Experimental investigation of forming forces in frictional stir incremental forming of aluminum alloy AA6061-T6

The incremental sheet forming (ISF) process is an emerging flexible sheet-forming process, which is adequate for the manufacturing of unique or small-volume batches. Single-point incremental forming (SPIF) is the original technology of incremental sheet-forming processes. In this article, frictional stir-assisted SPIF was used to deform AA6061-T6 aluminum alloy. Experimental tests were conducted to measure the forming forces during this process for the concerned lightweight material. The influence of process parameters was investigated, which included tool rotation speed, feed rate, step size and tool diameter on the produced forming forces. A Taguchi technique for the design of experiment (DOE) and the varying wall angle conical frustum (VWACF) test was employed in this study. The results show that the rotation spindle speed was the most dominant parameter that affects the forming forces, followed by the step size, feed rate and tool diameter. In addition, the interaction between the feed rate and step size has a notable impact on the values of the forming forces.


Introduction
Incremental sheet forming (ISF) is described as having an inherent flexibility, high formability, low cost and low-forming forces compared to traditional sheet metal forming processes. Based on the evident advantages of this process, ISF is a promising forming process, as it is highly impressive from both the academic and industrial perspectives [1][2][3]. In the beginning of the last century, high interest focused on improving and employing lightweight materials in various industrial applications, such as aerospace, marine and automobile sectors [4,5]. The present applications of ISF are in the aerospace [5], transportation [6] and medical [7] fields. One of the important applications of the incremental forming is the incremental roller burnishing technique, which is used to finish the coated surface of the forming tools [8] and sheets [9] with very smooth surfaces.
Increasing demands to utilize the lightweight materials in various applications has created a critical challenge in this developed process, which is namely how to deal with low formability materials at room temperature [4,5]. Consequently, heat-assisted ISF processes have been suggested to improve the formability at warm or hot conditions. These methods include electric-assisted ISF, laser-assisted ISF and frictional stir-assisted ISF [5,[10][11][12]. The deforming forces in SPIF cannot be initially selected by the designers, which usually occurs in conventional forming processes. There are several factors, which largely help determine these forming loads, such as the application of the forming strategy, tool-sheet interaction and the kinematics of the process [15,16]. The perfect forecasting of forming forces is a crucial task in the process optimization for selecting parameters and the choice of the proper forming equipment to perform the experiments. Therefore, when forming forces exceed the allowable levels, they will affect the tooling stiffness, product quality, jig and fixtures as well as the machines used.
The forming forces in SPIF are characterized by highly intensive and localized deformation that leads to high frictional forces at the tool-sheet contact interface. The prevailing force component is the axial component in the direction of the forming tool [17,18]. Thus, estimation of the maximum forces is an important issue, not for design requirements, but for other significant reasons. These reasons include preserving the tooling machine, guaranteeing the safe usage of hardware, ensuring the quality of the produced parts [13], determining the stress levels and therefore, plastic strains controlling the structure of the component.
Moreover, adjusting the rotational speed [17,[27][28][29][30] and applying lubricants [31,32] can effectively reduce these concentrated forces. A few studies have examined the effect of the tool rotation speed on the forming forces in SPIF. Durante et al. [17], during their investigation of the formability of AA7075-T0 with tool speeds ranging from 0-800 rpm, found that the friction decreased and therefore, the forming forces decreased as the tool speed increased. Bagudanch et al. [24] studied the effect of tool diameter, step size and tool rotational speed on the SPIF of AISI-304 stainless steel material. Their experimental results proved that the forming forces are proportional to the tool diameter and step size, while forces decrease with high rotational speeds. Xu et al. [26] conducted an experimental study on AA5052-H32 aluminum