Research on the Integral Forming Process of Thin walled and Thick Mouth Seamless Gas Cylinders

doi:10.21203/rs.3.rs-3243873/v1

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Research on the Integral Forming Process of Thin walled and Thick Mouth Seamless Gas Cylinders

https://doi.org/10.21203/rs.3.rs-3243873/v1

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published 09 Oct, 2023

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There is a considerable difference in wall thickness between the mouth and the cavity of thin-walled and thick-mouthed seamless gas cylinders, and the existing manufacturing processes are unable to effectively meet product requirements. To overcome such issue, a step-by-step boring-necking-spinning solution for gas cylinders was proposed, in which sufficient wall thickness is reserved for the mouth area of the cylinder blank, followed by necking-spinning to realize the overall forming of thin-walled, thick-mouthed seamless gas cylinders. The stress-strain distribution and geometric dimensional changes of gas cylinders during the spinning process were investigated by means of finite element simulation, and the effects of different process parameters on the stress and wall thickness of the bottle mouth were analyzed. Further, multi-objective optimization of the response surface model was performed using the NSGA-II algorithm to derive a set of optimal process parameters. Finally, the correctness of the simulation and optimization results was verified experimentally, and the expected geometry and optimal strain state of the gas cylinder were obtained. The newly developed processing solution represents a groundbreaking advancement in the manufacturing of thin-walled and thick-mouthed gas cylinders.

Physical sciences/Engineering/Mechanical engineering

Physical sciences/Materials science/Structural materials/Metals and alloys

Thin-walled and thick-mouthed seamless gas cylinders

Necking-spinning

Multi-objective optimization

As human civilization advances and science and technology continue to develop, the impact of energy consumption and global warming has attracted significant attention worldwide. Consequently, research into alternative energy sources, including the transportation and storage of clean energy sources such as hydrogen and natural gas, has become a priority.

Gas cylinders are widely used in the storage and transportation of clean energy. Azeem et al. ^[1] highlighted that a seamless gas cylinder liner, composed of a metal liner with a high-strength carbon fiber reinforced composite wrapped around the outer layer, is a promising option for high-pressure storage containers. Such design is advantageous owing to the lighter weight, increased strength, gas-tight properties, and adequate safety features.

Due to the limited volume of gas cylinders, gases are usually stored under high pressure. Such conditions require cylinders to be light in weight and large in volume, while ensuring sufficient strength. Therefore, the structural design of gas cylinders necessitates a thin wall thickness for the cavity to minimize weight. However, the mouth of the cylinder must have a sufficient thickness to meet the strength requirements of the thread. The development of the manufacturing process of thin-walled and thick-mounted cylinders, which can largely improve the storage efficiency of hydrogen, has also attracted considerable attention.

At present, a large number of domestic and international scholars have conducted research on gas cylinder-forming technology. The traditional production process of gas cylinders involves a stamping process to form the upper and lower head parts, respectively, followed by welding. Wang et al. ^[2] explored welded gas cylinders and found that residual stresses due to weld seams had a significant impact on strength, fatigue life, and gas tightness, thereby posing a considerable safety hazard to the cylinders.

Marini et al.^[3] claimed that the flow-forming process can be extensively adopted for production of thin-walled, high-precision tubular products. Wong et al.^[4] used a two-step forming process consisting of "bending" and flow forming. The method involved the flow of material along a mandrel to shape thin-walled cup-shaped parts, with the process employing two distinct profiles and axial rolling. Jin et al.^[5] researched a monolithic manufacturing process for large-diameter seamless steel cylinders. The monolithic forming of cylinders could be achieved by means of cold spinning of the cylindrical parts obtained by deep drawing. Through such means, the cylinder wall thickness uniformity was greatly improved and the dimensional accuracy was higher. By investigating the relationship between the microstructure and mechanical properties of gas cylinders, Li et al.^[6] improved the mechanical properties of gas cylinders based on the manufacturing process proposed by Jin et al.^[5]. Zoghi and Fallahi Arezoodar^[7] manufactured pressure vessels using a necking spinning process, which essentially involved forming parts by applying the required force and displacement to the rotating blank by means of one or more forming rolls. Wang et al.^[8] claimed that a combination of stamping and deep drawing using steel plates could produce cylinder blanks as well as cups. Cylinder blanks prepared through such process had the advantages of uniform thickness, high strength, and light oxidation.

