Numerical simulation of spinning forming of A356 aluminum alloy hub using dual spinning rollers

A finite element model of one-pass forming of an A356 aluminum alloy hub using dual spinning rollers was established, and the effectiveness of the finite element model was verified through experiment. The established finite element model was used to study the influence of the feed rate, the spindle speed, the axial distance of the two spinning rollers, and the friction coefficient on the forming quality of the hub. The result shows that a good forming quality could be obtained when the feed rate is 4 mm/s, the spindle speed is 220 rpm, the axial distance between the two spinning rollers is 3 mm or 7 mm, and the friction coefficient is 0.2. The simulation results can provide a reference for actual spinning production processes.


Introduction
In recent years, with the urgent need to save resources and protect the environment, automotive lightweight has become an important guiding direction for the development of the automotive parts industry.As one of the key components determining the driving safety of automobiles, aluminum alloy hubs are constantly improving and innovating their production and manufacturing technology while the automotive industry is developing rapidly [1] .For traditional aluminum alloy hub manufacturing enterprises, how to achieve the lightest wheel hub quality while ensuring product performance is a challenging issue.
The production and preparation processes of aluminum alloy hubs mainly include the casting method, forging method, and casting-spinning forming method.Among them, the spinning formed hubs have become an important development direction for hub production due to their advantages such as lightweight and good mechanical properties [2] .However, the spinning production of wheel hubs is a large plastic deformation process of metal, which is prone to defects such as wrinkling, uneven wall thickness, and unqualified dimensions, resulting in material waste and reducing the production efficiency of enterprises.Therefore, studying the quality control of spinning forming is of great significance for reducing energy consumption and improving production efficiency.At present, researchers mainly use numerical simulation and experimental methods to study the spinning process of hubs.For example, Chen et al. [3] used the Simufact platform to establish the spinning forming model of the aluminum alloy wheel hub, studied the influence of process parameters on the roundness of the wheel hub and the amount of spring back, and found that the feed rate and the thinning rate have the greatest influence on the forming quality of the wheel hub; Bi et al. [4][5] used the finite element software DEFORM 3D to improve the spinning forming process of aluminum alloy wheels and steel wheels and investigated the influence laws of different feed rates and spindle speeds on their forming process.Roy and Majer [6] established a thermal coupling model for hub spinning forming and predicted the final geometric shape of the results.The model predictions were consistent with the experimental results under small deformation conditions.Hwang et al. [7] studied the effects of spindle load, feed rate, radial thinning rate, and the geometric shape of the spinning roller on product accuracy through experiments and simulations, and obtained the optimal process parameters for each pass.Cha et al. [8] studied the mechanism of material backflow defects during the hub spinning process through simulation and experiments, and the results showed that the spindle load is the main factor causing material backflow.
The above research on hub spinning forming primarily concentrates on multi-pass spinning forming.There is limited research on the one-pass forming of hubs using dual rollers.Using two spinning rollers for one pass spinning has a faster production speed and a greater wall thickness reduction rate, which means it will achieve higher production efficiency and a better strengthening effect.At the same time, it will generate greater spinning pressure and more unstable factors, which affect the quality of spinning forming.Therefore, examining the one-pass spinning technique of aluminum alloy hubs with dual spinning rollers is of great importance for improving production efficiency and product quality.This study employs finite element analysis software to simulate the one-pass spinning process of an aluminum alloy hub using two spinning rollers and investigates the effects of spindle speed, feed rate, axial distance between the two rollers, and friction coefficient on the forming quality of the hub.The results identify optimal process parameters, which can guide actual hub-spinning production processes.

Establishment and verification of finite element model
The schematic diagram of the spinning forming process of the aluminum alloy hub is shown in Figure 1.At the beginning of forming, the workpiece is first compressed onto the mandrel by applying a certain amount of pressure through the tail stock, and then the mandrel rotates at a constant angular velocity  with the workpiece and the tail stock.During the forming process, the two spinning rollers maintain a certain axial distance y l on the y axis, and perform three degrees of freedom movements in the xy plane according to the preset motion trajectory, including linear motion in the x direction and y direction and rotational motion around the y axis under the frictional contact with the hub.Among them, the feed rate y v of the two spinning rollers in the y axis direction is the same.The spinning rollers keep in contact with the workpiece as it is fed in a straight line, applying a constant force to press and deform it until it finally takes the shape of a hub.Based on the diagram of the principle of hub spinning forming provided above, a one-pass spinning forming finite element model of aluminum alloy hub using dual spinning rollers is established in Figure 2. The tail stock, workpiece, and mandrel are fixed while the two spinning rollers rotate around the workpiece, feeding the movement in a straight line.
The aluminum alloy hubs used in production are made from cast A356 aluminum alloy, with a spinning forming temperature of 360°C.Table 1 and Figure 3 display the material parameters adopted in the finite element model and the simplified stress-strain curve obtained from the high-temperature hot pressing experiment at 360°C.4a, from which it can be seen that the rim has better final formability.Figure 4b illustrates the comparison between the cross-sectional features of the rim section produced by both experimentation and simulation under the same operating conditions.The results indicate that a satisfactory level of agreement exists between the two methods with respect to the rim profile.The rim thickness measurements were taken at varying distances from the start point as presented in Figure 5a.A comparison between simulation and experimental results is illustrated in Figure 5b, demonstrating that the relative error of the rim wall thickness is below 10%.This indicates the established finite element analysis model is dependable and enables further simulation studies into aluminum alloy hub spinning.

