 3} - m)}^{2}

(18)

where

m = (\frac{1}{9}) \sum_{i = 1}^{9} η_{i} = - 0.291

and

m_{ij} = (\frac{1}{3}) \sum_{i = 1}^{3} (η_{j})_{i}

(19)

Table 10.

Results obtained after calculation.

Factor	Average $η_{j}$ by level			Sum of squares	Contribution
	1	2	3
D (F_BH₂) (kN)	1.278^a	0.941	−2.219	22.339	36.4
E $(r_{ds})$ (mm)	−2.513	0.455	2.058^a	32.266	52.5
F $(w_{s})$ (mm)	−0.400	1.210^a	−0.810	6.841	11.1
Total				61.446

Indicates the optimal level.

The results ANOVA, shown in Table 10, support that the die-shoulder radius, r_d, was the most influential for shaping at 52.5%. The influence of BHF (F_BH) and the radial clearance between the punch and die were 36.4% and 11.1%, respectively. Thus, the die-shoulder radius was the most important factor of the formability of the final product after FEM simulation.

Via the combination of FEM simulations and Taguchi orthogonal arrays, the influence of component parameters on the formability of the final shape was analyzed for the second deformation stage. The selected parameters, D₁E₃F₂ (BHF (F) of 70 kN, die-shoulder radius (r_ds) of 6 mm, radial clearance between punch and die (w_s) of 1.1 mm, respectively) should be used for the deep-drawing process at the second deforming stage. To validate the FEM simulation result, the experiment was set up with a double-action hydraulic press of 500 kN and a punch speed of 1 mm/s. Table 11 and Figure 13 show the dimensions and geometrical parameters of the injection molds, respectively. Optimal result of FEM simulation and corresponding experiment are also presented in Figure 14, showing good agreement.

Table 11.

The geometric parameters of the mold set are optimized.

Blank	Blank diameter	302 mm
Blank	Blank thickness	0.6 mm
The first punch	Radius of the first punch	72 mm
The first punch	Nose radius of the first punch	5 mm
The first die	Radius of the first die	73.2 mm
	Shoulder radius of the first die	6 mm
	Radial clearance among the first punch and die	1.2 mm
The second punch	Nose radius of the second punch	54 mm
The second die	Radius of the second die	55.1 mm
	Shoulder radius of the second die	6 mm
	Radial clearance among he second punch and die	1.1 mm
The first blank holder	Outside radius	155 mm
The first blank holder	Inside radius	74 mm
The second blank holder	Outside radius	72 mm
The second blank holder	Inside radius	56 mm

Figure 13.

The composition of the mold after improving by FEM: (a) Blank holder, (b) the first punch, (c) the second punch, and (d) die for first and second stages.

Figure 14.

Deformed shape in FE simulation (a) and experiment (b) of the optimal case.

Conclusion

A combination of the FEM and our deep-drawing process was proposed to determine the optimal parameters for manufacturing the molds of fuel-filter cups. The results showed that

The similarity between the results of the uniformity of thickness of the plate in the experiment with the FEM was a very small range, not exceeding 1.6%.

During the first deformation stage, the fuel-filter cup with BHF, F_BH₁ = 100 kN; die-shoulder radius, r_df = 6 mm; and radial clearance between punch and die, w_f = 1.2 mm, ensuring more uniformity and a minimum thickness of the cup.

The second stage gave optimal results of FLDCRT = 0.7563, ensuring no cracks and no tearing with an optimal BHF, F_BH₂ = 70 kN. The die-shoulder radius, r_ds = 6 mm, and the radial clearance between punch and die, w_s = 1.1 mm, where the die-shoulder radius was the most important parameter affecting the formability of the final shape with a 52.5% contribution.

Our experiment with optimal parameters provides a reliable method of fabricating a final product without wrinkling and tearing, and it guarantees the formability of the deep-drawing cup according to technical requirements.

Footnotes

Handling Editor: Jianbo Yu

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Tran The-Van

Nguyen Duc-Toan

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