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A new rotary forming process for rim thickening of a disc-like sheet metal part
Journal of Materials Processing Technology 212 (2012) 2247–2254
Contents lists available at SciVerse ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
A new rotary forming process for rim thickening of a disc-like sheet metal part Jun-Song Jin, Lei Deng, Xin-Yun Wang ∗ , Ju-Chen Xia State Key Lab of Material Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
a r t i c l e
i n f o
Article history: Received 4 January 2012 Received in revised form 20 June 2012 Accepted 20 June 2012 Available online 28 June 2012 Keywords: Rotary forming Disc-like part Sheet metal Thickening
a b s t r a c t A new rotary forming process used to thicken the rim of a disc-like part was proposed. The paper details the results, design and manufacture of the corresponding apparatus. The center point of a ring roller moves around the axis of a stationary work-piece in a plane spiral locus, like a rounding hula hoop. Thereby, the rim of stationary work-piece is rolled and thickened. A design rule for the rotary thickening process of the disc-like part was proposed, and a formula for calculating the feeding force of the roller was deduced. Both the design rule and the formula were verified by the results of experiment and finite element simulation. The forming and flow law during the thickening process were also illustrated. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The rotary forming process of sheet metal is widely used to manufacture components for automotive, aerospace, and other industries. As one of the important rotary forming processes for sheet metal parts, spinning is normally divided into conventional spinning, shear spinning, and tube spinning. Components made by spinning always possess the feature of a hollow and axial symmetric structure. Musica et al. (2010) stated that the main difference among them is the wall thickness of the formed part. The wall thickness remains nearly constant throughout the process in conventional spinning. In contrast, the wall thickness decreases in shear and tube spinning. The decrease in value is decided by the angle between the wall of the component and the axis of rotation in shear spinning, or, by the increase in the length of the work-piece in tube spinning. Since a specific mandrel is required for each product in the normal spinning process, some flexible spinning processes have been developed. Kitazawa et al. (1994) investigated the mandrel-free spinning of pre-formed shells. In this process, a rotating preformed sheet was clamped around the rim instead of centrally. A cylinder tool could therefore form the part from both sides. Matsubara (2001) proposed a method to clamp the blank, both in the center and around the blank rim. The rim blank holder could move in an axial direction during the forming process. Shima et al. (1997) replaced the mandrel by an inner roller, where the inner roller was opposite the outer roller, and the two rollers moved together to
∗ Corresponding author. Tel.: +86 27 87543491; fax: +86 27 87543491. E-mail address: wangxy [email protected] (X.-Y. Wang). 0924-0136/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2012.06.013
form the work-piece. Kawai et al. (2007) developed a mandrel free configuration to produce hemispherical parts, in which the sheet is clamped in the center, but the work-pieces did not touch the mandrel during the forming process. In recent years, ball spinning, using balls instead of rollers as the deformation tool, was developed to form tube parts. Zhang et al. (2005) introduced a new CNC ball spinning machine. The main difference between the new machine and other ball spinning machines is that the rolling balls in the machine can be forced to move in a radial direction to shape tube work-pieces according to CNC programs. Jiang et al. (2009) investigated the influence of the ball size on the deformability of backward ball spinning processes for thin-walled tubular parts with longitudinal inner ribs by FEM and experiments. Rotarescu (1995) gave a theoretical analysis of the variation of deformation zone geometry, contact surface, forming force, and torsion moments. Huang et al. (2008) used a 3D-FE method to investigate the influence of material parameters on the splitting spinning process of aluminum alloy and determined the relationship of the material parameters, forming force and deviation of part shape. Huang et al. (2009) also studied the forming characteristics based on the behaviors of the roller and obtained the relationship between continuous feed conditions and feed amount of the roller for splitting spinning. Awiszus and Meyer (2005) investigated asymmetric spinning to produce triangular parts. Awiszus and Härtel (2011) presented an FEM model for the non-circular spinning process using motion controlled roller tools and compared the model to the experimental results of “Tripode” part and “Pagoda” part. Amano and Tamura (1984) used a radically offset roller on a modified spinning lathe to form elliptical parts. Gao et al. (1999) proposed a spinning process by offsetting the mandrel instead of the roller to produce elliptical
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Fig. 1. Schematic of rotary forming apparatus.
