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A flexible shear spinning of axi-symmetrical shells with a general-purpose mandrel
Journal of Materials Processing Technology 192–193 (2007) 13–17
A flexible shear spinning of axi-symmetrical shells with a general-purpose mandrel K. Kawai ∗ , L.-N. Yang, H. Kudo Department of Mechanical Engineering and Materials Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-85-1, Japan
Abstract An experimental study is conducted to survey the technological possibility of the shear spinning of truncated hemispherical shells with a cylindrical mandrel for general purposes using A1050-H and A1050-O commercially pure aluminum sheets of 1 mm thickness. It is found that there exist forming limits to prevent the occurrence of wall fractures and flange wrinkles during the spinning process of truncated hemispherical shells. It is also found that the sine law is not realized exactly in shear spinning of truncated hemispherical shells with a cylindrical mandrel for general purposes due to the spring back of the workpiece. © 2007 Elsevier B.V. All rights reserved. Keywords: Spinning; Shear spinning; Rotary forming; Flexible forming; Metal forming
1. Introduction The shear spinning process is sometimes called spin forging or shear forming in the literature. The process of shear spinning is characterized by the fact that the radial position of any element in the blank remains the same radial position during deformation. This demands that the initial thickness of the blank t0 and the final thickness of the axi-symmetrical shell tf are related by the sine law for the tangential angle in the meridian plane of the axi-symmetrical shell α: tf = t0 sin α [1]. While the recent spinning technology including conventional spinning, shear spinning and tube spinning has been reviewed elsewhere [2], it has been considered that the outer shape of the mandrel should be identical with the inner shape of the product to be formed in shear spinning. In the ordinary process of shear spinning, a mandrel whose outer shape is identical with the inner shape of the product has been used as shown in Fig. 1. On the other hand, the path of the forming roller 0–1–2–3–0 as shown in Fig. 2 can also form a conical shell supported on the end of a cylindrical mandrel that rotates with the main spindle of a spinning lathe [3]. If a workpiece has the rigidity that is sufficient to maintain the shape of shell to be formed during the process, an
∗
Corresponding author. Tel.: +81 45 339 3872; fax: +81 45 331 6593. E-mail address: [email protected] (K. Kawai).
0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.04.008
ironing process between the forming roller and the mandrel is not so essential to the shear spinning process. In other words, there is no need to use a mandrel that has an identical outer shape with the inner shape of the product to be formed if the workpiece has sufficient rigidity to maintain the shape of the shell to be formed during the process. If the path of the forming roller is controlled to satisfy the sine law corresponding to the product to be formed, various axi-symmetrical shells can be spun by a combination of a forming roller and a cylindrical mandrel for general purposes. This flexible process will be applicable to form axi-symmetrical shells of a great variety and small-batch production if various axi-symmetrical shells can be manufactured practically with a certain degree of accuracy. In the earlier papers [3,4], an experimental study was conducted to survey the technological possibility of the shear spinning of truncated conical shells with a cylindrical mandrel for general purposes. There exist forming limits to prevent the occurrence of wall fractures and flange wrinkles as shown in Fig. 3 [3]. The sine law is also realized in shear spinning of truncated conical shells with a general-purpose cylindrical mandrel as shown in Fig. 4 [4]. While a sudden change in the wall thickness is observed in Fig. 4, the thinning phenomenon of the wall thickness at an early stage of shear spinning can be prevented by the use of a non-linear path of the forming roller to allow a gradual change in the wall thickness from the initial value to the final value, as shown in Fig. 5 [4].
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K. Kawai et al. / Journal of Materials Processing Technology 192–193 (2007) 13–17
Fig. 1. Shear spinning of a truncated conical sell with a mandrel whose outer shape is identical with the inner shape of the product.
This paper deals with an experimental study of the technological possibility of the shear spinning of truncated hemispherical shells with a general-purpose mandrel.
Fig. 3. Experimental results and forming limits for conical shells with a residual flange width of 10 mm for A1050-H aluminum sheet.