alloy with 1.27 mm thickness to analyze the effect of tool rotation in a range of 0-7000 rpm on forming forces, generated temperature and formability. It was demonstrated that in a range of 0-1000 rpm, the friction is the main factor. However, in a range of 2000-7000 rpm, the thermal and dynamic recrystallization effects were the dominant factors. It proved that increasing the rotation speed helped in enhancing the formability, reducing the forming forces and raising the temperature during the process. Moreover, a tool with a laser surface texture (LST) was utilized during the forming process and this study proved that this designed tool played The deforming forces in SPIF cannot be initially selected by the designers, which usually occurs in conventional forming processes. There are several factors, which largely help determine these forming loads, such as the application of the forming strategy, tool-sheet interaction and the kinematics of the process [15,16]. The perfect forecasting of forming forces is a crucial task in the process optimization for selecting parameters and the choice of the proper forming equipment to perform the experiments. Therefore, when forming forces exceed the allowable levels, they will affect the tooling stiffness, product quality, jig and fixtures as well as the machines used.
The forming forces in SPIF are characterized by highly intensive and localized deformation that leads to high frictional forces at the tool-sheet contact interface. The prevailing force component is the axial component in the direction of the forming tool [17,18]. Thus, estimation of the maximum forces is an important issue, not for design requirements, but for other significant reasons. These reasons include preserving the tooling machine, guaranteeing the safe usage of hardware, ensuring the quality of the produced parts [13], determining the stress levels and therefore, plastic strains controlling the structure of the component.
Moreover, adjusting the rotational speed [17,[27][28][29][30] and applying lubricants [31,32] can effectively reduce these concentrated forces. A few studies have examined the effect of the tool rotation speed on the forming forces in SPIF. Durante et al. [17], during their investigation of the formability of AA7075-T0 with tool speeds ranging from 0-800 rpm, found that the friction decreased and therefore, the forming forces decreased as the tool speed increased. Bagudanch et al. [24] studied the effect of tool diameter, step size and tool rotational speed on the SPIF of AISI-304 stainless steel material. Their experimental results proved that the forming forces are proportional to the tool diameter and step size, while forces decrease with high rotational speeds. Xu et al. [26] conducted an experimental study on AA5052-H32 aluminum alloy with 1.27 mm thickness to analyze the effect of tool rotation in a range of 0-7000 rpm on forming forces, generated temperature and formability. It was demonstrated that in a range of 0-1000 rpm, the friction is the main factor. However, in a range of 2000-7000 rpm, the thermal and dynamic recrystallization effects were the dominant factors. It proved that increasing the rotation speed helped in enhancing the formability, reducing the forming forces and raising the temperature during the process. Moreover, a tool with a laser surface texture (LST) was utilized during the forming process and this study proved that this designed tool played a crucial role in the reduction of friction due to micro channels and the generated hydrodynamic pressure by this texture.
Duflou et al. [13] carried out an experimental investigation to determine the effect of some parameters, such as tool size, wall angle, step size and sheet thickness, on SPIF forces. It was found that increasing the values of these parameters led to increasing forming forces. The effect of the same process parameters was studied by Bahloul et al. [33] to evaluate their outcomes on two important responses: sheet-thinning rates and maximum process forces. Based on the obtained results, the sheet thickness and the wall angle have the most significant effect on the two afore-mentioned responses. In addition, a genetic algorithm was applied to optimize these responses.
In this study, among heat-assisted incremental forming techniques, frictional stir-assisted SPIF has been applied to deform AA6061-T6 aluminum alloy, which has been employed in a wide range of applications in different industrial sectors. In addition to the advantages of heat-assisted ISF, frictional stir-assisted SPIF displays superior benefits, as it does not require an external heating source and has a better final surface finish.