parts. Xia et al. (2008) studied the spinning process without a mandrel to form a non-straight axle tube part. One of the common features of the forming processes mentioned above is that the work-piece actively rotates whilst the tooling rotates passively. Another feature is that the forming zone of the work-piece contacts the outer profiled surface of the tooling. A further, and the most important feature is that the thickness of the parts is kept nearly constant, or is smaller than that of the initial blank. So far, the literature regarding the spinning of thickening sheet metal is sparse. Thus, a new rotary forming process is proposed for thickening sheet metal. The work-piece part in this paper is a disk with a higher rim thickness. Conventionally, these kinds of parts are assembled by welding several components of different thickness together. The disadvantages of the welding assembly process are the low material utilization ratio and productivity, and the reduced mechanical properties. Furthermore, with the increasing demands for lightweight products and usage properties, this kind of part is required to be formed integrally with the plastic forming. The proposed process could perfectly satisfy the lightweight products requirement, have better usage properties, and overcome the disadvantages of the conventional method.
In this paper, the authors present the new rotary forming method. The corresponding apparatus is designed and manufactured to form these kinds of parts.
2. Structure and principle of the apparatus 2.1. Apparatus structure and working operation The essential elements of the proposed rotary apparatus are shown in Fig. 1 and Table 1. The magnified and exploded threedimensional view of the dies is shown in Fig. 2. The top hydraulic cylinder (1) is fixed on the top cross-beam (3). The piston (4) of the top hydraulic cylinder connects the movable cross-beam (5), and they move up and down together. The piston (16), fastened together with the upper spindle (17), is installed in the piston (4), and can move up and down, relative to each other. The lower spindle (28) is fixed on the base-plate (27). The rotary die seat (24) is installed outside of the spindle (28), and is restricted to an axial rotation by a ball bearing (25) and a roller bearing (26). The detailed sequence of action of the proposed apparatus during rotary forming is as follows.
J.-S. Jin et al. / Journal of Materials Processing Technology 212 (2012) 2247–2254
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Table 1 List of the components of the rotary forming apparatus. Part no.
Part name
Part no.
Part name
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hydro cylinder body Hydraulic liquid Top cross-beam Piston Movable cross-beam Stand beam Load transfer beam Spring Driven gear Driving gear Electromotor Piston Hydro cylinder body Hydraulic liquid Hydraulic liquid
16 17 18 19 20 21 22 23 24 25 26 27 28 29
Piston Upper spindle Blank Ring roller Bolster plate Ball Wedge Sliding die seat Rotary die seat Ball bearing Roller bearing Base-plate Lower spindle Ejector
Firstly, the disc blank (18) with a pre-punched center hole is positioned by the ejector (29), and clamped by the lower spindle (28) and the upper spindle (17). Secondly, the electromotor (11) starts to drive the rotary die seat (24), the sliding die seat (23) and the ring roller (19) to rotate together. Thirdly, the load transfer beam (7) pushes the wedge (22) to drive the sliding die seat (23) and ring roller (19), sliding inside the rotary die seat (24). Thereby, the ring roller (19) shows a plane spiral locus motion. Fourthly, the moving ring roller (19) deforms the rim of the disc blank (18) incrementally. The required disc-like part with a thickened rim is obtained. Finally, the ejector (29) moves upwards to eject the part, and the working step finishes. If the expected rim thickness value could not be obtained in one forming step, a multi-step thickening process will be performed.
As shown in Fig. 3, A and O are the initial and current contact points between the work-piece and the ring roller, respectively. Ob is the center point of the work-piece; ϕ is the angular displacement of the ring roller. In coordinate system x O y , the coordinates of the ring roller center point Or can be expressed as: xo r = −Rr yo r = 0
In coordinate system xOb y, the coordinates of point O can be expressed as:
⎧ ϕ ⎪ ⎨ xo = Rb − 2 cos ϕ ⎪ ϕ ⎩ sin ϕ yo = Rb −
(2)
2
2.2. Locus equation of the ring roller
Fig. 3. Motion of the roller.