Music et al.^[9] reported that metal spinning can improve the surface finish and mechanical strength of molded parts compared with stamping. M.L. According to A et al.^[10], the utilization of numerical modeling via finite element flow formulation can effectively facilitate the comprehension and prediction of different modes of deformation during the end forming of thin-walled tubes.

Kuang et al.^[11] used Ansys finite element software to establish a three-dimensional finite element model of offset circular tube header spinning. Using the model, during three-dimensional non-axisymmetric spinning, the effects of metal flow, stress and strain distribution, spinning pressure, and different process parameters on the spinning results were investigated.

In analyzing the evolution of the material shape and thickness as well as the stress and strain distribution generated during the spinning process, Iguchi et al.^[12] used the dynamic explicit code DYNA-3D to analyze the spinning manufacturing process of motor vehicle exhaust system components to further understand the failure mechanisms such as fracture and buckling during the spinning process. The results could provide useful information for failure prediction during the actual spinning process.

Xia et al.^[13] proposed a finite element model for non-axisymmetric neck spinning using the finite element software MSC to obtain the transient Mises stress distribution in the contact zone between the roll and the billet, as well as the equivalent plastic strain after spinning. Further, numerical and experimental studies on the thickness distribution of the spun workpiece were conducted. Such studies provided reasonable suggestions for addressing the occurrence of excessively thin or thick wall thickness in the workpiece. Yao and Makoto^[14] conducted an experimental study on the near-axis spinning of tube ends and investigated the effects on thickness strain, torsion angle, spinning force and surface finish of aluminum products with the parameters of spinning pitch and diameter reduction. Through experiments and 3D finite element simulations, Yt et al.^[15] investigated the effect of neck length on crack generation during the spinning of SUS409, and determined the spinning conditions under which cracking would not occur based on the calculated damage values. Huang et al.^[16] explored the thickness distribution and outer profile of the tube necking spinning process using the finite element model established by the shell cell. that the research revealed that the thickness of the spun tube had a small amount of thickening with the spinning process, but there was no explanation given for the deformation in the material thickness. Hamed et al.^[17] established a three-dimensional finite element model of circular tube spin forming to investigate the strain distribution in different thickness layers of a tube during the spin-forming process. An increasing trend of strain in the middle layer thickness toward the free end was reported, which indicated an increase in the tube wall thickness.

Based on the aforementioned studies, the gas cylinder forming process has attained greater maturity, with necking-spinning becoming the dominant production method. During the necking-spinning process, one end of the billet with uniform wall thickness undergoes a certain degree of thickening in the mouth region. However, in the case of gas cylinders with considerable differences in wall thickness between the mouth and the cavity, necking-spinning alone cannot achieve the ideal level of thickening.

In consideration of such issues, in the present study, a step-by-step boring-necking spinning scheme was proposed for the integral forming of thin-walled and thick-necked seamless gas cylinders. Finite element analysis was used to analyze the necking spinning of gas cylinders, and the stress-strain distribution and geometric dimensional changes of gas cylinders during the spinning process were explored. At the same time, the effects of spindle speed, friction block working angle and friction coefficient on the forming results were also systematically investigated. Finally, the simulation results were compared and analyzed with the experimental results.

2.1 Analysis of forming difficulties

The geometric structure of a thin-walled, thick-mouthed seamless gas cylinder is shown in Fig. 1(a). The cylinder was made of 2Cr13 martensitic stainless steel and had a total length of 300 mm, consisting of the cavity and the mouth. The cylinder had a wall thickness of 5 mm at both ends of the mouth and 0.7 mm in the cavity, resulting in a ratio of over 7 between the two wall thicknesses.