2. Experimental procedure A scheme of shear spinning of truncated conical shells with a generalpurpose mandrel is shown in Fig. 2. A circular blank disk of outer diameter D0 = 120 mm and thickness t0 = 1 mm was supported on the end of a cylindrical mandrel of outer diameter dM = 50 mm. The cylindrical mandrel rotated at a constant number of revolutions N = 187.5 rpm with the main spindle of a spinning lathe. A forming roller of outer diameter of dR = 74 mm and round-off radius of ρR = 2 mm was fixed to a tool post on an XY-table. The position of the XY-table was controlled by servomotors and ball screws. The angle δ between Y-axis of the XY-table and the centerline of the cylindrical mandrel was 50◦ . The path of the forming roller was controlled numerically by servo control units. The experimental apparatus can perform shear spinning of a truncated conical shell with a single passage of the forming roller, which satisfied the sine law according to
Fig. 4. Distribution of the wall thickness of conical shells with a residual flange width of 10 mm for A1050-O annealed aluminum sheet.
Fig. 2. Scheme of shear spinning of truncated conical shell with a cylindrical mandrel for general purposes.
Fig. 5. Distribution of the wall thickness improved by the use of a non-linear path of the forming roller for A1050-O annealed aluminum sheet.
K. Kawai et al. / Journal of Materials Processing Technology 192–193 (2007) 13–17
Fig. 6. Scheme of shear spinning of a truncated hemispherical shell with a cylindrical mandrel for general purposes. Table 1 Mechanical properties in uniaxial tension of the sheet metals used Material
F (MPa)
n
A1050-H A1050-O
154–159 183–189
0.050–0.057 0.23–0.26
the semi-cone angle of the product, as 0–1–2–3–0 in Fig. 2. In case of truncated hemispherical shell of outer radius R, the path of the forming roller to form the truncated hemispherical sphere with a residual flange width W is shown in Fig. 6. The tangential angle in the meridian plane of the hemispherical shell decreases gradually along the circular paths 2–3 in Fig. 6. The materials of the blank disk were commercially pure aluminum sheets, JIS A1050H and A1050-O. Assuming their stress-strain relation to be σ = Fεn in uniaxial tension, their F- and n-values are listed in Table 1. Spinning experiments were carried out at room temperature. Diamond RO10 was used as lubricant.
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Fig. 7. Experimental results for hemispherical shells with a residual flange width of 10 mm for A1050-H and A1050-O aluminum sheets.
formed. The symbols × and + in Fig. 7 denote the occurrence of wall fractures during the process due to the combination of the feed rate of the forming roller v and the radius of hemisphere R for a certain residual flange width of the product W. The triangle symbols and mean the occurrence of flange wrinkles of the product during the process. Under certain working conditions, the flange bent forward, i.e. toward the headstock of the spinning lathe. This resulted in the decrease of the outer diameter of the product with a flange. This diametral shrinkage of the product with a flange is plotted by the symbol of diamond ♦ in Fig. 7. The symbols and in Fig. 7 denote the combination of successful working conditions under which a sound hemispherical shell can be spun without any defects. 3.2. Forming limit in shear spinning
3. Results and discussion 3.1. Performance of shear spinning operation Based on the results of preliminary experiment, experiments of shear spinning of truncated hemispherical shells with a cylindrical mandrel for general purposes were carried out under various working conditions listed in Table 2. Typical experimental results under the working condition of a residual flange width of 10 mm for A1050-H and A1050-O aluminum sheets are shown in Fig. 7. The abscissa of Fig. 7 denotes the value of radius R of the hemispherical shell to be Table 2 Changeable working conditions in the spinning experiment Material
Final tangential angle θ (◦ )
Feed rate v (mm/rev)
Flange width W (mm)
A1050-H A1050-O
12.5–17.5 8–15
0.005–1.0 0.001–1.0
8–14 6–14
In case of shear spinning of truncated conical shells with a cylindrical mandrel for general purposes, it is easy to find the forming limits to prevent the occurrence of wall fractures and flange wrinkles as shown in Fig. 3. As for shear spinning of truncated hemispherical shells, it is not so easy to find the forming limits in shear spinning with a cylindrical mandrel for general purposes. Fig. 8 shows experimental results in shear spinning of hemispherical shells with a cylindrical mandrel for general purposes for A1050-H aluminum sheet. When the feed rate of the forming roller became faster, wall fractures tended to occur or flange wrinkles tended to form as shown in Fig. 8. It is found that there exist forming limits in shear spinning for A1050H aluminum sheet with a general-purpose mandrel, however, they depend on the value of the residual flange width W as in Fig. 8. On the other hand, it is not easy to find the forming limit to prevent the occurrence of wall fractures in shear spinning of hemispherical shells with a cylindrical mandrel for general purposes for A1050-O annealed aluminum sheet, as shown in Fig. 9.