(1)
where Rr is the inner groove radius of the roller.
where Rb is the radii of the work-piece, is the radial feed value per cycle. After the coordinate transformation, the coordinates of point Or in a coordinate system xOb y can be expressed as:
⎧ ϕ ⎪ ⎨ xor = Rb − Rr − 2 cos ϕ ⎪ ⎩ yo = Rb − Rr − ϕ sin ϕ r
(3)
2
According to Eq. (3), the locus of point Or is a uniform plane spiral. 3. Process design and feeding force calculation The following calculation is based on the assumption of plane deformation, that is, the meridian plane of the work-piece is kept planar during the forming process. Then, the deformation can be treated as a process of axisymmetric radial compression. 3.1. Design of multi-step thickening process
Fig. 2. Die set and its exploded view. (18) Blank, (19) ring roller, (23) sliding die seat and (24) rotary die seat.
In the rotary thickening process, the thickening ratio was defined as = tN /tN−1 . Jin et al. (2011) point out that the thickening ratio should be less than 1.4 in a single step thickening. If ≥ 1.4, the thickening process will be unstable and cause folding defect. In a multi-step forming, the thickness of the rim tn after the nth thickening step is a key design parameter, which is crucial to the roller design and success of the process. Assuming
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Fig. 4. The four step thickening process.
Fig. 5. Shape of ring roller.
that the average strain in each forming step is equivalent, there is ln(t1 /t0 ) = . . . = ln(tN /tN−1 ). It equals to n/N N−n t0
tn = tN
(4)
where N is the total number of forming steps, n is the number of forming step, 1 ≤ n ≤ N. Fig. 4e shows a disk like part whose is 9.5 mm rim thickness and rib thickness is 3 mm. Because of 3 9.5/3 > 1.4 > 4 9.5/3, a four-step thickening process was designed. The average thickness of the rim in each step was given by Eq. (4). The designed shape of the work-piece in each step is shown in Fig. 4. Correspondingly, the dies were designed and are shown in Fig. 5. Two angular parameters, c1 and c2 were designed between the groove walls and middle plane, and a fillet with r1 was created to avoid scratching of the work-piece. The parameter values of the tooling are given in Table 2.
3.2. Calculation of the feeding force The feeding force is a key factor in the forming process, it is critical to the choice and design of the apparatus capacity. An analytical model for calculating the forming forces is very useful, especially when fast prediction of forming force is required. As shown in Fig. 6, the final filled zone is the corner formed by roller, spindles and work-piece, in the forming process. A small sector body with a thickness of one unit is analyzed to calculate the feeding force with the main stress method. According to Fig. 6, the force equilibrium equation of the small sector body in direction is (2 + h)d × 1 + ( + d )h × 1 − h × 1 = 0
By substituting the boundary condition = 1 , = 0 plasticity condition − r = s = 2, and integrating r along the cylinder face, the mean feeding force f on the body with thickness of one unit can be expressed as:
f =
Table 2 Values of die dimension.
1
r cos d = s
m m m m1 + · sin 1 − sin 1 − · sin 1 − · cos 1 2 2 2 2
0
Step no.
a
b1
c1
c2
r1
r2
1 2 3 4
1.5 1.5 1.5 1.5
4.00 5.34 7.12 9.50
4 4 4 4
5 5 5 5
0.5 0.5 0.5 0.5
1.5 2.0 2.6 0
d 21 16.5 12.5 9
(5)
(6)
a2 + b2 , = (w − where m = −(2 + h)/h, 1 = tan−1 (a/b), h = a)h/a. h is the width of the sector body in a radial direction, and r are stresses in tangential and radial directions, respectively. s is the tensile, is the shear yield stresses.
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Fig. 6. Sketch of main stress on sector unit body.