The formability of thin-walled, thick-mouthed seamless gas cylinders could be analyzed from both structural and material aspects. Firstly, from a structural formation perspective of gas cylinders, the ratio of wall thickness between the cylinder's mouth and the cavity exceeded 7 times, making it challenging to thicken the cylinder's mouth solely through a neck reduction spinning process. Secondly, there was a transition zone with gradually increasing wall thickness between the bottle body and the mouth of the bottle, and the cylinder's cross-section may pose a potential hazard by leading to cracking during the formation process. Finally, 2Cr13 stainless steel exhibits high yield strength and severe hardening during forming, which also results in higher deformation resistance and increases the risk of cracking.

2.2 New method

Considering the large variability of the wall thickness between the cavity and the mouth of a thin-walled, thick-mouthed seamless gas cylinder, solely using a single processing method is not possible.

As such, a step-by-step boring-necking-spin-forming scheme for gas cylinders was proposed in the present study. The flow chart of the new scheme is shown in Fig. 1(b). The two-step processing scheme was proposed for achieving desired wall thickness characteristics of thin-walled, thick-mouthed seamless gas cylinders.

(b). Boring-necking spinning step-by-step forming method

(c). Geometry of straight seamless tube after boring

In the first step, according to the overall geometry of the gas cylinder, a straight seamless tube is selected as raw material and divided into two areas: the part of the mouth to be necked reduction and the part of the cavity to be thinned. Boring tools are used to thin the inner wall of the cavity to the target wall thickness, so as to achieve a thin-walled cavity, while retaining the wall thickness in the mouth area to meet the required thickness after forming. Notably, if there is a section with gradually decreasing wall thickness between the mouth and the cavity of the gas cylinder blanks, a workpiece with thicker wall thickness at both ends and thinner wall thickness in the middle should be formed (as shown in Fig. 1(c)).
In the second step, both ends of the workpiece are processed separately by means of the necking-spinning process to finally form a thin-walled, thick-mouthed seamless gas cylinder.

The neck reduction spinning of gas cylinders can be formed by multi-pass spinning with rolls or by spinning with friction blocks of a certain type of surface. The multi-pass spin-forming process for rolls is more complex and has high production requirements. When the friction block is used for spinning, the entire surface of the friction block is in contact with the billet, the contact area is large, and the required forming force is large. Under such conditions, one-time forming can be achieved, and there will be a better thickening effect on the mouth of the gas cylinder, which is suitable for small size workpieces. Owing to the simplicity and efficiency of the process, the friction block spinning method was adopted for processing of the gas cylinder blanks in the present study. Figure 2(a) shows the experimental setup for gas cylinder forming and a photo of the processed finished product.

2.3. Experimental procedure

The experimental process of neck-spinning of gas cylinders mainly includes the following steps.

First, the workpiece is clamped in the rotary jig, and the workpiece is exposed to the necked portion using a positioning post at a certain distance.
Secondly, after the mandrel rotates at high speed, the part of the workpiece to be necked and rotated is heated to the required temperature for forming using a high-frequency induction heater.
Finally, the position of the friction block is adjusted according to the amount of necking needed to shape the gas cylinder's mouth, and the friction block is not rotated more than 90° around the axis of rotation, resulting in the final formation of the gas cylinder's mouth.

The described steps are repeated for the other end for neck spinning so as to finally form the finished gas cylinder, as shown in Fig. 2(b).

2.4. Finite element modeling

To investigate the law of neck-spin forming of thin-walled thick nozzle seamless gas cylinders, a 3D finite element model was developed based on ABAQUS software. Additionally, due to the symmetry of the workpiece itself, a 1/2 finite element model was established, as shown in Fig. 3(a). In the model, the slewing fixture and friction block were defined as a rigid body, the workpiece was set as a deformable body, and the unit body type was C3d8r.

Initially, the overall mesh size was 2mm*1mm, and to ensure the forming accuracy and simulation efficiency, the mesh of the bottle mouth area was further refined to 1mm*1mm, with the total number of meshes being 29000. To improve the calculation efficiency, the mass scaling factor was selected as 1000, and the ratio of kinetic energy to internal energy was less than 10% in more than 90% of the spinning process. As such, the simulation was stable.

The material properties are shown in Table 1^{[18, 19]}. The main process parameters used in the finite element model are given in Table 2. The mandrel speed, friction block working angle, and friction factor were temporarily set to 480r/min, 30° and 0.3, respectively. The schematic diagram of the friction block working angle is shown in Fig. 3(b).