Material Characterization
In this section, the uniaxial tensile test was used to obtain the true stress-strain curve and subsequently, the mechanical properties of AA 6060-T6 with a nominal sheet thickness of 2 mm. The dimensions of the specimen are obtained according to ASTM E8M standard. Figure 2 presents the sub-size tensile test specimen. a crucial role in the reduction of friction due to micro channels and the generated hydrodynamic pressure by this texture. Duflou et al. [13] carried out an experimental investigation to determine the effect of some parameters, such as tool size, wall angle, step size and sheet thickness, on SPIF forces. It was found that increasing the values of these parameters led to increasing forming forces. The effect of the same process parameters was studied by Bahloul et al. [33] to evaluate their outcomes on two important responses: sheet-thinning rates and maximum process forces. Based on the obtained results, the sheet thickness and the wall angle have the most significant effect on the two afore-mentioned responses. In addition, a genetic algorithm was applied to optimize these responses.
In this study, among heat-assisted incremental forming techniques, frictional stir-assisted SPIF has been applied to deform AA6061-T6 aluminum alloy, which has been employed in a wide range of applications in different industrial sectors. In addition to the advantages of heat-assisted ISF, frictional stir-assisted SPIF displays superior benefits, as it does not require an external heating source and has a better final surface finish.

Material Characterization
In this section, the uniaxial tensile test was used to obtain the true stress-strain curve and subsequently, the mechanical properties of AA 6060-T6 with a nominal sheet thickness of 2 mm. The dimensions of the specimen are obtained according to ASTM E8M standard. Figure 2 presents the sub-size tensile test specimen.  Figure 3 shows the true stress-strain curve of the aluminum alloy AA6061-T6, while the chemical composition is listed in Table 1 below. From Figure 3, it is noted that the material has an adequate percentage elongation, which is necessary in incremental sheet forming.  Figure 3 shows the true stress-strain curve of the aluminum alloy AA6061-T6, while the chemical composition is listed in Table 1 below. From Figure 3, it is noted that the material has an adequate percentage elongation, which is necessary in incremental sheet forming. a crucial role in the reduction of friction due to micro channels and the generated hydrodynamic pressure by this texture. Duflou et al. [13] carried out an experimental investigation to determine the effect of some parameters, such as tool size, wall angle, step size and sheet thickness, on SPIF forces. It was found that increasing the values of these parameters led to increasing forming forces. The effect of the same process parameters was studied by Bahloul et al. [33] to evaluate their outcomes on two important responses: sheet-thinning rates and maximum process forces. Based on the obtained results, the sheet thickness and the wall angle have the most significant effect on the two afore-mentioned responses. In addition, a genetic algorithm was applied to optimize these responses.
In this study, among heat-assisted incremental forming techniques, frictional stir-assisted SPIF has been applied to deform AA6061-T6 aluminum alloy, which has been employed in a wide range of applications in different industrial sectors. In addition to the advantages of heat-assisted ISF, frictional stir-assisted SPIF displays superior benefits, as it does not require an external heating source and has a better final surface finish.

Material Characterization
In this section, the uniaxial tensile test was used to obtain the true stress-strain curve and subsequently, the mechanical properties of AA 6060-T6 with a nominal sheet thickness of 2 mm. The dimensions of the specimen are obtained according to ASTM E8M standard. Figure 2 presents the sub-size tensile test specimen.  Figure 3 shows the true stress-strain curve of the aluminum alloy AA6061-T6, while the chemical composition is listed in Table 1 below. From Figure 3, it is noted that the material has an adequate percentage elongation, which is necessary in incremental sheet forming.

Experimental Setup
The essential task of the forming jig is to tightly hold the sheet metal specimen for the forming process. The forming jig used in this work was made from mild steel and comprised of a clamping plate, backing plate, four columns and a lower or base plate. The sheet metal with dimensions of 150 mm × 150 mm × 2 mm was placed between the two clamping and backing plates. The size of the backing plate was 170 mm × 170 mm × 20 mm with a central diameter of 70 mm and rounded by a fillet of 60 mm, which helped to allow the smooth manufacturing of the final part. Moreover, the lower plate is mounted well to the Kistler-type dynamometer (9129AA, Kistler Group, Winterthur, Switzerland), which was used to measure the forming forces. The complete design of the forming jig developed in the current study was attached to the dynamometer and mounted to the CNC (OKUMA MX-45VA) milling machine bed, as depicted in Figure 4.