Fig. 7 shows the compressed zone of the work-piece, the total feeding force F can be expressed as:
F=
l
fdt = s
m m m m1 + · sin 1 − sin 1 − · sin 1 − · cos 1 l 2 2 2 2
(7)
0
where Rr and Rw are the radius of the roller groove and final workpiece, respectively. The radii of the work-piece before the last circle is Rw + , the length of contacted zone is l ≈ Rb ˇ. The angle of compressed zone, ˇ, can be expressed as: ˇ = 180 − cos−1
2(Rw − )(Rw − Rr ) + 2 2Rw (Rr − Rw ) + 2Rw 2
(8)
4. Finite element analysis (FEA)
same size as the spindles. A solid brick element with reduced integration points was employed to divide the work-piece into elements, and the ALE adaptive mesh method was adopted to remesh the large deformed area during the process (Huang et al., 2008). The initial thickness of the blank is 3 mm, and the outer diameter is 326 mm. The material parameters of ANSI 1045 steel were obtained from the results of the testing experiment carried out on the GLEEBLE 3500 material testing machine at room temperature. The compressed strain rate is 0.1/s, 0.5/s and 2/s and the Young’s modulus is 2.1 × 105 MPa. The difference in the stress–strain curve at different strain rate is slight, so the effect of strain rate was ignored. The parameters of the unified constitutive equation = C ε¯ n are C = 1019.7 MPa and n = 0.11, respectively. The roller shape and dimension is shown in Fig. 5 and Table 2.
4.1. Elastic–plastic FEA model 4.2. Boundary conditions The commercial software Abaqus/explicit was used to analyze the proposed rotary forming process. The finite element analysis model was constructed as shown in Fig. 8. The toolings were set as analytical rigid bodies, and the work-piece was set as an elasticplastic body. Considering that no deformation was allowed for in the center portion of the work-piece where it was clamped by the spindles, the blank was modeled to be a ring to reduce the simulation time. The inner diameter of the ring is 272 mm, the
As shown in Fig. 8, the reference point C1 of the work-piece and the two spindles were fixed. The ring roller center, C2 rotated around point C1 with angular velocity ω = 6.28 rad/s and translated −−−→ in C1 C2 direction with a velocity v = 0.05 mm/s to maintain the roller center moving along a path described by Eq. (3). The translational freedoms in the z direction and rotational freedoms about coordinate x-axis and y-axis were constrained for point C2 . The
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Fig. 9. The work-piece in each step.
a capacity of 2000 kN. The tooling action was controlled by a PLC unit. The groove of the ring roller was heat-treated to a hardness of HRC 58-62, and polished to a surface roughness of 0.4 m. A center hole was pre-punched in the sheet blank to be in position with the ejector. The clamping force was set to be 500 kN during the rotary forming process. Graphite emulsion was used as a lubricant and for cooling. Fig. 7. Sketch of compressed zone.
6. Results and discussion Coulomb law with a friction coefficient of 0.12 was used to describe the frictional behaviors among the work-piece and toolings. 5. Experimental setup Using the FEA results, a four-step forming experiment was performed on the rotary forming apparatus mentioned previously with
Fig. 8. Finite element model and schematic movement of the objects.
6.1. Forming process Fig. 9 shows the formed work-pieces at each step. In the position shown in Fig. 6, the simulated forming process and comparison of the final shape between FEA and experiments in each step are shown in Fig. 10. According to Fig. 10, both step one and step two can be divided into two forming stages. In the first stage, the blank rim was compressed by the roller in a radial direction until its lateral surface was fully in contact with the groove bottom as shown in Fig. 10b and f, respectively. In the second stage, the rim was thickened gradually from the lateral side to the inner side, as shown in Fig. 10c and g, respectively. Comparing Fig. 10d with q, and Fig. 10h with r, the rim width and thickness of the final section shapes of the simulation showed significant agreement with those in the experiments. The only difference between the simulated data and experimental results is that during the experiments, a small flash formed in the gaps between the spindles and ring roller (shown in enlarged views I and II of Fig. 10). However, no flash occurred in the simulation. According to Fig. 10, both step three and step four can be divided into three forming stages. The deformation of stage one is similar to that of the first stage in the former two steps. In the second stage, the rim was thickened until its upper surface contacted the groove wall, as indicated in Fig. 10k and o. In the third stage, the lower surface of the rim contacted the groove wall gradually, from the lateral side to the inner side. The final section shapes are shown in Fig. 10l and p, respectively. Comparing Fig. 10l with s, and Fig. 10p with t, the rim width and thickness of the final section shapes in the simulation showed significant agreement with those in the experiments. In these two steps, flashes were formed in both experiments (shown in enlarged views VI and VI of Fig. 10) and simulation results (shown in enlarged views III and V of Fig. 10).
J.-S. Jin et al. / Journal of Materials Processing Technology 212 (2012) 2247–2254
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Fig. 10. The forming process in FEA and the sectional results of experiments.
