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Integrated Design of D.D.I., Filament Winding and Curing Processes for Manufacturing the High Pressure Vessel (Type II)


As energy crisis and environment pollution all around the world threaten the widespread use of fossil fuels, compressed natural gas (CNG) vehicles are explored as an alternative to the conventional gasoline powered vehicles. Because of the limited space available for the car, the composite pressure vessel (Type II) has been applied to the CNG vehicles to reach large capacity and weight lightening vehicles. High pressure vessel (Type II) is composed of a composite layer and a metal liner. The metal liner is formed by the deep drawing and ironing (D.D.I.) process, which is a complex process of deep drawing and ironing. The cylinder part is reinforced by composite layer wrapped through the filament winding process and is bonded to the liner by the curing process. In this study, an integrated design method was presented by establishing the techniques for FE analysis of entire processes (D.D.I., filament winding and curing processes) to manufacture the CNG composite pressure vessel (Type II). Dimensions of the dies and the punches of the 1st (cup drawing), 2nd (redrawing-ironing 1-ironing 2) and 3rd (redrawing-ironing) stages were calculated theoretically, and shape of tractrix die to be satisfied with the minimum forming load was suggested for life improvement and manufacturing costs in the D.D.I. process. Thickness of the composite material was determined in the filament winding process, finally, conditions of the curing process (number of heating stage, curing temperature, heating rate and time) were proposed to reinforce adhesive strength between the composite layers.

1 Introduction

Composite high pressure vessels are more and more frequently used in automotive industry, aviation, emergency services and power industry due to strength/stiffness-to-weight ratio [1, 2]. Because of the limited space available for the car, the composite pressure vessel (Type II) has been applied to the CNG vehicles to reach large capacity and weight lightening. There are previous studies to manufacture the vessel (D.D.I., filament winding and curing processes). They had been limited to only individual processes, but a study with respect to an integrated system dealt with entire manufacturing processes hasn’t been performed yet. Karen described how to use intelligent die design based on topology optimization using a new improved differential evolution [2]. Narayanasamya dealt with the wrinkling limit diagrams of annealed three different pure sheets, using conical and tractrix dies [3]. But, it is deficient in design of the tractrix curve, which has been used in the 1st cup drawing die of the D.D.I. process, to improve die life and to reduce manufacturing costs. Geng et al. [4] derived stresses of a thick cylinder with multi-angle winding filament and proposed an optimization model of FW vessel to maximize the lowest strength ratio. Zu et al. [5] proposed a design approach for determining the optimal winding parameters of composite vessels based on non-geodesic trajectories. But they has considered only composite material, not including thickness and material properties of liner. This results in a waste of composite material due to an excessive thickness of the composite layer, and an analysis method using a coupled model with liner and composite layer is necessary. Minakuchi et al. [6] proposes an approach to determine material parameters for stress calculation of curing composite laminates and validate the simulation using fiber Bragg grating (FBG) strain sensors, and Li et al. [7] proposed a new cyclic heating and cooling methodology for microwave curing control of composite by analyzing mechanisms of heat conduction, stress generation and curing kinetics. But design of the curing process applying to the CNG pressure vessel (Type II) hasn’t been conducted yet.

In this study, an integrated design method was presented by establishing FEA techniques of D.D.I., filament winding and curing processes to manufacture the CNG composite pressure vessel (Type II). Especially, deep drawing analysis was performed according to the heights of the tractrix die, and its shape with the minimum forming load was suggested for life improvement and reduction of manufacturing costs. Minimum thickness of the composite material to ensure a structural safety was determined considering the liner and the composite layer. Also by observation of curing degree and residual strain, conditions of the curing process were proposed to reinforce adhesive strength between the composite layers [1‒3]. Configuration of the integrated design method is illustrated in Figure 1.

Figure 1
figure 1

Configuration of the integrated design of CNG composite pressure vessel (Type II)

2 Theory of Manufacturing Process for the CNG Composite Pressure Vessel -Type II

The CNG pressure vessel (Type II), composed of a metal liner (34CrMo4) and E-glass fiber/epoxy composite wound layers as shown in Figure 2, requires different manufacturing processes to form each part: a deep drawing and ironing (D.D.I.) process for cylinder part of liner, a hot spinning process for dome part, a filament winding process to laminate the composite layers on cylinder part to endure the inner pressure, and a curing process to reinforce adhesive strength between composite layers [8].