Experimental Setup
The essential task of the forming jig is to tightly hold the sheet metal specimen for the forming process. The forming jig used in this work was made from mild steel and comprised of a clamping plate, backing plate, four columns and a lower or base plate. The sheet metal with dimensions of 150 mm × 150 mm × 2 mm was placed between the two clamping and backing plates. The size of the backing plate was 170 mm × 170 mm × 20 mm with a central diameter of 70 mm and rounded by a fillet of 60 mm, which helped to allow the smooth manufacturing of the final part. Moreover, the lower plate is mounted well to the Kistler-type dynamometer (9129AA, Kistler Group, Winterthur, Switzerland), which was used to measure the forming forces. The complete design of the forming jig developed in the current study was attached to the dynamometer and mounted to the CNC (OKUMA MX-45VA) milling machine bed, as depicted in Figure 4. The forming tools with two diameters, 10 mm and 15 mm, and with a total length of 110 mm, were designed with a hemispherical end to use in the SPIF experiments. These tools are made from high speed steel (HSS), before being hardened and tempered with 60 HRC. The tools tips were polished to reduce the friction action at the tool-sheet contact area, thereby increasing the tool life and decreasing the surface roughness of the final parts. Figure 5 shows the forming tools.  The forming tools with two diameters, 10 mm and 15 mm, and with a total length of 110 mm, were designed with a hemispherical end to use in the SPIF experiments. These tools are made from high speed steel (HSS), before being hardened and tempered with 60 HRC. The tools tips were polished to reduce the friction action at the tool-sheet contact area, thereby increasing the tool life and decreasing the surface roughness of the final parts. Figure 5 shows the forming tools.

Experimental Setup
The essential task of the forming jig is to tightly hold the sheet metal specimen for the forming process. The forming jig used in this work was made from mild steel and comprised of a clamping plate, backing plate, four columns and a lower or base plate. The sheet metal with dimensions of 150 mm × 150 mm × 2 mm was placed between the two clamping and backing plates. The size of the backing plate was 170 mm × 170 mm × 20 mm with a central diameter of 70 mm and rounded by a fillet of 60 mm, which helped to allow the smooth manufacturing of the final part. Moreover, the lower plate is mounted well to the Kistler-type dynamometer (9129AA, Kistler Group, Winterthur, Switzerland), which was used to measure the forming forces. The complete design of the forming jig developed in the current study was attached to the dynamometer and mounted to the CNC (OKUMA MX-45VA) milling machine bed, as depicted in Figure 4. The forming tools with two diameters, 10 mm and 15 mm, and with a total length of 110 mm, were designed with a hemispherical end to use in the SPIF experiments. These tools are made from high speed steel (HSS), before being hardened and tempered with 60 HRC. The tools tips were polished to reduce the friction action at the tool-sheet contact area, thereby increasing the tool life and decreasing the surface roughness of the final parts. Figure 5 shows the forming tools.

Experiments
Studying the forming forces in SPIF is the crucial objective when preparing for this new technology as the obtained plastic deformation is mainly related to the magnitudes of these forces. Moreover, selecting the appropriate forming machine, designing the forming tools, determining the excessive sheet thinning, investigating the forming mechanisms and understanding the failure conditions of the sheet metal are critical when determining the values and directions of these forces. Some methods were utilized to measure the forming forces, such as the cantilever sensor employed by Jeswiet [16]; the dynamometer applied by several researchers, such as Duflou et al. [13,27,28,[34][35][36]; and the Wheatstone bridge designed in a previous study [37].
Usually, the forming forces in SPIF can be represented with the three orthogonal Cartesian coordinates system: x, y and z ( Figure 6). F x and F y are the forming force components that act in the workpiece plane. F z is the force that is applied along the forming tool axis and is normal to the workpiece plane, while F x-p is the value of F z at the peak point. F xy is the resultant force that acts in the xy plane. Therefore, the F xy and the resultant force (F R ) in SPIF can be estimated by the two equations below [29]: Metals 2017, 7, 484 5 of 15