According to the forming results of the FEA and experiments, it proves that the proposed new process and the design rule based on Eq. (4) in Section 3.1 is feasible to thicken the rim of disk-like parts.
6.2. Feeding force Fig. 11 shows the simulated force–displacement curves during the rotary forming process. Meanwhile, the triangles mark the experimental force in each step, and the quadrangles indicate the calculated force from Eq. (7), whose parameters a = 1.7 and b = 1.8, in step three, and a = 1.1 and b = 1.2, in step four, are illustrated in an enlarged views of VIII and IX of Fig. 10, respectively. The curves
of step one and step two can be divided into two stages, according to the slope, which corresponds to the two forming stages of step one and step two in Fig. 10. The curves of step three and step four can also be divided into three stages, according to the slope, which corresponds to the three forming stages of step three and step four in Fig. 10. According to Fig. 11, the final feeding force of the experiment is 8.55% higher than that of the simulation in step one, 4.96% higher than that of the simulation in step two, 5.22% higher in step three, and 4.33% higher in step four. The feeding force, in step three and step four, calculated by Eq. (7) were 41.8 kN and 119.4 kN, respectively. The calculated value is only 46.1% of the experimental value and 48.5% of the simulation in step three, and 101.2%
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3) A design rule for multi-step thickening for disc-like parts was proposed, which can provide an initial experimental process design. FEA and experimental results showed that the rim of a disc-like part can be thickened successfully by using the proposed rule. Acknowledgments The research was supported by the NCET-11-0185 and ‘the Fundamental Research funds for the Central Universities’ (HUST: No. 2010MS095). The authors gratefully extend their acknowledgements to Hubei Tri-ring metal forming equipment Co. Ltd. for manufacturing the equipment. References Fig. 11. Feeding force versus displacement.
of the experimental value and 105.6% of the simulation in step four. In step one and step two, no small corner was finally formed (see Fig. 10q and r), which does not match the assumptive conditions of Eq. (7), therefore the feeding force could not be calculated. In step three, due to the formation of a big round corner as shown in Fig. 10s, the principle stress assumptions of the main stress method were not satisfied. Therefore the feeding force showed a large difference between the experimental and FEA results when calculated by Eq. (7). In step four, the calculated feeding force is nearly the same as that shown by experiment and simulation. It indicates that Eq. (7) can be reasonably used to calculate the final feeding force. The key point in using this equation is to obtain the values of a and b. In fact, we could assume that a equals b, and set the value to be the allowable radii of the required parts. For example, in step four in this experiment, the final allowable radii is 1.2 mm, so there is a = b = 1.2. The force calculated by Eq. (7) was 114.3 kN, which is only 4.3% lower than that calculated with a = 1.1 and b = 1.2. Based on the results and analysis above, the calculated feeding force by Eq. (7) shows significant agreement with that of the FEA and experiment, when the small corner is formed on the workpiece. The equation is therefore reasonable. 7. Conclusions 1) A new rotary forming process used to thicken the rim portion of a disc-like part was proposed, and the corresponding apparatus was also designed and manufactured. The presented rotary forming process was tested by experiment and FEA. 2) A formula for calculating the feeding force was deduced and FEA and experimental results proved the rationality in the prediction of the feeding force according to the given assumptions.