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K. Kawai et al. / Journal of Materials Processing Technology 192–193 (2007) 13–17
Fig. 8. Experimental results in shear spinning of hemispherical shells for A1050H aluminum sheet.
Fig. 10. Measured outer radius of hemispherical shells with a residual flange width of 12 mm for A1050-H and A1050-O aluminum sheets.
3.3. Wall thickness distribution
A1050-O annealed aluminum sheet. This difference is due to the spring back of the product as in bending of sheet metal. When the feed rate of the forming roller increases, the outer radius of the spun product also increases as shown in Fig. 10. The wall thickness distribution of the products with a flange width of 12 mm for A1050-H and A1050-O aluminum sheets are shown in Fig. 11. The predicted thickness in Fig. 11 is given by the following equation:
In shear spinning of a truncated hemispherical shell with a general-purpose mandrel, the path of the forming roller was designed to be a circular path whose radius is equal to R + ρR , as in Fig. 6. The outer radii of spun hemispherical shells were measured at a few points. The measured results are shown in Fig. 10 for A1050-H and A1050-O aluminum sheets. In Fig. 10, the abscissa x denotes the distance from the bottom of the product and the ordinate y denotes the outer radius of axi-symmetrical shell at axial position x, respectively as in Fig. 6. The predicted radius in Fig. 10 means the designed outer radius of the product to be formed in Fig. 6. It can be shown that the outer radius of the product for A1050-H aluminum sheet is larger than that for
where t is the wall thickness of spun product, t0 the initial thickness of sheet metal blank, R the radius of hemispherical shell to be formed, and a and x are defined in Fig. 6, respectively. The
Fig. 9. Experimental results in shear spinning of hemispherical shells for A1050O annealed aluminum sheet.
Fig. 11. Distribution of the wall thickness of hemispherical shells with a residual flange width of 12 mm for A1050-H and A1050-O aluminum sheets.
t = t0
a−x R
(1)
K. Kawai et al. / Journal of Materials Processing Technology 192–193 (2007) 13–17
wall thickness of the product for A1050-H aluminum sheet is thinner than that for A1050-O annealed aluminum sheet. While the sine law is realized in shear spinning of truncated conical shells with a general-purpose mandrel as in Fig. 4, it is not realized exactly in shear spinning of truncated hemispherical shells with a general-purpose mandrel due to the spring back of the workpiece. 4. Conclusions Truncated hemispherical shells can be manufactured practically by shear spinning with a cylindrical mandrel for general purposes. However, the dimensional accuracy of the spun product in shear spinning of truncated hemispherical shells with a
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general-purpose mandrel is not so high as in shear spinning of truncated conical shells. References [1] E. Siebel, K.H. Dr¨oge, Kr¨afte und Materialsfluß beim Dr¨ucken, Werkstattstechnik und Maschinenbau, 45 (1) (1955) 6–9. [2] C.C. Wong, T.A. Dean, J. Lin, A review of spinning, shear forming and flow forming processes, Int. J. Mach. Tools Manuf. 43 (2003) 1419– 1435. [3] K. Kawai, L.-N. Yang, H. Kudo, Dieless shear spinning of truncated conical shells, in: M. Geiger (Ed.), Advanced Technology of Plasticity 1999, 2, Springer-Verlag, 1999, pp. 1089–1094. [4] K. Kawai, L.-N. Yang, H. Kudo, A flexible shear spinning of truncated conical shells with a general-purpose mandrel, J. Mater. Process. Technol. 113 (2001) 28–33.