Figure 2
figure 2

CNG pressure vessel (Type II)

2.1 D.D.I. Process

The D.D.I. process to form the cylinder part of liner includes a drawing process to reduce diameter of the billet and an ironing process to reduce thickness of the billet. In the 1st stage, an initial blank is fabricated into cup shape using the tractrix die to prevent a wrinkling without the blank holder. Redrawing and two ironing processes (D.I.I.) are continuously performed using the horizontal press in the 2nd stage, and finally redrawing and ironing processes (D.I.) are operated to obtain the final thickness and diameter of the liner in the 3rd stage as shown in Figure 3 [9, 10].

Figure 3
figure 3

Manufacturing process of CNG pressure vessel (Type II)

Theoretical design rules of the D.D.I. process are shown in Eqs. (1)‒(11) [4]. The limit drawing ratios (b1 = 2.1 and b2 = 1.35) and tip clearance between the drawing die and the workpiece (C1 = 5%, C2 = 0 and C3 = −5%) are suggested from the actual field [11]. When the dimensions of the initial blank and the final liner are given in Table 1 and Figure 4, the calculation results obtained from the above procedures are shown in Table 2 and Figure 5. Where dpi, ddij and diij are diameters of punch, drawing die and ironing dies at ith stage and jth process. bi, tij and Aij are draw ratio, thickness of material and cross sectional area, respectively.

Table 1 Dimension of the initial blank and the liner
Figure 4
figure 4

Dimension of the liner

Table 2 Calculation result of D.D.I. process design
Figure 5
figure 5

Dimensions of punches and dies calculated from the theoretical design rules of the D.D.I. process

$$dp_{1} = dm_{1} - \left( {1 + C_{1} } \right) \times t_{0} ,$$
$$dd_{1} = dm_{1} + \left( {1 + C_{1} } \right) \times t_{0} ,$$
$$b_{1} = \frac{{D_{0} }}{{dm_{1} }},$$
$$dp_{2} = dm_{21} - \left( {1 + C_{2} } \right) \times t_{0} ,$$
$$dd_{21} = dm_{21} + \left( {1 + C_{2} } \right) \times t_{0} ,$$
$$b_{2} = \frac{{dm_{1} }}{{dm_{2,1} }},$$
$$di_{23} = \sqrt {\frac{{4A_{23} }}{\pi } + dp_{2}^{2} } ,\quad 0.5A_{1} = A_{23} ,$$
$$dp_{3} = dm_{31} - \left( {1 + C_{3} } \right) \times t_{2,3} ,$$
$$dd_{3} = dm_{31} + \left( {1 + C_{3} } \right) \times t_{2,3} ,$$
$$b_{3} = \frac{{dm_{23} }}{{dm_{31} }}dm_{23} = \frac{{dp_{2} + di_{23} }}{2},$$
$$t_{23} = \frac{{di_{23} - dp_{2} }}{2} di_{32} = dp_{3} + 2t_{32} .$$

A forming load (F) is computed by using effective stain (\(\overline{\varepsilon }\)), cross sectional area (A) and strain-flow stress equation of 34CrMo4 (\(\overline{\sigma }\)), shown in Eq. (12). Where the plastic modulus (K) is 90.42, and work hardening exponent (n) is 0.213. After finishing the D.D.I. process, dome part of the liner is formed through the hot spinning process. A cylinder of metal is rotated at high speed (1000 r/min), and a roller moves along the rotation path (\(\overline{{R_{n} O_{n} }}\)) and then back by feeding distance (\(\overline{{R_{n - 1} R_{n} }}\)) as shown in Figure 6, finally, workpiece is formed into an axially symmetric dome part.

Figure 6
figure 6

Spinning process to manufacture the dome part of liner

$$F = \overline{\sigma } A = K\overline{{\varepsilon^{n} }} A = KA\smallint \sqrt 2 /3\left\{ {\left( {\text{d}\varepsilon_{r} - \text{d}\varepsilon_{\theta } } \right)^{2} + \left( {\text{d}\varepsilon_{\theta } - \text{d}\varepsilon_{z} } \right)^{2} + \left( {\text{d}\varepsilon_{z} - \text{d}\varepsilon_{r} } \right)^{2} } \right\}.$$

2.2 Filament Winding Process

Filament winding of the composite material, which involves winding filaments under tension over a rotating mandrel, is a fabrication technique mainly used for manufacturing pressure vessels [12]. The liner is wound by E-glass with winding angle of 90°. The laminated composite pressure vessel is expressed in cylindrical coordinates with r (radial coordinate), θ (hoop coordinate) and z (axial coordinate) as illustrated in Figure 7. The differential equations relating to displacements (u) and stiffness constants (\(\overline{C}\)) are determined by Eqs. (13) and (14). τθr and τzr are obtained from Eq. (15). Where γ0 has physical interpretation which is twist of vessel per unit length. The axial strain of all layers are equal to a constant ε0, and A(k) and B(k) are unknown integration constants.