Amano, T., Tamura, K., 1984. The study of an elliptical cone spinning by the trial equipment. In: Proceedings of the Third International Conference on Rotary Metalworking Processes, 8–10 September, Kyoto, Japan, pp. 213–224. Awiszus, B., Meyer, F., 2005. Metal spinning of non-circular hollow parts. In: 8th International Conference on Technology of Plasticity, Italy, October 9–13. Awiszus, B., Härtel, S., 2011. Numerical simulation of non-circular spinning: a rotationally non-symmetric spinning process. Production Engineering 5, 605–612. Gao, X.C., Kang, D.C., Meng, X.F., Wu, H.J., 1999. Experimental research on a new technology – ellipse spinning. Journal of Materials Processing Technology 94, 197–200. Huang, L., Yang, H., Zhan, M., Hu, L.J., 2008. Numerical simulation of influence of material parameters on splitting spinning of aluminum alloy. Transactions of Nonferrous Metals Society of China 18, 674–681. Huang, L., Yang, H., Zhan, M., Hu, L.J., 2009. Forming characteristics of splitting spinning based on the behaviors of roller. Computational Materials Science 45, 449–461. Jiang, S.Y., Ren, Z.Y., Li, C.F., Xue, K.M., 2009. Role of ball size in backward ball spinning of thin-walled tubular part with longitudinal inner ribs. Journal of Materials Processing Technology 209, 2167–2174. Jin, J.S., Xia, J.C., Wang, X.Y., Deng, L., 2011. A new process of thickening sheet metal by spinning. In: Proceedings of the 12th National Conference on Technology of Plasticity, 8–10 August, Chongqing, China, pp. 56–58. Kawai, K., Yang, L.N., Kudo, H., 2007. A flexible shear spinning of axi-symmetrical shells with a general-purpose mandrel. Journal of Materials Processing Technology 192–193, 13–17. Kitazawa, K., Wakabayashi, A., Murata, K., Seino, J., 1994. A CNC incremental sheet metal forming method for producing the shell components having sharp components. Journal of the Japan Society for Technology of Plasticity 35 (406), 1348–1353. Matsubara, S., 2001. A computer numerically controlled dieless incremental forming of a sheet metal. Proceedings of the Institution of Mechanical Engineers Part B. Journal of Engineering Manufacture 215 (7), 959–966. Musica, O., Allwood, J.M., Kawai, K., 2010. A review of the mechanics of metal spinning. Journal of Materials Processing Technology 210, 3–23. Rotarescu, M.I., 1995. A theoretical analysis of tube spinning using balls. Journal of Materials Processing Technology 54, 224–229. Shima, S., Kotera, H., Murakami, H., 1997. Development of flexible spin-forming method. Journal of the Japan Society for Technology of Plasticity 38 (440), 814–818. Xia, Q.X., Xie, S.W., Huo, Y.L., Ruan, F., 2008. Numerical simulation and experimental research on the multi-pass neck-spinning of non-axisymmetric offset tube. Journal of Materials Processing Technology 206, 500–508. Zhang, S.H., Li, M.S., Xu, Y., Kang, D.C., Li, C.Z., 2005. Introduction to a new CNC ballspinning machine. Journal of Materials Processing Technology 170, 112–114.
Contents lists available at SciVerse ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
A new rotary forming process for rim thickening of a disc-like sheet metal part Jun-Song Jin, Lei Deng, Xin-Yun Wang ∗ , Ju-Chen Xia State Key Lab of Material Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
a r t i c l e
i n f o
Article history: Received 4 January 2012 Received in revised form 20 June 2012 Accepted 20 June 2012 Available online 28 June 2012 Keywords: Rotary forming Disc-like part Sheet metal Thickening
a b s t r a c t A new rotary forming process used to thicken the rim of a disc-like part was proposed. The paper details the results, design and manufacture of the corresponding apparatus. The center point of a ring roller moves around the axis of a stationary work-piece in a plane spiral locus, like a rounding hula hoop. Thereby, the rim of stationary work-piece is rolled and thickened. A design rule for the rotary thickening process of the disc-like part was proposed, and a formula for calculating the feeding force of the roller was deduced. Both the design rule and the formula were verified by the results of experiment and finite element simulation. The forming and flow law during the thickening process were also illustrated. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The rotary forming process of sheet metal is widely used to manufacture components for automotive, aerospace, and other industries. As one of the important rotary forming processes for sheet metal parts, spinning is normally divided into conventional spinning, shear spinning, and tube spinning. Components made by spinning always possess the feature of a hollow and axial symmetric structure. Musica et al. (2010) stated that the main difference among them is the wall thickness of the formed part. The wall thickness remains nearly constant throughout the process in conventional spinning. In contrast, the wall thickness decreases in shear and tube spinning. The decrease in value is decided by the angle between the wall of the component and the axis of rotation in shear spinning, or, by the increase in the length of the work-piece in tube spinning. Since a specific mandrel is required for each product in the normal spinning process, some flexible spinning processes have been developed. Kitazawa et al. (1994) investigated the mandrel-free spinning of pre-formed shells. In this process, a rotating preformed sheet was clamped around the rim instead of centrally. A cylinder tool could therefore form the part from both sides. Matsubara (2001) proposed a method to clamp the blank, both in the center and around the blank rim. The rim blank holder could move in an axial direction during the forming process. Shima et al. (1997) replaced the mandrel by an inner roller, where the inner roller was opposite the outer roller, and the two rollers moved together to