A flexible shear spinning of axi-symmetrical shells with a general-purpose mandrel K. Kawai ∗ , L.-N. Yang, H. Kudo Department of Mechanical Engineering and Materials Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-85-1, Japan
Abstract An experimental study is conducted to survey the technological possibility of the shear spinning of truncated hemispherical shells with a cylindrical mandrel for general purposes using A1050-H and A1050-O commercially pure aluminum sheets of 1 mm thickness. It is found that there exist forming limits to prevent the occurrence of wall fractures and flange wrinkles during the spinning process of truncated hemispherical shells. It is also found that the sine law is not realized exactly in shear spinning of truncated hemispherical shells with a cylindrical mandrel for general purposes due to the spring back of the workpiece. © 2007 Elsevier B.V. All rights reserved. Keywords: Spinning; Shear spinning; Rotary forming; Flexible forming; Metal forming
1. Introduction The shear spinning process is sometimes called spin forging or shear forming in the literature. The process of shear spinning is characterized by the fact that the radial position of any element in the blank remains the same radial position during deformation. This demands that the initial thickness of the blank t0 and the final thickness of the axi-symmetrical shell tf are related by the sine law for the tangential angle in the meridian plane of the axi-symmetrical shell α: tf = t0 sin α [1]. While the recent spinning technology including conventional spinning, shear spinning and tube spinning has been reviewed elsewhere [2], it has been considered that the outer shape of the mandrel should be identical with the inner shape of the product to be formed in shear spinning. In the ordinary process of shear spinning, a mandrel whose outer shape is identical with the inner shape of the product has been used as shown in Fig. 1. On the other hand, the path of the forming roller 0–1–2–3–0 as shown in Fig. 2 can also form a conical shell supported on the end of a cylindrical mandrel that rotates with the main spindle of a spinning lathe [3]. If a workpiece has the rigidity that is sufficient to maintain the shape of shell to be formed during the process, an
∗
Corresponding author. Tel.: +81 45 339 3872; fax: +81 45 331 6593. E-mail address: [email protected] (K. Kawai).
0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.04.008
ironing process between the forming roller and the mandrel is not so essential to the shear spinning process. In other words, there is no need to use a mandrel that has an identical outer shape with the inner shape of the product to be formed if the workpiece has sufficient rigidity to maintain the shape of the shell to be formed during the process. If the path of the forming roller is controlled to satisfy the sine law corresponding to the product to be formed, various axi-symmetrical shells can be spun by a combination of a forming roller and a cylindrical mandrel for general purposes. This flexible process will be applicable to form axi-symmetrical shells of a great variety and small-batch production if various axi-symmetrical shells can be manufactured practically with a certain degree of accuracy. In the earlier papers [3,4], an experimental study was conducted to survey the technological possibility of the shear spinning of truncated conical shells with a cylindrical mandrel for general purposes. There exist forming limits to prevent the occurrence of wall fractures and flange wrinkles as shown in Fig. 3 [3]. The sine law is also realized in shear spinning of truncated conical shells with a general-purpose cylindrical mandrel as shown in Fig. 4 [4]. While a sudden change in the wall thickness is observed in Fig. 4, the thinning phenomenon of the wall thickness at an early stage of shear spinning can be prevented by the use of a non-linear path of the forming roller to allow a gradual change in the wall thickness from the initial value to the final value, as shown in Fig. 5 [4].
14
K. Kawai et al. / Journal of Materials Processing Technology 192–193 (2007) 13–17
Fig. 1. Shear spinning of a truncated conical sell with a mandrel whose outer shape is identical with the inner shape of the product.
This paper deals with an experimental study of the technological possibility of the shear spinning of truncated hemispherical shells with a general-purpose mandrel.
Fig. 3. Experimental results and forming limits for conical shells with a residual flange width of 10 mm for A1050-H aluminum sheet.