Figure 7
figure 7

Mathematical model of multi-layered filament wound composite pressure vessel

$$\begin{aligned} & \frac{{ \text{d}^{2} u_{r}^{\left( k \right)} }}{{{\text{d}r}^{2} }} + \frac{1}{r}\frac{{\text{d}u_{r}^{\left( k \right)} }}{\text{d}r} - \frac{{\overline{C}_{22}^{\left( k \right)} /\overline{C}_{33}^{\left( k \right)} }}{{r^{2} }}u_{r}^{\left( k \right)} \\ & = \frac{{\overline{C}_{12}^{\left( k \right)} - \overline{C}_{13}^{\left( k \right)} }}{{\overline{C}_{33}^{\left( k \right)} }}\frac{{\varepsilon_{0} }}{r} + \frac{{\overline{C}_{26}^{\left( k \right)} - 2\overline{C}_{36}^{\left( k \right)} }}{{\overline{C}_{33}^{\left( k \right)} }}\gamma_{0} , \\ \end{aligned}$$
$$\begin{aligned} & \frac{{\text{d}u_{\theta }^{\left( k \right)} }}{\text{d}r} - \frac{{u_{\theta }^{\left( k \right)} }}{r} \\ & = \frac{{ - \;\overline{C}_{55}^{\left( k \right)} }}{{\left( {\overline{C}_{33}^{\left( k \right)} } \right)^{2} - \overline{C}_{44}^{\left( k \right)} \overline{C}_{55}^{\left( k \right)} }}\frac{{A^{\left( k \right)} }}{{r^{2} }} + \frac{{\overline{C}_{45}^{\left( k \right)} }}{{\left( {\overline{C}_{45}^{\left( k \right)} } \right)^{2} - \overline{C}_{44}^{\left( k \right)} \overline{C}_{55}^{\left( k \right)} }}\frac{{B^{\left( k \right)} }}{r}, \\ \end{aligned}$$
$$\tau_{\theta r}^{\left( k \right)} = A^{\left( k \right)} /r^{2} ,\quad \tau_{zr}^{\left( k \right)} = B^{\left( k \right)} /r.$$

For the anisotropic materials, there exist \(\overline{{C_{22} }}^{\left( k \right)} /\overline{{C_{33} }}^{\left( k \right)} > 0\) and \(\overline{{C_{22} }}^{\left( k \right)} /\overline{{C_{33} }}^{\left( k \right)} \ne 1\). If \(\beta^{\left( k \right)} = \sqrt {\overline{{C_{22} }}^{\left( k \right)} /\overline{{C_{33} }}^{\left( k \right)} }\), the solution for Eqs. (13) and (14) is given by Eqs. (16), (17), where \(D^{\left( k \right)}\) and \(E^{\left( k \right)}\) are integration constants [13]:

$$u_{r}^{\left( k \right)} = D^{\left( k \right)} r^{\beta \left( k \right)} + E^{\left( k \right)} r^{ - \beta \left( k \right)} + \alpha_{1}^{\left( k \right)} \varepsilon_{0} r + \alpha_{2}^{\left( k \right)} \gamma_{0} r^{2} ,$$
$$\begin{aligned} \alpha_{1}^{\left( k \right)} & = \overline{C}_{12}^{\left( k \right)} - \overline{C}_{13}^{\left( k \right)} /\overline{C}_{33}^{\left( k \right)} - \overline{C}_{22}^{\left( k \right)} , \\ \alpha_{2}^{\left( k \right)} & = \overline{C}_{26}^{\left( k \right)} - 2\overline{C}_{36}^{\left( k \right)} /4\overline{C}_{33}^{\left( k \right)} - \overline{C}_{22}^{\left( k \right)} . \\ \end{aligned}$$

The on-axis stiffness constants, \(\left\{ {C_{ij}^{\left( k \right)} } \right\}\), can be calculated using Eq. (18):

$$\left\{ {C_{ij}^{{\left( {k} \right)}} } \right\} = \left\{ {C_{xx}^{{\left( {k} \right)}} ,C_{yy}^{{\left({k} \right)}} ,C_{zz}^{{\left({k} \right)}} ,C_{xy}^{{\left( {k} \right)}} ,C_{xz}^{{\left( {k} \right)}} ,C_{yz}^{{\left({k} \right)}} ,C_{xx}^{{\left( {k} \right)}} ,C_{yy}^{{\left({k} \right)}} ,C_{zz}^{{\left( {k} \right)}} } \right\}^{\text{T}}.$$