∗ Corresponding author. Tel.: +86 27 87543491; fax: +86 27 87543491. E-mail address: wangxy [email protected] (X.-Y. Wang). 0924-0136/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2012.06.013
form the work-piece. Kawai et al. (2007) developed a mandrel free configuration to produce hemispherical parts, in which the sheet is clamped in the center, but the work-pieces did not touch the mandrel during the forming process. In recent years, ball spinning, using balls instead of rollers as the deformation tool, was developed to form tube parts. Zhang et al. (2005) introduced a new CNC ball spinning machine. The main difference between the new machine and other ball spinning machines is that the rolling balls in the machine can be forced to move in a radial direction to shape tube work-pieces according to CNC programs. Jiang et al. (2009) investigated the influence of the ball size on the deformability of backward ball spinning processes for thin-walled tubular parts with longitudinal inner ribs by FEM and experiments. Rotarescu (1995) gave a theoretical analysis of the variation of deformation zone geometry, contact surface, forming force, and torsion moments. Huang et al. (2008) used a 3D-FE method to investigate the influence of material parameters on the splitting spinning process of aluminum alloy and determined the relationship of the material parameters, forming force and deviation of part shape. Huang et al. (2009) also studied the forming characteristics based on the behaviors of the roller and obtained the relationship between continuous feed conditions and feed amount of the roller for splitting spinning. Awiszus and Meyer (2005) investigated asymmetric spinning to produce triangular parts. Awiszus and Härtel (2011) presented an FEM model for the non-circular spinning process using motion controlled roller tools and compared the model to the experimental results of “Tripode” part and “Pagoda” part. Amano and Tamura (1984) used a radically offset roller on a modified spinning lathe to form elliptical parts. Gao et al. (1999) proposed a spinning process by offsetting the mandrel instead of the roller to produce elliptical
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Fig. 1. Schematic of rotary forming apparatus.
parts. Xia et al. (2008) studied the spinning process without a mandrel to form a non-straight axle tube part. One of the common features of the forming processes mentioned above is that the work-piece actively rotates whilst the tooling rotates passively. Another feature is that the forming zone of the work-piece contacts the outer profiled surface of the tooling. A further, and the most important feature is that the thickness of the parts is kept nearly constant, or is smaller than that of the initial blank. So far, the literature regarding the spinning of thickening sheet metal is sparse. Thus, a new rotary forming process is proposed for thickening sheet metal. The work-piece part in this paper is a disk with a higher rim thickness. Conventionally, these kinds of parts are assembled by welding several components of different thickness together. The disadvantages of the welding assembly process are the low material utilization ratio and productivity, and the reduced mechanical properties. Furthermore, with the increasing demands for lightweight products and usage properties, this kind of part is required to be formed integrally with the plastic forming. The proposed process could perfectly satisfy the lightweight products requirement, have better usage properties, and overcome the disadvantages of the conventional method.
In this paper, the authors present the new rotary forming method. The corresponding apparatus is designed and manufactured to form these kinds of parts.
2. Structure and principle of the apparatus 2.1. Apparatus structure and working operation The essential elements of the proposed rotary apparatus are shown in Fig. 1 and Table 1. The magnified and exploded threedimensional view of the dies is shown in Fig. 2. The top hydraulic cylinder (1) is fixed on the top cross-beam (3). The piston (4) of the top hydraulic cylinder connects the movable cross-beam (5), and they move up and down together. The piston (16), fastened together with the upper spindle (17), is installed in the piston (4), and can move up and down, relative to each other. The lower spindle (28) is fixed on the base-plate (27). The rotary die seat (24) is installed outside of the spindle (28), and is restricted to an axial rotation by a ball bearing (25) and a roller bearing (26). The detailed sequence of action of the proposed apparatus during rotary forming is as follows.
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Table 1 List of the components of the rotary forming apparatus. Part no.
Part name
Part no.