Results and discussion
After establishing a dependable finite element analysis model, we conducted four spinning simulation tests in accordance with the process parameters specified in Table 2.The purpose of these tests was to analyze the effect of process parameters such as feed rate, spindle speed, axial distance between the two rollers, and friction coefficient on the forming quality of the formed rims.samples were measured at the same axial measurement position and circumferential direction of the rim after simulated forming, as illustrated in Figure 6.The simulation's dimensional accuracy was evaluated by calculating the average deviation of the wall thickness at the axial position from the design dimensions d  and the average deviation of the inner diameter at the axial position from the design dimensions r  .Additionally, the homogeneity of the rim forming in the circumferential direction was assessed by calculating the standard deviation of the wall thickness d  and the inner diameter r  .
Figure 6.Schematic of post-simulation measurement.

Impact of feed rate on rim forming quality
The impact of varying feed rates of the spinning rollers on the quality of the rim is shown in Figures 7a,  7b, 7c, and 7d. Figure 7a illustrates that the rim's wall thickness deviation is minimal in the midpoint and highest at the starting point when using different feed rates.This trend can be linked to the finite element analysis model's simplification.The model in this study employs the beginning end face as a fixed boundary condition with little deformation, resulting in the highest wall thickness deviation value.Furthermore, the diagram illustrates an increase in wall thickness deviation of the rim between 0-60 mm from the starting point, corresponding with the increase in feed rates.However, in the second half of the rim, there is a decrease in wall thickness deviation with the rise of feed rate.Figure 7b illustrates the correlation between the rim's inner diameter deviation and the feed rate.The results indicate that the deviation in the middle section of the rim is the most substantial for varying feed rates, while it is the smallest at both ends.This phenomenon is known as inner diameter expansion and should be avoided during the spinning process [9] .Meanwhile, it can be seen from the figure that the deviation of the inner diameter of the rim increases with the increase of the feed rate.
Figures 7c and 7d present how the standard deviation of wall thickness and inner diameter varies with the feed rate.The wall thickness uniformity in the center of the rim is the most optimal, while the inner diameter uniformity is the least favorable.Both the wall thickness and inner diameter uniformity increase as the feed rate increases, suggesting that lower feed rates produce more uniform forming.
In summary, the lower the feed rate of the spinning roller is, the better the dimensional accuracy and forming uniformity of the rim is, but a too-low feed rate will seriously reduce the production efficiency.Combined with the above figure, the 4 mm/s feed rate of the spinning roller has both better forming quality and production efficiency.

Effect of spindle speed on rim forming quality
Figures 8a, 8b, 8c, and 8d show the effect of spindle speed on the forming quality of the rim.From Figure 8a, thickness deviation of the rim decreases with the increase of spindle speed in the rim part between 0 to 60 mm from the starting point and increases with the rise of spindle speed in the second half, indicating that the spindle speed can be appropriately increased in the first half of the spinning forming process and can be decreased to reduce the wall thickness deviation of the rim in the second half.
The variation of the wall thickness standard deviation of the rim with spindle speed is shown in Figure 8c, from which the wall thickness standard deviation of the rim decreases as the spindle speed increases, so the wall thickness uniformity of the rim is better at higher spindle speeds.
The variation of internal diameter deviation and internal diameter standard deviation with spindle speed is shown in Figures 8b and 8d.Both internal diameter deviation and internal diameter standard deviation rise with increasing spindle speed, which indicates that the accuracy of internal diameter dimensions of the rim is improved with decreasing spindle speed.The same pattern has been found in the paper [10] , because the centrifugal force on the material also increases by increasing the spindle speed, thus gradually deflecting it from the mandrel.In summary, by selecting a spindle speed of 220 rpm, the rim can achieve both better wall thickness accuracy and internal diameter accuracy.