All the unknown integration constants in Eqs. (13) and (14) are determined by substituting these equations into boundary conditions. The traction pressure (p0) at the inner surface and the traction-free condition at the outer surface are written as Eqs. (19) and (20). Where r0 and ra are the inner and outer radii, respectively.

$$\sigma_{r}^{\left( 1 \right)} \left( {r_{0} } \right) = - p_{0} ,\quad \sigma_{r}^{\left( n \right)} \left( {r_{a} } \right) = 0,$$
$$\begin{aligned} & \tau_{\theta r}^{\left( 1 \right)} \left( {r_{0} } \right) = \tau_{zr}^{\left( 1 \right)} \left( {r_{0} } \right) = 0, \\ & \tau_{\theta r}^{\left( n \right)} \left( {r_{a} } \right) = \tau_{zr}^{\left( n \right)} \left( {r_{a} } \right) = 0. \\ \end{aligned}$$

Assuming that the interfaces between the core and skin layers are perfectly bonded, the continuity conditions for the displacement and stresses in the interfaces lead to Eqs. (21) and (22):

$$u_{r}^{\left( k \right)} \left( {r_{k} } \right) = u_{r}^{{\left( {k + 1} \right)}} \left( {r_{k} } \right),\quad u_{\theta }^{\left( k \right)} \left( {r_{k} } \right) = u_{\theta }^{{\left( {k + 1} \right)}} \left( {r_{k} } \right),$$
$$\begin{aligned} \sigma_{r}^{\left( k \right)} \left( {r_{k} } \right) & = \sigma_{r}^{{\left( {k + 1} \right)}} \left( {r_{k} } \right), \\ \tau_{zr}^{\left( k \right)} \left( {r_{k} } \right) & = \tau_{zr}^{{\left( {k + 1} \right)}} \left( {r_{k} } \right), \\ \tau_{\theta r}^{\left( k \right)} \left( {r_{k} } \right) & = \tau_{\theta r}^{{\left( {k + 1} \right)}} \left( {r_{k} } \right). \\ \end{aligned}$$

In addition, the axial equilibrium and the zero torsion condition for a cylinder with closed ends are expressed as Eq. (23):

$$2\pi \mathop \sum \limits_{k = 1}^{n} \mathop \smallint \limits_{{r_{k - 1} }}^{{r_{k} }} \sigma_{z}^{\left( k \right)} \left( r \right)r\text{d}r = \pi r_{0}^{2} p_{0} ,\quad 2\pi \mathop \sum \limits_{k = 1}^{n} \mathop \smallint \limits_{{r_{k - 1} }}^{{r_{k} }} \tau_{z\theta }^{\left( k \right)} \left( r \right)r^{2} \text{d}r = 0.$$

Substituting Eqs. (19) and (20) into Eqs. (13) and (14), the integration constants, \(A^{\left( k \right)} = B^{\left( k \right)} = 0\). Therefore, the solution for the hoop displacement (\(u_{\theta }\)) is obtained from Eq. (24):

$$u_{\theta }^{\left( k \right)} = \gamma_{0} rz.$$

Eqs. (19)‒(23) give a set of equations to determine 2N + 2 unknown constants (\(D^{\left( k \right)} , E^{\left( k \right)} \left( {k = 1, 2, \ldots , N} \right)\), and \(\varepsilon_{0} , \gamma_{0}\)) for N-layered composite tube.

Tsai-Hill criterion shown in Eq. (25) is employed to characterize the failure of the composite materials (E-glass/epoxy) due to multiaxial loading conditions. Where X, Y, and Z are the yield strength in each direction, and Q, R and S are the shear strength in each direction.

$$\begin{aligned} & \frac{{\sigma_{1}^{2} }}{{X^{2} }} + \frac{{\sigma_{2}^{2} }}{{Y^{2} }} + \frac{{\sigma_{3}^{2} }}{{Z^{2} }} - \sigma_{1} \sigma_{2} \left( {\frac{1}{{X^{2} }} + \frac{1}{{Y^{2} }} - \frac{1}{{Z^{2} }}} \right) - \sigma_{1} \sigma_{3} \left( {\frac{1}{{X^{2} }} - \frac{1}{{Y^{2} }} + \frac{1}{{Z^{2} }}} \right) \\ & - \sigma_{2} \sigma_{3} \left( { - \frac{1}{{X^{2} }} + \frac{1}{{Y^{2} }} + \frac{1}{{Z^{2} }}} \right) + \frac{{\sigma_{4}^{2} }}{{Q^{2} }} + \frac{{\sigma_{5}^{2} }}{{R^{2} }} + \frac{{\sigma_{6}^{2} }}{{S^{2} }} = 1. \\ \end{aligned}$$

2.3 Curing Process

After the filament winding process, curing process is performed to reinforce adhesive strength between composite layers to keep working pressure and structural safety of pressure vessel. The composite is cured in an IR oven to infuse liquid resin [14].