To facilitate the investigation into the deformation of the bottle mouth, the bottle mouth was divided into three deformation zones. Zone Ⅰ is the portion close to the bottle cavity, Zone Ⅲ is the free end portion, and Zone Ⅱ (the current contact area) is the portion between Zone Ⅰ and Ⅲ. Moreover, 25 mesh nodes were selected as feature nodes along the axial direction on each of the three thickness layers. The positions of the feature nodes are shown in Fig. 3(c).

Table 1

Material parameters^{[18, 19]}
Parameters	Temperature/℃	Density ρ ($\text{k}\text{g}/{\text{m}}^{3}$)	Young’s modulus E(GPa)	Poisson’s ratio$\nu$	Yield strength ${\sigma }_{s}$ (MPa)
Values	950	7500	103	0.33	146

Table 2

Parameters of FE models.
Parameters	Values
Necking volume (mm)	10
Mandrel speed (r/min)	480
The working angle of the friction block (°)	30
Friction block speed (r/min)	56.52
Friction factor between friction block and workpiece	0.1

3.1 The stress and strain distribution during the forming process

Figure 4 shows the stress and strain distribution of the gas cylinder mouth at different stages of the spinning process. The neck spinning process of a gas cylinder can be divided into three stages: Stage 1, the neck of the bottle mouth forming; Stage 2, the cylinder mouth forming, also the neck shape trimming process; and Stage 3, the cylinder bending forming, but also the neck and mouth finishing process.

Figure 4(a) shows that the equivalent stress is predominantly distributed within the vicinity of the contact area, with the maximum stress concentration observed at the bottleneck region and the friction block's contact position. Moreover, as the distance from the contact region increases, the equivalent force diminishes. Such local plastic deformation features of the friction block's neck rotation spinning govern the observed phenomenon. In the spinning process, the contact area increases first, and then gradually decreases after reaching a certain peak, so the distribution range and size of the equivalent force also show a trend of increasing and then decreasing. When the free end of the bottle mouth is no longer in contact with the friction block, the free end of the bottle mouth is less constrained and its stress value becomes small.

Figure 4(b) shows that the equivalent effect variation was distributed hierarchically along the axial direction, and the size of the equivalent effect variation was equal in the same circumferential direction. With the gradual feeding of the friction block, the equivalent variation of the bottle mouth increased until the end of spinning. The maximum equivalent effect variation value was located at the neck of the bottle curvature, which indicates that there was a large metal flow, with the potential occurrence of cracks and buildup (as shown in Fig. S1).

3.2 Geometric changes (thickness, elongation, and profile)

Xia et al.^[20] explored tube neck spinning and reported that the thickness deviation between the actual dimensions of the workpiece and the nominal dimensions of the part must be satisfied. After the neck-spinning of the cylinder mouth, it is essential to create threaded holes in its inner wall. However, due to the limited thickness of the mouth, the tolerance of the fit may be impacted. Therefore, it is crucial to ensure that the thickness of the mouth meets the required wall thickness.

Figure 5(a) shows the thickness and elongation of the bottleneck at different stages of the spinning process. An observation can be made the elongation of the bottleneck increased from the beginning to the end of the spinning, while the wall thickness exhibited a process of decreasing and then increasing, and the final wall thickness increased compared with the original wall thickness.

Figure 5(b) shows the internal and external profiles of the bottle mouth during the rotary feeding of the friction block. An observation can be made that as the spinning proceeded, the mouth of the bottle was gradually compressed to form a bend and the elongation band became more pronounced. The maximum wall thickness value of the bottle mouth was 5.2mm, which occurred at the inflection point, as shown in the lead in Fig. 5(b). The minimum thickness value appeared at the edge of the free end of the bottle mouth area, and there was an obvious thinning band at the free end of the bottle mouth. The wall thickness reduction at the edge of the free end became more serious as the friction block was gradually rotated and fed.