Experiments
Studying the forming forces in SPIF is the crucial objective when preparing for this new technology as the obtained plastic deformation is mainly related to the magnitudes of these forces. Moreover, selecting the appropriate forming machine, designing the forming tools, determining the excessive sheet thinning, investigating the forming mechanisms and understanding the failure conditions of the sheet metal are critical when determining the values and directions of these forces. Some methods were utilized to measure the forming forces, such as the cantilever sensor employed by Jeswiet [16]; the dynamometer applied by several researchers, such as Duflou et al. [13,27,28,[34][35][36]; and the Wheatstone bridge designed in a previous study [37].
Usually, the forming forces in SPIF can be represented with the three orthogonal Cartesian coordinates system: x, y and z ( Figure 6). Fx and Fy are the forming force components that act in the workpiece plane. Fz is the force that is applied along the forming tool axis and is normal to the workpiece plane, while Fx-p is the value of Fz at the peak point. Fxy is the resultant force that acts in the xy plane. Therefore, the Fxy and the resultant force (FR) in SPIF can be estimated by the two equations below [29]: (2) Figure 6. The forming forces in SPIF (modified from [29]).
In this work, a force measuring system was used to measure the forming forces in three directions. This system is consisted of a Kistler 9129AA type dynamometer, a 5070A signal amplifier (PRIAMUS SYSTEM TECHNOLOGIES AG, Schaffhausen, Switzerland), a type 5697A DAQ data card and Dyno Ware (Version 2.6.5.16, Kistler Group, Winterthur, Switzerland, 2010), which were used to record the force values.
A varying wall angle conical frustum test (VWACF) was employed to conduct the experiments due to its homogeneous geometry with a symmetrical section [38]. Figure 7 shows the designed dimensions of the required conical frustum.
In this work, a force measuring system was used to measure the forming forces in three directions. This system is consisted of a Kistler 9129AA type dynamometer, a 5070A signal amplifier (PRIAMUS SYSTEM TECHNOLOGIES AG, Schaffhausen, Switzerland), a type 5697A DAQ data card and Dyno Ware (Version 2.6.5.16, Kistler Group, Winterthur, Switzerland, 2010), which were used to record the force values.
A varying wall angle conical frustum test (VWACF) was employed to conduct the experiments due to its homogeneous geometry with a symmetrical section [38]. Figure 7 shows the designed dimensions of the required conical frustum. In this study, the spiral tool path with a constant step size was chosen to create the tool trajectory because it almost creates a pure stretch deformation and therefore, generates a uniform sheet thickness [39]. In addition, it helps to eliminate the force peaks and simultaneously does not leave stretch marks on the sheet surface. In contrast, these cons usually take place with the counter tool path. The CAD/CAM software CATIA (V5.19, Dassault systems, 2010) was employed to model the required profile and create the spiral tool path using NC (numerical control) codes, as shown in  In this study, the spiral tool path with a constant step size was chosen to create the tool trajectory because it almost creates a pure stretch deformation and therefore, generates a uniform sheet thickness [39]. In addition, it helps to eliminate the force peaks and simultaneously does not leave stretch marks on the sheet surface. In contrast, these cons usually take place with the counter tool path. The CAD/CAM software CATIA (V5.19, Dassault systems, 2010) was employed to model the required profile and create the spiral tool path using NC (numerical control) codes, as shown in Figure 8. The part model of the VWACF was designed to have a maximum diameter of 70 mm, a depth of 42.102 mm and the radius of varying slopes of the modeled part of 60 mm, as shown in Figure 7. In this study, the spiral tool path with a constant step size was chosen to create the tool trajectory because it almost creates a pure stretch deformation and therefore, generates a uniform sheet thickness [39]. In addition, it helps to eliminate the force peaks and simultaneously does not leave stretch marks on the sheet surface. In contrast, these cons usually take place with the counter tool path. The CAD/CAM software CATIA (V5.19, Dassault systems, 2010) was employed to model the required profile and create the spiral tool path using NC (numerical control) codes, as shown in Figure 8. The part model of the VWACF was designed to have a maximum diameter of 70 mm, a depth of 42.102 mm and the radius of varying slopes of the modeled part of 60 mm, as shown in Figure 7. During the process, the continuous movement of the tool generates a local heating process and increases the rates of tool wear due to the friction at the tool-sheet contact zone. These two aspects affect both the geometric accuracy and surface finish, which simultaneously leads to an increase in forming forces. Different types of lubricants have been used for SPIF methods to minimize these harmful effects. In the current study, the lubricant SAE (BLAZE RACING SYNTHETIC BLEND 10W-40) was applied to reduce the effects of the friction. The Taguchi method was used to design the experiments with a minimum number to save costs and time consumption during the experiments [40,41]. The design of experiment, which includes selecting the main process parameters and their levels, was in accordance with previous literature. From this literature, it was found that these parameters and their levels depend highly on the material properties. Additionally, the primary tests were conducted to ensure the correct choosing of these parameters and their levels to get satisfactory During the process, the continuous movement of the tool generates a local heating process and increases the rates of tool wear due to the friction at the tool-sheet contact zone. These two aspects affect both the geometric accuracy and surface finish, which simultaneously leads to an increase in forming forces. Different types of lubricants have been used for SPIF methods to minimize these harmful effects. In the current study, the lubricant SAE (BLAZE RACING SYNTHETIC BLEND 10W-40) was applied to reduce the effects of the friction. The Taguchi method was used to design the experiments with a minimum number to save costs and time consumption during the experiments [40,41]. The design of experiment, which includes selecting the main process parameters and their levels, was in accordance with previous literature. From this literature, it was found that these parameters and their levels depend highly on the material properties. Additionally, the primary tests were conducted to ensure the correct choosing of these parameters and their levels to get satisfactory results. The main process parameters and their selected levels are presented in Table 2, while Table 3 summarized the orthogonal array (L8).