Temperature change of the vessel including thermal transmission and resin exothermic reaction, is a transient process. The thermal conductivity model is expressed as Eq. (26). Where \(\rho_{r}\), \(v_{r}\) and \(\dot{Q}_{r}\) are density, volume fraction and heat release rate of the resin, respectively [15].

$$\rho \dot{Q} = \rho_{r} v_{r} \dot{Q}_{r} .$$

Released heat quality of the resin is solved by the kinetics model of curing rate of the epoxy resin shown in Eqs. (27)‒(29). Hr is the total heat of the reaction per unit mass released by curing process. dα/dt and α are curing rate and curing degree of resin, respectively. m and n are exponents, and k1 and k2 are defined by the Arrhenius rate expressions. A1 and A2 are pre-exponential coefficients, and ΔE1 and ΔE2 are activation energies. R is universal gas constant.

$$\dot{Q}_{r} = \frac{{{\text{d}}\alpha }}{{{\text{d}}t}}H_{r} ,$$
$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \left( {k_{1} + k_{2} \alpha^{m} } \right)\left( {1 - \alpha } \right)^{n} ,$$
$$k_{1} = A_{1} { \exp }\left( { - \frac{{\Delta E_{1} }}{RT}} \right),\quad k_{2} = A_{2} { \exp }\left( { - \frac{{\Delta E_{2} }}{RT}} \right).$$

The curing kinetics model is solved by finite difference method as shown in Eq. (30). It has been assumed that temperature in a period of time Δt is a constant so that the time integral method can be used to calculate a curing degree. αt is the known value of curing degree at the previous calculation [16, 17].

$$\alpha^{t + \Delta t} = \alpha^{t} + \left( {\frac{{{\text{d}}\alpha }}{{{\text{d}}t}}} \right)^{t + \Delta t} \Delta t.$$

The total residual strain (\(\Delta \varepsilon\)), considering the thermal residual strain of composite (\(\Delta \varepsilon^{th}\)) and the curing shrinkage residual strain (\(\Delta \varepsilon^{ch}\)) of the composite material, is computed by Eq. (31). Where γ (0.11) is the coefficient of composite thermal expansion and \(\beta\) (0.05) is the volume shrinkage ratio [18, 19].

$$\Delta \varepsilon = \Delta \varepsilon^{th} + \Delta \varepsilon^{ch} = \gamma \Delta T + \sqrt[3]{1 + \beta \Delta \alpha } - 1.$$

3 Finite Element Analysis for Manufacturing Processes of the Composite Pressure Vessel-Type II

3.1 Finite Element Analysis of D.D.I. Process

To minimize forming load in the 1st deep drawing, design of tractrix die was conducted through FE analysis according to heights of the die. Forming analyses in the 2nd (D.I.I.) and the 3rd (D.I.) stages were performed with the results shown in Table 2, and the final liner shape (tf = 4 mm, Din = 306 mm) was obtained.

3.1.1 Modeling and Boundary Conditions

The D.D.I. process was simulated using commercial software, Forge NxT 2.0, and 3D modeling of an analysis model in each forming stage, which consists of a workpiece, a die and a punch, was conducted based on Tables 1 and 2 as shown in Figure 8. Distances between the dies were suggested in the actual filed, and tetrahedron meshes of the workpiece are generated. The workpieces are set to deformable domain, and the dies and punches rigid bodies. Strain-flow stress of 34CrMo4 according to the temperatures offered by Forge NxT 2.0 was adopted as shown in Figure 9. Friction coefficient (μ) and friction constant (m) are defined as 0.056 and 0.11, respectively [20]. Velocity of the punch is 50 mm/s, which is used in the actual field [21, 22].