3.3 The plastic strain distribution of different thickness layers

To analyze the variation of the bottle mouth thickness and elongation, the radial, circumferential, axial, and equivalent plastic strains at the gas bottle mouth were examined, as shown in Fig. 6. In manufacturing certain pressure vessels using the tube spinning process, Zoghi and Fallahi Arezoodar^[7], highlighted the existence of thickening, thinning, elongation, compression, bending, and shearing in the deformation zone during the neck spinning process of the bottle mouth. To further investigate the strain state of the bottle mouth, the plastic strain distribution on each thickness layer in Fig. 3(c) was examined. Figures 7(a)-(d) depict the distribution of radial, circumferential, axial, and equivalent variation for different thickness layers, respectively.

From Fig. 6, an observation can be made that the strain distribution of each thickness layer within Zones 1 and Ⅲ was relatively uniform, and the differences between thickness layers were mainly reflected in Zone Ⅱ (contact area).

Figures 6(a)-(b) depict the distribution of the radial strain, which is usually negative due to the necking behavior of the free end of the workpiece. An observation can be made that in Zone Ⅲ, the strain state was reflected as a compression strain. Figure 6(b) shows that positive strain existed in Zone Ⅱ and the radial positive strain decreased from the outer layer to the inner layer. Combined with Fig. 7(a), a conclusion could be drawn that there was no significant difference in radial strain between the three thickness layers in the bottle mouth region, indicating that the decrease in diameter during necking rotation was uniform between the thickness layers. Biglari^[21] reported a similar pattern of radial strain when rotating the plate with a hemispherical mandrel.

Figures 6(c)-(d) show the distribution of circumferential strains, which were consistently reflected as positive strains (tensile strains) in different zones between the three thickness layers. As seen in Fig. 6(d), the positive strain in Zone Ⅱ decreased gradually along the outer layer to the inner layer. While directly subjected to the force of the friction block, the outer layer of the tube was still undergoing positive circumferential strain (contact area) as a result of the constant volume during plastic deformation. In combination with Fig. 7(b), the strain values of the three thickness layers in Zone Ⅱ gradually increased, implying an increase in thickness. The strain value of the thickness layer in Zone Ⅲ gradually decreased, and the circumferential strain at the edge of Zone Ⅲ sharply decreased, which indicates a slight thinning in the thickness direction.

Figures 6(e)-(f) show the distribution of the axial strain. The axial strains in the three thickness layers in Zones Ⅰ and Ⅱ were reflected as negative strains (compressive strains), and the axial strains in Zone Ⅲ were positive (tensile strains). In combination with Fig. 7(c), a conclusion could be drawn that the negative strain in Zone Ⅰ gradually increased, which was caused by the local force of the friction block causing the bending of each thickness layer by axial compression. The negative strain in Zone Ⅱ gradually decreases and then rapidly changes direction. The axial strain in each thickness layer in Zone Ⅲ was in a tensile state after the direction of strain transition, and the strain value gradually increased towards the free end. The reduction of circumferential strain in Zone Ⅲ was a result of volume constancy, which compensated to some extent the positive axial strain of volume constancy. The bending due to compressive strain along the axial direction in Zone Ⅱ and the axial extension in Zone Ⅲ together amplified the positive strain. Such findings are consistent with the deformation pattern of Zoghi and Fallahi Arezoodar^[7] in their research on neck spinning. The excessive elongation of the outer metal at the rim in Zone Ⅲ was caused by the unconstrained material at the rim of the bottle mouth, which is consistent with the behavior mentioned by Hamed et al.^[17] in their research on tube spinning.

According to the principle of volume invariance, due to the necking behavior of the bottle mouth, the metal flowed more along the axial direction at the free end, then the flow in the circumferential direction had to be reduced. Moreover, the radial flow of the material gradually slowed down along the wall thickness direction, as shown in Fig. 8. Therefore, the deformation of the gas cylinder mouth was mainly reflected in the axial elongation, while the thickening in the thickness direction was small.

Figures 6(g)-(h) show the distribution of the equivalent strain. As expected, there was a larger equivalent strain in Zone Ⅱ. From Fig. 6(h), an observation can be made that the values of the equivalent strain in the same circumferential direction remained consistent, and the equivalent strain in Zone Ⅱ gradually decreased from the outer to the inner layers. As can be seen in Fig. 7(d), in the axial direction, the value of the equivalent strain increased and then decreased. The outer layer strain had a larger growth rate. The maximum equivalent strain value was located at the intersection of Zone Ⅲ and Zone Ⅱ (near node 14). Such findings indicate that there was a large amount of metal flow here and the strain gradient was more intense, which could be attributed to the presence of curvature mutations in Zone Ⅱ.