Effect of axial distance on rim forming quality
The influence of axial distance on rim forming quality is shown in Figures 9a, 9b, 9c, and 9d.From Figures 9a and 9c, the deviation and the standard deviation of the wall thickness of the rim do not change significantly with the axial distance.From Figures 9b and 9d, the deviation and the standard deviation of the inner diameter of the rim increase with the rise of the axial distance from 3 mm to 6 mm, while the difference between the values of the axial distance of 7 mm and 3 mm is very small.Therefore, a better forming quality can be obtained by selecting 3 mm or 7 mm for the axial distance.

Effect of friction coefficient on rim forming quality
The impact of different friction coefficients on rim forming quality is shown in Figures 10b, 10c, and 10d.From Figure 10a, the wall thickness deviation of the rim increases with the rise of friction coefficient in the rim part between 0 to 60 mm from the starting point and decreases with the rise of friction coefficient in the second half, but there's very little difference between them.The wall thickness standard deviation, as shown in Figure 10c, increases with the increase of friction coefficient.Therefore, it can be concluded that to obtain higher wall thickness accuracy, the friction coefficient needs to be reduced appropriately.
It is obvious from Figure 10b and Figure 10d that the inner diameter deviation and the inner diameter standard deviation of the rim decrease as the friction coefficient increases, indicating that the larger the friction coefficient is, the higher the dimensional accuracy of the inner diameter of the rim is.This is because a high coefficient of friction allows the inner surface of the rim to be closely fitted to the mandrel during the spinning process.It is advisable to choose a coefficient of friction of 0.2.A too-high coefficient will reduce the dimensional accuracy of the wall thickness, so the coefficient should be neither too high nor too low.

Conclusions
A finite element model of one-pass forming of an A356 aluminum alloy hub using dual spinning rollers was established, and the accuracy of the model was verified by experiment.A simulation experiment was conducted by using the established finite element model to investigate the effects of feed rate, spindle speed, axial distance between the two rollers, and friction coefficient on rim forming quality.
The following conclusions were obtained: (1) The feed rate of 4 mm/s can simultaneously achieve better forming accuracy and production efficiency.However, to get a higher production speed, the feed rate must be increased, which reduces dimensional accuracy.
(2) A higher spindle speed will improve the forming accuracy of the rim wall thickness, but it will cause serious expansion of the inner diameter of the rim, so the forming quality of the rim is best when the spindle speed is 220 rpm.
(3) The forming quality of the rim is better at the axial distance of 3 mm and 7 mm, and the forming accuracy of the inner diameter of the rim decreases with increasing axial distance in the range of 3 mm to 6 mm.
(4) The forming quality of the rim is better when the friction coefficient is 0.2.A larger coefficient of friction will reduce its wall thickness forming accuracy, while a smaller coefficient of friction will reduce its inner diameter forming accuracy.

Figure 2 .
Figure 2. Finite element model for hub spinning forming.

Figure 3 .
Figure 3. True stress-true strain curve of A356at 360°C.To verify the accuracy of the established finite element model, the actual spinning manufacturing process parameters are substituted into the finite element model, and the final spinning forming result of the aluminum alloy hub is obtained as shown in Figure4a, from which it can be seen that the rim has better final formability.Figure4billustrates the comparison between the cross-sectional features of the rim section produced by both experimentation and simulation under the same operating conditions.The results indicate that a satisfactory level of agreement exists between the two methods with respect to the rim profile.The rim thickness measurements were taken at varying distances from the start point as presented in Figure5a.A comparison between simulation and experimental results is illustrated in Figure5b, demonstrating that the relative error of the rim wall thickness is below 10%.This indicates the established finite element analysis model is dependable and enables further simulation studies into aluminum alloy hub spinning.
a) Finite element simulation results b) Comparison of rim sections

Figure 4 .Figure 5 .
Figure 4. Finite element simulation results and comparison of experimental and simulation results.

Figure 7 .
Figure 7. Influence of feed rate on rim forming quality.

Figure 8 .
Figure 8. Influence of spindle speed on rim forming quality.

Figure 9 .
Figure 9. Influence of axial distance on rim forming quality.

Figure 10 .
Figure 10.Influence of friction coefficients on rim forming quality.

Table 1 .
Material properties employed in the finite element model.

Table 2 .
Spinning process parameters in the finite element model.
3.1 Quality assessment criteria for spin formingThe values of the wall thickness i d ( i =1-3) with 50 samples and inner diameter i r ( i =1-3) with 50