2. Experimental procedure A scheme of shear spinning of truncated conical shells with a generalpurpose mandrel is shown in Fig. 2. A circular blank disk of outer diameter D0 = 120 mm and thickness t0 = 1 mm was supported on the end of a cylindrical mandrel of outer diameter dM = 50 mm. The cylindrical mandrel rotated at a constant number of revolutions N = 187.5 rpm with the main spindle of a spinning lathe. A forming roller of outer diameter of dR = 74 mm and round-off radius of ρR = 2 mm was fixed to a tool post on an XY-table. The position of the XY-table was controlled by servomotors and ball screws. The angle δ between Y-axis of the XY-table and the centerline of the cylindrical mandrel was 50◦ . The path of the forming roller was controlled numerically by servo control units. The experimental apparatus can perform shear spinning of a truncated conical shell with a single passage of the forming roller, which satisfied the sine law according to
Fig. 4. Distribution of the wall thickness of conical shells with a residual flange width of 10 mm for A1050-O annealed aluminum sheet.
Fig. 2. Scheme of shear spinning of truncated conical shell with a cylindrical mandrel for general purposes.
Fig. 5. Distribution of the wall thickness improved by the use of a non-linear path of the forming roller for A1050-O annealed aluminum sheet.
K. Kawai et al. / Journal of Materials Processing Technology 192–193 (2007) 13–17
Fig. 6. Scheme of shear spinning of a truncated hemispherical shell with a cylindrical mandrel for general purposes. Table 1 Mechanical properties in uniaxial tension of the sheet metals used Material
F (MPa)
n
A1050-H A1050-O
154–159 183–189
0.050–0.057 0.23–0.26
the semi-cone angle of the product, as 0–1–2–3–0 in Fig. 2. In case of truncated hemispherical shell of outer radius R, the path of the forming roller to form the truncated hemispherical sphere with a residual flange width W is shown in Fig. 6. The tangential angle in the meridian plane of the hemispherical shell decreases gradually along the circular paths 2–3 in Fig. 6. The materials of the blank disk were commercially pure aluminum sheets, JIS A1050H and A1050-O. Assuming their stress-strain relation to be σ = Fεn in uniaxial tension, their F- and n-values are listed in Table 1. Spinning experiments were carried out at room temperature. Diamond RO10 was used as lubricant.
15
Fig. 7. Experimental results for hemispherical shells with a residual flange width of 10 mm for A1050-H and A1050-O aluminum sheets.
formed. The symbols × and + in Fig. 7 denote the occurrence of wall fractures during the process due to the combination of the feed rate of the forming roller v and the radius of hemisphere R for a certain residual flange width of the product W. The triangle symbols and mean the occurrence of flange wrinkles of the product during the process. Under certain working conditions, the flange bent forward, i.e. toward the headstock of the spinning lathe. This resulted in the decrease of the outer diameter of the product with a flange. This diametral shrinkage of the product with a flange is plotted by the symbol of diamond ♦ in Fig. 7. The symbols and in Fig. 7 denote the combination of successful working conditions under which a sound hemispherical shell can be spun without any defects. 3.2. Forming limit in shear spinning
3. Results and discussion 3.1. Performance of shear spinning operation Based on the results of preliminary experiment, experiments of shear spinning of truncated hemispherical shells with a cylindrical mandrel for general purposes were carried out under various working conditions listed in Table 2. Typical experimental results under the working condition of a residual flange width of 10 mm for A1050-H and A1050-O aluminum sheets are shown in Fig. 7. The abscissa of Fig. 7 denotes the value of radius R of the hemispherical shell to be Table 2 Changeable working conditions in the spinning experiment Material
Final tangential angle θ (◦ )
Feed rate v (mm/rev)
Flange width W (mm)
A1050-H A1050-O
12.5–17.5 8–15
0.005–1.0 0.001–1.0
8–14 6–14
In case of shear spinning of truncated conical shells with a cylindrical mandrel for general purposes, it is easy to find the forming limits to prevent the occurrence of wall fractures and flange wrinkles as shown in Fig. 3. As for shear spinning of truncated hemispherical shells, it is not so easy to find the forming limits in shear spinning with a cylindrical mandrel for general purposes. Fig. 8 shows experimental results in shear spinning of hemispherical shells with a cylindrical mandrel for general purposes for A1050-H aluminum sheet. When the feed rate of the forming roller became faster, wall fractures tended to occur or flange wrinkles tended to form as shown in Fig. 8. It is found that there exist forming limits in shear spinning for A1050H aluminum sheet with a general-purpose mandrel, however, they depend on the value of the residual flange width W as in Fig. 8. On the other hand, it is not easy to find the forming limit to prevent the occurrence of wall fractures in shear spinning of hemispherical shells with a cylindrical mandrel for general purposes for A1050-O annealed aluminum sheet, as shown in Fig. 9.