The central composite experimental design response surface methodology (RSM) is a combination of mathematical and statistical techniques used to develop, improve and optimize processes. Using the central composite experimental method, multiple sets of experiments were designed and numerically simulated to analyze the effects of each process parameter on the spinning results, and the mapping relationship between each process parameter and the optimization variables was established by means of the response surface method. The resulting mapping relations were used to perform multi-objective optimization using the NSGA-II algorithm and obtain the Pareto optimal solution, so as to optimize the process parameters and improve the quality of gas cylinders^[22].

4.1 Central composite experimental design

The maximum stress, and minimum thickness were selected as the optimization objectives, and the three parameters of spindle speed, friction block working angle and friction coefficient were taken as the influencing factors of the central composite experimental design to construct the response surface model. Such means could avoid the stress concentration during the forming process of the gas cylinder mouth causing damage to the workpiece and further control the wall thickness of the mouth. Table 3 shows the range of values for each parameter. Table S1 shows the central composite experimental parameters obtained by numerical simulation.

The effects of each variable on the maximum stress and minimum wall thickness and their interactions were calculated using Design-Expert13 software. The relationship between the factors (independent variables) and each response (dependent variable) was modeled by fitting a second-order polynomial equation given by the following equation.

Table 3

Range of experimental parameter variation
Parameters	Max. value	Min. value	Average value
$\text{M}\text{a}\text{n}\text{d}\text{r}\text{e}\text{l} \text{s}\text{p}\text{e}\text{e}\text{d} {x}_{1}(\text{r}·{\text{m}\text{i}\text{n}}^{-1}$)	600	400	500
friction block working angle ${x}_{2}$(°)	35	25	30
Friction factor${x}_{3}$	0.1	0.3	0.2

$$Y={\alpha }_{0}+{\alpha }_{1}{X}_{1}+{\alpha }_{2}{X}_{2}+{\alpha }_{3}{X}_{3}+{\alpha }_{12}{X}_{1}{X}_{2}+{\alpha }_{13}{X}_{1}{X}_{3}+{\alpha }_{23}{X}_{2}{X}_{3}+{\alpha }_{11}{{X}_{1}}^{2}+{\alpha }_{22}{{X}_{2}}^{2}+{\alpha }_{33}{{X}_{3}}^{2}$$

in which ${X}_{1}$, ${X}_{2}$, and ${X}_{3}$ are the independent variables in the response surface model parameters, ${\alpha }_{0}$, ${\alpha }_{1}$, ${\alpha }_{2}$, ${\alpha }_{3}$, ${\alpha }_{11}$, ${\alpha }_{12}$, ${\alpha }_{13}$, ${\alpha }_{22}$, ${\alpha }_{23}$, and ${\alpha }_{33}$ are the regression coefficients, and $Y$ is the response function.

4.2 Response surface results

(1) Mapping relationship between a maximum stress and independent variables and response surface model

The prediction model of the regression equation for the independent variables ${X}_{1}$, ${X}_{2}$, ${X}_{3}$ and the dependent variable ${Y}_{1}$ (maximum stress) is shown in Eq. (1). Figure 9(a) shows the response surface of the maximum stress (${Y}_{1}$) with the variation of mandrel speed (${x}_{1}$) and friction block working angle (${x}_{2}$), and Fig. 9(b) shows the response surface of the maximum stress (${Y}_{1}$) with the variation of friction block working angle (${x}_{2}$) and friction factor (${x}_{3}$).

$${Y}_{1}=-190.43150+0.990726{x}_{1}-0.3416{x}_{2}+1034.84125{x}_{3}-0.001684{x}_{1}{x}_{2}-0.151075{x}_{1}{x}_{3}-14.03200{x}_{2}{x}_{3}-0.000969{{x}_{1}}^{2}+0.067795{{x}_{2}}^{2}-1267.28750{{x}_{3}}^{2}$$

Figure 9(a) reflects that the maximum stress decreased with the gradual increase of the spindle speed, which could be ascribed to the increased mobility of the material in the circumferential and axial directions with the increase in spindle speed, rendering a decrease in the internal stress. Figure 9(b) reflects that the maximum stress increased with the gradual increase in the friction factor, which was due to the increase in the resistance to the flow of the metal at the mouth of the bottle with the increase in the friction factor, and the formation of larger stress. The effect of the working angle on the maximum stress was smaller.