Results and Discussion
A series of experiments was conducted to evaluate the impact of rotation speed, feed rate, step size and tool diameter on the forming forces during the frictional stir-assisted SPIF. The experiments stopped after the part fractured ( Figure 9). results. The main process parameters and their selected levels are presented in Table 2, while Table 3 summarized the orthogonal array (L8). Step size (mm) 0.2 0.5 --D Tool tip diameter (mm) 10 15 --

Results and Discussion
A series of experiments was conducted to evaluate the impact of rotation speed, feed rate, step size and tool diameter on the forming forces during the frictional stir-assisted SPIF. The experiments stopped after the part fractured ( Figure 9).                 Table 4 shows the forming forces in the three directions of x, y and z at peak point and the resultant forces at this point, which is calculated according to Equations (1) and (2). From Table 4, it can be noted that the Fz-p has a greater magnitude than the Fx and Fy forces so it can be considered as a more significant force because it has a direct effect on the magnitude of the resultant forces at the peak point. To evaluate the impact of the various parameters on trends of these forces, analysis of variance (ANOVA) was utilized to obtain the main effects of these parameters on Fz-p ( Figure 18). From this figure, it can be demonstrated that the rotation speed has the greater effect on the produced Fz-p, followed by the step size, feed rate and tool diameter, which was shown as a previous study [27]. The dotted line in this figure refers to the mean value of the Fz-p. Using a high  Table 4 shows the forming forces in the three directions of x, y and z at peak point and the resultant forces at this point, which is calculated according to Equations (1) and (2).  Table 4, it can be noted that the F z-p has a greater magnitude than the F x and F y forces so it can be considered as a more significant force because it has a direct effect on the magnitude of the resultant forces at the peak point. To evaluate the impact of the various parameters on trends of these forces, analysis of variance (ANOVA) was utilized to obtain the main effects of these parameters on F z-p (Figure 18). From this figure, it can be demonstrated that the rotation speed has the greater effect on the produced F z-p , followed by the step size, feed rate and tool diameter, which was shown as a previous study [27]. The dotted line in this figure refers to the mean value of the F z-p . Using a high rotation speed leads to high friction at the tool-sheet zone and generates a highly localized heat, which helps to reduce the forming forces [17,29]. Moreover, the increase in the values of the step size and tool diameter causes an increase in the forming forces. To complete the part, the tool needs to travel continuously inside the profile and this required more pushing of the material during forming. The reaction of the material will be greater with high step size values, finally increasing the forces. In addition, when using a large diameter, the contact area is greater than that of a small diameter, so the forming forces increase as the tool diameter increases [27]. The decrease in Fz-p is not always proportional to an increase in the rotation speed where after ω = 800 rpm, this force returned to have an increasing trend with an increase in the rotation speed. This is due to the interaction effects between the different studied parameters as they appear in Figures  19-21. It can be noted from Figure 19 that the main interaction was between the feed rate and step size on the maximum value of the axial force, while Figure 20 shows this interaction in the surface plot. Figure 21 shows that the minimum axial forming force Fz-p happened at ω = 800 rpm, f = 500 mm/min, z = 0.2 mm and D = 15 mm (run 6).  