Figure 8
figure 8

Analysis models in the D.D.I. process

Figure 9
figure 9

Strain-flow stress curve of 34CrMo4 according to the temperatures

Equation of tractrix curve, applied to the 1st deep drawing die, is shown in Eq. (32), where B is distance between asymptote and y-axis and a is shape factor. The height (h) of the tractrix die and inflow angle (\(\theta\)) of blank change according to shape factor (a) as shown in Figure 10. To minimize forming load, design of the shape of tractrix die was implemented by varying die heights (375‒750 mm) at the interval of asymptote (25 mm). Inflow angles of material according to die height are listed in Table 3, and dd1 (536.94 mm) is fixed value in the basis of Table 2 [23,24,25].

Figure 10
figure 10

Shapes of tractrix die according to the heights

Table 3 Die height and inflow angle of material
$$x = B + {\text{sech}}\left( t \right),\quad y = - a\left( {t - { \tanh }\left( t \right)} \right).$$

3.1.2 Result and Discussion

As the punch stroke proceeded, thicker sheet due to the amount of inflowing into the die causes the forming load to increase, and the peak load has the largest thickness variation during the drawing process as shown in Figure 11. Trend line of the peak forming load obtained by varying the die heights plotted in Figure 12 indicated that the load changes according to inflow angle of material and die height, and the minimum value, 919.4 t, was obtained at the height of 513 mm as shown in Figure 13.

Figure 11
figure 11

Forming loads according to the times (die height: 500mm)

Figure 12
figure 12

Peak forming load according to the die heights

Figure 13
figure 13

Suggested shape of the tractrix die with height of 513 mm

In case of the die heights (375 mm to 513 mm), the forming load was decreased due to reduction of the maximum equivalent strain (375 mm: 2.04, 513 mm: 1.22) as shown in Figure 14. As the reduction of stain has a greater influence on forming load than the increase of the contact area, the forming load was decreased in the rages (550‒575 mm and 600‒625 mm), otherwise, the forming load was increased in the rages (513‒550 mm and 575‒600 mm), and fluctuations of the forming load were observed in the transition range (500‒650 mm). After then (650‒750 mm), the larger contact area allowed to increase the forming load as shown in Figure 15.

Figure 14
figure 14

Equivalent strain distributions when the die heights are 375 mm and 513 mm

Figure 15
figure 15

Contact areas when the die heights are 513mm and 750mm

The workpiece shape obtained from the 1st deep drawing using the suggested tractrix die was imported to the initial billet of the 2nd stage with which forming analyses in the 2nd (D.I.I.) and the 3rd (D.I.) stages were performed based on the theoretical calculation results shown in Table 2. When the adjacent nodes overlap because of folding phenomenon, “Fold value” calculated form Forge NxT-Post processor is 1, otherwise, “Fold value” is 0. “Fold value” of the final workpiece shape in each stage is 0 as shown in Table 4, so that forming defects such as wrinkling and folding did not occur. The maximum forming loads of each stage were 919.4 t, 1030.5 t and 753.7 t, respectively, and the above values are below the press capacity (1500 t) used in the actual field, so feasibility of the D.D.I. process was confirmed.

Table 4 Results of each forming stage

Dimensions of the final liner shape obtained from after the 3rd stage process were compared with those of the desired product (tf = 4 mm, Din = 306 mm) shown in Table 1: Inner diameter (305.9 mm) measured from the y-coordinate of a node at inside surface of the cylinder part, the thickness (3.99 mm) as shown in Figure 16. The D.D.I. process design and FEA technique were verified through the above minor errors, 0.03% and 0.25% respectively.

Figure 16
figure 16

Dimensions of the final liner shape after 3rd stage

3.2 Finite Element Analysis of Composite Layer

Thickness of the composite layer of the pressure vessel (Type II) was decided based on the results of static structural analyses using ACP (ANSYS Composite PrepPost).

3.2.1 Modeling and Boundary Conditions

3D model of the liner (tf = 4 mm, Din = 306 mm) and mechanical properties of 34CrMo4 were inputted in the Mechanical Model module as shown in Figure 17(a). In the ACP Pre module, anisotropic material properties, thickness and laminated angle (90°) of the E-glass fiber were set in the 3D modeling of the composite layer generated, as shown in Figure 17(b). Two models generated through above procedures were imported to the Static Structural module, and then pressure vessel (Type II) with liner and composite layer was created as shown in Figure 17(c). Equivalent stresses of the liner and the composite layer are obtained in the Static Structural module, and Tsai-Hill value to check failure of the composite layer are checked in ACP-Post module.