(2) Mapping relationship between minimum thickness and independent variables and response surface model

The prediction model of the regression equation for the independent variables ${x}_{1}$, ${x}_{2}$, ${x}_{3}$, and the dependent variable ${Y}_{2}$ is shown in Eq. (2). Figure 9(c) shows the response surface of the wall thickness value (${Y}_{2}$) with the variation of spindle speed (${x}_{1}$) and working angle (X2), and Fig. 9(d) shows the response surface of the wall thickness value (${Y}_{2}$) with the variation of working angle (${x}_{2}$) and friction factor (${x}_{3}$).

$${Y}_{2}=4.13938+0.004942{x}_{1}-0.003977{x}_{2}-0.245801{x}_{3}-0.000051{x}_{1}{x}_{2}+0.001461{x}_{1}{x}_{3}+0.030487{x}_{2}{x}_{3}-4.62650E-06{{x}_{1}}^{2}+0.00024{{x}_{2}}^{2}-3.19512{{x}_{3}}^{2}$$

Figures 9(c)~(d) reflect that the wall thickness value decreased with the increase in spindle speed and friction factor, which could be attributed to the increase in spindle speed and friction factor, as well as the metal flow at the mouth of the bottle being enhanced and retaining less metal the thickness direction. of the increase in working angle tended to lead to a decrease in the wall thickness value, which was because the increase in working angle led to the corresponding increase in contact area between the friction block and the mouth of the bottle, thereby accelerating the material flow along the axial direction leading to a decrease in wall thickness.

4.3 Multi-objective optimization

According to the parameter equations discussed in Section 4.2 for the multi-objective optimization, the problem to be investigated could be described in the context of the actual situation, where 400≤${x}_{1}$≤600, 25≤${x}_{2}$≤35, and 0.1≤${x}_{3}$≤0.3.

In order to prevent cylinder failure caused by excessive stress at the bottle mouth and to ensure adequate thickness in the same Zone, it was necessary to simultaneously achieve the minimum value of the stress variable ${Y}_{1}$ and the maximum value of the thickness variable ${Y}_{2}$, while keeping the independent variables ${x}_{1}$, ${x}_{2}$, and ${x}_{3}$ within the allowed variation range.

Using Design Gateway for multi-objective optimization, the regression equations were entered into the computer component, the initial values of the design variables ${x}_{1}$, ${x}_{2}$, and ${x}_{3}$ were entered, the upper and lower limits of the variables were set, and the NSGA-II algorithm was selected to solve for all of the Pareto solutions, some of which are shown in Table S2.

In the Design Gateway window, the scatter plot between the maximum stress ${Y}_{1}$, the thickness increment ${Y}_{2}$, and the independent variables can be observed, as shown in Fig. S2 (a). The highlighted points in the plot are the scatter points on the axes for the top 10 solutions in the order of the Pareto-optimized solutions. Fig. S2 (b) shows the distribution of the Pareto-optimized solution set on the 3D coordinate axis.

By analyzing the distribution of the Pareto optimized solution set on the 3D coordinate axes, combined with the specific data given in Table S2, an observation can be made that the optimized solution set was mainly concentrated in a specific range, being a significant reference value for the optimization and design of the target quantities. The optimal set of solutions provided by Design in the optimized solution set was the spindle speed of 490.4, a working angle of 34.439°, and a friction coefficient of 0.248.

Based on the experimental setup shown in Fig. 2(a), spinning experiments were performed on the workpiece. The process scheme was designed based on the process parameters determined by multi-objective optimization, discussed in Section 4.3. Finite element simulations and experiments were performed on the process scheme, and the simulation results were compared with the experimental results, as shown in Fig. S3(a)-(b).