The decrease in F z-p is not always proportional to an increase in the rotation speed where after ω = 800 rpm, this force returned to have an increasing trend with an increase in the rotation speed. This is due to the interaction effects between the different studied parameters as they appear in Figures 19-21. It can be noted from Figure 19 that the main interaction was between the feed rate and step size on the maximum value of the axial force, while Figure 20 shows this interaction in the surface plot. Figure 21 shows that the minimum axial forming force F z-p happened at ω = 800 rpm, f = 500 mm/min, z = 0.2 mm and D = 15 mm (run 6). The decrease in Fz-p is not always proportional to an increase in the rotation speed where after ω = 800 rpm, this force returned to have an increasing trend with an increase in the rotation speed. This is due to the interaction effects between the different studied parameters as they appear in Figures  19-21. It can be noted from Figure 19 that the main interaction was between the feed rate and step size on the maximum value of the axial force, while Figure 20 shows this interaction in the surface plot. Figure 21 shows that the minimum axial forming force Fz-p happened at ω = 800 rpm, f = 500 mm/min, z = 0.2 mm and D = 15 mm (run 6).     The normal distributions of the values of the Fz-p are explained in Figure 22. The values of this force follow the normal distribution.

Conclusions
In the current study, frictional stir-assisted SPIF was applied for deformation of the AA6061-T6 aluminum alloy. The aim was to investigate the impact of rotational tool speed, feed rate, step size and tool diameter on the values of the forming forces during the forming process. The results showed the following interesting points: (1) Increasing the rotation speed has the main effect of reducing the forming forces.
(2) In addition, the interaction between the different process parameters has a notable influence on these forces, especially the interaction between the feed rate and step size as discussed above. The normal distributions of the values of the F z-p are explained in Figure 22. The values of this force follow the normal distribution. The normal distributions of the values of the Fz-p are explained in Figure 22. The values of this force follow the normal distribution.

Conclusions
In the current study, frictional stir-assisted SPIF was applied for deformation of the AA6061-T6 aluminum alloy. The aim was to investigate the impact of rotational tool speed, feed rate, step size and tool diameter on the values of the forming forces during the forming process. The results showed the following interesting points: (1) Increasing the rotation speed has the main effect of reducing the forming forces.

Conclusions
In the current study, frictional stir-assisted SPIF was applied for deformation of the AA6061-T6 aluminum alloy. The aim was to investigate the impact of rotational tool speed, feed rate, step size and tool diameter on the values of the forming forces during the forming process. The results showed the following interesting points: (1) Increasing the rotation speed has the main effect of reducing the forming forces.
(2) In addition, the interaction between the different process parameters has a notable influence on these forces, especially the interaction between the feed rate and step size as discussed above. (3) The other parameter had a smaller effect compared with the rotation speed. Thus, controlling the tool rotation speed is an important issue in reducing the forming forces in SPIF.