Figure 17
figure 17

Static structural analysis of the pressure vessel (Type II) in the each module

The internal pressure of 30.75 MPa, which is 1.5 times the working pressure (20.5 MPa), based on the Korea gas safety C016-2000 safety regulations, was imposed on the inner surface of the liner. When the CNG vessel is installed in the bus, inlet part is bolted to the valve, which does not allow to move all rotational and translational directions, including circumferential and axial directions. So the fully fixed support condition was applied to the upper surface of the inlet as shown in Figure 18.

Figure 18
figure 18

Load and boundary conditions of static structural analysis

3.2.2 Result and Discussion

Based on the international regulation, following requirements have to be taken into account to prevent fracture of composite pressure vessel, when being subjected to the internal pressure (30.75 MPa): Maximum equivalent stress of the liner < the yield strength of the liner (840.0 MPa), maximum Tsai-Hill value of composite (Eq. (5)) < the critical value (1). The thinner composite layer is required to achieve weight lightening and cost reduction, and thickness (5‒7 mm) of the composite layers for the Type II vessel is used in the actual field. So case study with different thicknesses (5 mm, 6 mm, 6.3 mm, 6.6 mm and 7 mm) was conducted to obtain better condition for structural safety and weight lightening as shown in Table 5.

Table 5 Results of structural analysis of liner and composite layer according to the thicknesses of composite layer

The thickness of 6.3 mm, in which the maximum equivalent stress (834.2 MPa) is less than the yield strength (840.0 MPa)), and in which the maximum Tsai-Hill value (0.96) is less than the critical value (1), was chosen as shown in Figure 19.

Figure 19
figure 19

Results of static structural analysis in case of the thickness of composite layer (6.3 mm)

3.3 Finite Element Analysis of Curing Process

3.3.1 Modeling and Boundary Conditions

In order to compregnate the E-glass fibers on the liner, the epoxy resin and the fiber are laminated alternately as shown in Figure 20. The higher volume fraction of the fiber increases the longitudinal and the transverse Young’s moduli (E1 and E2) and decreases the major Poisson’s ratio (v12), which alleviates strain occurred due to the internal pressure. The high elasticity of the composite, which leads to larger compressive residual stress of the liner in the autofrettage process, reinforces strength and fatigue life of the high pressure vessel subjected to the working pressure (20.5 MPa) [26]. Also, the thermoplastic property of the composite improves as the volume fraction increases, this enhances resistance for deformation occurred due to the curing temperature.

Figure 20
figure 20

Analysis model of the curing process

In the thermal analysis, the convection coefficient of 5 W/(m2·°C) was adopted to the inner surfaces of the liner, and the curing temperature was applied to the outside surfaces of the liner and the composites, which were subjected to the external heat resource generated from the oven. In the stress & strain analysis, the fully fixed support condition was adopted to the upper surface of the inlet. The material properties of the E-glass fiber and epoxy resin are listed in Table 6.

Table 6 Material properties of E-glass fiber and resin

Curing kinetics model offers the internal heat resource to the thermal conductivity model, and the temperature field of the composite is calculated by the thermal conductivity model, which influences on the curing rate of the resin, so both kinetics and thermal conductivity models were calculated at the same time, by using Eqs. (26)‒(30) [14, 15]. The APDL code for iterative calculation of kinetic-thermal conductivity analysis is shown in Figure 21(a).

Figure 21
figure 21

APDL code to simulate curing analysis

In the first calculation, the initial temperature (30 °C), the initial curing degree (α = 0), the curing kinetic parameters of epoxy resin and external heat resource were inputted. Curing degree (α1) was computed by using kinetics model, and then internal heat resource released by the resin (Qr,1) and the temperature field (T1) by the external heat were calculated by using thermal conductivity model. The outputs of 1st calculation (α1Qr,1 and T1) are to be input parameters of 2nd calculation, and the above mentioned calculation processes were repeated. When the value of curing degree is less than 1, the program continually calculates curing degree and released heat, which are defined as the initial value for next calculation. In order to calculate total residual strain of the composite layer, thermal-structural coupled field analysis is conducted by transference of temperature field and curing degree. Based on APDL code illustrated in Figure 21(b), total residual strain considering thermal and curing shrinkage phenomenon was computed by using Eq. (31) [27, 28].