Due to the high temperature of the spinning process, there were difficulties in performing real-time measurements, and it was not possible to investigate the deformation by microstructure due to the reversion and recrystallization at high temperatures. As such, a decision was made to use the internal and external contours of the gas cylinder after molding, as well as the wall thickness distribution to verify the simulation. Several researchers^{[23, 24]} used a similar approach to perform a validation of the reliability of the model.

A comparison of the wall thickness distribution and the cross-sectional profile dimensions is shown in Fig. S3 (c) and Fig. S3 (d), respectively. The maximum difference between the measured thickness from the workpiece and the predicted thickness obtained from the simulation was about 8.02%, being within the allowable range. In the experiments and simulations, the minimum wall thicknesses were 5.2 and 5.014 mm, respectively. In the actual working conditions, with heat dissipation and local heating of the supplemental heat device, the temperature in the deformation area of the billet was not uniform, while the simulated temperature was constant in the simulation, thereby resulting in errors between the simulation and the actual machining.

Such results indicate a good agreement between the simulation and the experiment. In conclusion, the developed finite element model is reliable and the cross-sectional profile of the part is essentially consistent with the target shape after spinning. The deviations of both wall thickness and profile are within acceptable limits. Therefore, the proposed scheme can be considered an effective method to achieve thin-walled and thick-mouthed gas cylinder forming.

In the present study, a step-by-step boring-neck spinning process scheme was developed for forming thin-walled and thick-mouthed seamless gas cylinders. Based on finite element analysis and experimental studies, the following conclusions were drawn:

(1) In the process of neck-spinning of gas cylinders, there was a large stress in the mouth region and the axial elongation of the mouth was more significant, while there was a smaller thickening effect in the thickness direction.

(2) As the mandrel speed, friction block working angle, and friction factor increased, the wall thickness of the bottle mouth decreased, while the maximum stress increased rapidly. Considering the influence of process parameters on the aforementioned factors, a process parameter scheme was determined as follows: spindle speed of 490r/min, friction block working angle of 34°, and friction coefficient of 0.25.

(3) Experimental studies revealed that the desired thin-walled, thick-mouthed seamless gas cylinders can be formed using a step-by-step boring-necking spinning scheme and defined process parameters. The minimum wall thickness of the gas cylinder mouth in the experiment was 5.2mm, and the geometric profile accuracy as well as the wall thickness after forming was within the error range. As such, the proposed step-by-step boring-neck-spinning scheme may become an advanced processing technology for forming thin-walled and thick-mouthed gas cylinder liners.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This research was funded by the Key Research and Development Project of Shanxi Province (202202050201017). National Natural Science Foundation of China (52275358).

Data Availability

During the current study, the datasets in Table1 Material parameters were available from the corresponding author upon reasonable request. The rest of the data generated or analyzed are included in this publication and in the supplementary information.

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No competing interests reported.

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Research on the Integral Forming Process of Thin walled and Thick Mouth Seamless Gas Cylinders

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Abstract

Figures

1. Introduction

2. Proposal for integral forming of thin-walled and thick-mouthed seamless gas cylinders

2.1 Analysis of forming difficulties

2.2 New method

2.3. Experimental procedure

2.4. Finite element modeling

3. Analysis of the forming process

3.1 The stress and strain distribution during the forming process

3.2 Geometric changes (thickness, elongation, and profile)

3.3 The plastic strain distribution of different thickness layers

4. Response surface and parametric equations for spinning process parameter optimization

4.1 Central composite experimental design

4.2 Response surface results

4.3 Multi-objective optimization

5 Verification of finite element simulation

Conclusions

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

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Parameters	Max. value	Min. value	Average value
\(\text{M}\text{a}\text{n}\text{d}\text{r}\text{e}\text{l} \text{s}\text{p}\text{e}\text{e}\text{d} {x}_{1}(\text{r}·{\text{m}\text{i}\text{n}}^{-1}\))	600	400	500
friction block working angle \({x}_{2}\)(°)	35	25	30
Friction factor\({x}_{3}\)	0.1	0.3	0.2