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K. Kawai et al. / Journal of Materials Processing Technology 192–193 (2007) 13–17
Fig. 8. Experimental results in shear spinning of hemispherical shells for A1050H aluminum sheet.
Fig. 10. Measured outer radius of hemispherical shells with a residual flange width of 12 mm for A1050-H and A1050-O aluminum sheets.
3.3. Wall thickness distribution
A1050-O annealed aluminum sheet. This difference is due to the spring back of the product as in bending of sheet metal. When the feed rate of the forming roller increases, the outer radius of the spun product also increases as shown in Fig. 10. The wall thickness distribution of the products with a flange width of 12 mm for A1050-H and A1050-O aluminum sheets are shown in Fig. 11. The predicted thickness in Fig. 11 is given by the following equation:
In shear spinning of a truncated hemispherical shell with a general-purpose mandrel, the path of the forming roller was designed to be a circular path whose radius is equal to R + ρR , as in Fig. 6. The outer radii of spun hemispherical shells were measured at a few points. The measured results are shown in Fig. 10 for A1050-H and A1050-O aluminum sheets. In Fig. 10, the abscissa x denotes the distance from the bottom of the product and the ordinate y denotes the outer radius of axi-symmetrical shell at axial position x, respectively as in Fig. 6. The predicted radius in Fig. 10 means the designed outer radius of the product to be formed in Fig. 6. It can be shown that the outer radius of the product for A1050-H aluminum sheet is larger than that for
where t is the wall thickness of spun product, t0 the initial thickness of sheet metal blank, R the radius of hemispherical shell to be formed, and a and x are defined in Fig. 6, respectively. The
Fig. 9. Experimental results in shear spinning of hemispherical shells for A1050O annealed aluminum sheet.
Fig. 11. Distribution of the wall thickness of hemispherical shells with a residual flange width of 12 mm for A1050-H and A1050-O aluminum sheets.
t = t0
a−x R
(1)
K. Kawai et al. / Journal of Materials Processing Technology 192–193 (2007) 13–17
wall thickness of the product for A1050-H aluminum sheet is thinner than that for A1050-O annealed aluminum sheet. While the sine law is realized in shear spinning of truncated conical shells with a general-purpose mandrel as in Fig. 4, it is not realized exactly in shear spinning of truncated hemispherical shells with a general-purpose mandrel due to the spring back of the workpiece. 4. Conclusions Truncated hemispherical shells can be manufactured practically by shear spinning with a cylindrical mandrel for general purposes. However, the dimensional accuracy of the spun product in shear spinning of truncated hemispherical shells with a
17
general-purpose mandrel is not so high as in shear spinning of truncated conical shells. References [1] E. Siebel, K.H. Dr¨oge, Kr¨afte und Materialsfluß beim Dr¨ucken, Werkstattstechnik und Maschinenbau, 45 (1) (1955) 6–9. [2] C.C. Wong, T.A. Dean, J. Lin, A review of spinning, shear forming and flow forming processes, Int. J. Mach. Tools Manuf. 43 (2003) 1419– 1435. [3] K. Kawai, L.-N. Yang, H. Kudo, Dieless shear spinning of truncated conical shells, in: M. Geiger (Ed.), Advanced Technology of Plasticity 1999, 2, Springer-Verlag, 1999, pp. 1089–1094. [4] K. Kawai, L.-N. Yang, H. Kudo, A flexible shear spinning of truncated conical shells with a general-purpose mandrel, J. Mater. Process. Technol. 113 (2001) 28–33.