3.3.2 Result and Discussion

Curing analyses were implemented according to the three design parameters; temperatures of external heat resource (60 °C, 80 °C, 100 °C, 120 °C and 140 °C) [29], the number of heating stages (two stages, three stages, four stages and five stages) [30] and heating rates at the second stage (0.0075 °C/s, 0.015 °C/s, 0.02 °C/s, 0.03 °C/s and 0.04 °C/s) [31]. The external starting temperature of first step is fixed to 80 °C. The analysis results according the temperature of the external heat resource indicated that the high constant temperature enables the curing process to be completed more quickly, and even if the external temperature is low, the curing degree reaches 1 when the heating time is long enough as shown in Figure 22. Based on the analysis results according to the number of heating stage, the curing processes with 4 and 5 heating stages have not been reached to 1, and this means they have not been completed within the inputted curing time. But, the higher the number of heating stage is, the lower maximum strain is as shown in Figure 23. Higher heating rate accelerated the curing process, and the differences between the maximum total residual strains were small as shown in Figure 24. Considering the results of curing analyses, the best curing conditions to reduce the maximum residual strain and to reach the curing degree (α = 1) in a short time were suggested in Table 7.

Figure 22
figure 22

Results of curing analyses according to the temperatures of external heat resource

Figure 23
figure 23

Results of curing analyses according to the number of heating stages

Figure 24
figure 24

Results of curing analyses according to the heating rates

Table 7 Best curing conditions of the pressure vessel

4 Conclusions

In this study, an integrated design method (D.D.I., spinning, filament winding and curing processes) to manufacture the CNG composite pressure vessel (Type II) (tf = 4 mm, Din = 306 mm, Dout = 314 mm and L = 1830 mm) was presented to ensure structural safety and to reduce production costs. The summaries are as follows.

  1. 1)

    Dimensions of the dies and the punches are theoretically calculated by applying the design rules of the D.D.I. process. (dp1 = 510.69 mm, dd1 = 536.94 mm, dp2 = 380.25 mm, dd21 = 405.25 mm, di22 = 401.19 mm, di23 = 397.10 mm, dp3 = 306.00 mm, dd31 = 322.00 mm, di32 = 314.00 mm). Design of the tractrix die was conducted to improve die life and reduce manufacturing costs (height = 513 mm).

  2. 2)

    The thickness of the composite layer to ensure structural safety and minimum use of material was chosen as 6.3 mm to have the maximum equivalent stress of the liner (834.18 MPa), which do not exceed the yield strength (840 MPa), and the maximum value of Tsai-Hill is 0.96, which is below critical value of 1.

  3. 3)

    The curing conditions (1st stage: 80 °C, 0.04 °C/s, 0‒2000 s, 2nd stage: 140 °C, 0.03 °C/s, 5000‒7000 s, 3rd stage: 180 °C, 0.02 °C/s, 10000‒19000s) to complete curing process in a short time with low residual strain were suggested.


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Authors’ Contributions

HK designed and debugged the analyses and wrote the manuscript; GP and HS assisted with FEA analyses; CK was in charge of the whole trial. All authors read and approved the final manuscript.

Authors’ Information

Hyoseo Kwak received her B.S. and M.S. degrees from School of Creative Engineering and a Ph.D. degree in Mechanical Convergence Technology from Pusan National University, Korea, in 2012, 2014, and 2017, respectively. She is currently a Research at the Research Institute of Mechanical Technology, Pusan National University, Korea. Her research interests include machine design and FEM simulation (forming, structures, dynamics, and fluid analyses).

Gunyoung Park received his B.S. degree from School of Mechanical Engineering, Pusan National University, Korea. Now he is studying for the master course in Mechanical Convergence Technology at Pusan National University, Korea. His research interests include machine design and FEM simulation (forming, structure analyses).

Hansaem Seong received B.S. degree from School of Mechanical Engineering and M.S. degree from Mechanical Convergence Technology. Now he is studying for the doctorate in Mechanical Convergence Technology at Pusan National University, Korea. His research interests include machine design and FEM simulation (forming, structures, and thermal analyses).

Chul Kim received his M.S. and Ph.D. degrees in 1987 and 1997. Professor Kim is currently a Professor at the Research Institute of Mechanical Technology of Pusan National University, Korea. His research fields include FEM simulation (structures, dynamics, and fluid analysis), optimal structural design, and CAD/CAM.


The authors would like to express gratitude to National Research Foundation of Korea (NRF) for funding and NK Co., Ltd. for critical discussion and technical assistance.

Competing Interests

The authors declare that they have no competing interests.


Supported by National Research Foundation of Korea (NRF) and Korea Government (MSIT) (Grant No. 2019R1F1A1058521).

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Kwak, H., Park, G., Seong, H. et al. Integrated Design of D.D.I., Filament Winding and Curing Processes for Manufacturing the High Pressure Vessel (Type II). Chin. J. Mech. Eng. 32, 83 (2019).

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  • Pressure vessel (Type II)
  • D.D.I.
  • Filament winding
  • Curing process
  • FEM