Part name
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hydro cylinder body Hydraulic liquid Top cross-beam Piston Movable cross-beam Stand beam Load transfer beam Spring Driven gear Driving gear Electromotor Piston Hydro cylinder body Hydraulic liquid Hydraulic liquid
16 17 18 19 20 21 22 23 24 25 26 27 28 29
Piston Upper spindle Blank Ring roller Bolster plate Ball Wedge Sliding die seat Rotary die seat Ball bearing Roller bearing Base-plate Lower spindle Ejector
Firstly, the disc blank (18) with a pre-punched center hole is positioned by the ejector (29), and clamped by the lower spindle (28) and the upper spindle (17). Secondly, the electromotor (11) starts to drive the rotary die seat (24), the sliding die seat (23) and the ring roller (19) to rotate together. Thirdly, the load transfer beam (7) pushes the wedge (22) to drive the sliding die seat (23) and ring roller (19), sliding inside the rotary die seat (24). Thereby, the ring roller (19) shows a plane spiral locus motion. Fourthly, the moving ring roller (19) deforms the rim of the disc blank (18) incrementally. The required disc-like part with a thickened rim is obtained. Finally, the ejector (29) moves upwards to eject the part, and the working step finishes. If the expected rim thickness value could not be obtained in one forming step, a multi-step thickening process will be performed.
As shown in Fig. 3, A and O are the initial and current contact points between the work-piece and the ring roller, respectively. Ob is the center point of the work-piece; ϕ is the angular displacement of the ring roller. In coordinate system x O y , the coordinates of the ring roller center point Or can be expressed as: xo r = −Rr yo r = 0
In coordinate system xOb y, the coordinates of point O can be expressed as:
⎧ ϕ ⎪ ⎨ xo = Rb − 2 cos ϕ ⎪ ϕ ⎩ sin ϕ yo = Rb −
(2)
2
2.2. Locus equation of the ring roller
Fig. 3. Motion of the roller.
(1)
where Rr is the inner groove radius of the roller.
where Rb is the radii of the work-piece, is the radial feed value per cycle. After the coordinate transformation, the coordinates of point Or in a coordinate system xOb y can be expressed as:
⎧ ϕ ⎪ ⎨ xor = Rb − Rr − 2 cos ϕ ⎪ ⎩ yo = Rb − Rr − ϕ sin ϕ r
(3)
2
According to Eq. (3), the locus of point Or is a uniform plane spiral. 3. Process design and feeding force calculation The following calculation is based on the assumption of plane deformation, that is, the meridian plane of the work-piece is kept planar during the forming process. Then, the deformation can be treated as a process of axisymmetric radial compression. 3.1. Design of multi-step thickening process
Fig. 2. Die set and its exploded view. (18) Blank, (19) ring roller, (23) sliding die seat and (24) rotary die seat.
In the rotary thickening process, the thickening ratio was defined as = tN /tN−1 . Jin et al. (2011) point out that the thickening ratio should be less than 1.4 in a single step thickening. If ≥ 1.4, the thickening process will be unstable and cause folding defect. In a multi-step forming, the thickness of the rim tn after the nth thickening step is a key design parameter, which is crucial to the roller design and success of the process. Assuming
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Fig. 4. The four step thickening process.
Fig. 5. Shape of ring roller.
that the average strain in each forming step is equivalent, there is ln(t1 /t0 ) = . . . = ln(tN /tN−1 ). It equals to n/N N−n t0
tn = tN
(4)
where N is the total number of forming steps, n is the number of forming step, 1 ≤ n ≤ N. Fig. 4e shows a disk like part whose is 9.5 mm rim thickness and rib thickness is 3 mm. Because of 3 9.5/3 > 1.4 > 4 9.5/3, a four-step thickening process was designed. The average thickness of the rim in each step was given by Eq. (4). The designed shape of the work-piece in each step is shown in Fig. 4. Correspondingly, the dies were designed and are shown in Fig. 5. Two angular parameters, c1 and c2 were designed between the groove walls and middle plane, and a fillet with r1 was created to avoid scratching of the work-piece. The parameter values of the tooling are given in Table 2.
3.2. Calculation of the feeding force The feeding force is a key factor in the forming process, it is critical to the choice and design of the apparatus capacity. An analytical model for calculating the forming forces is very useful, especially when fast prediction of forming force is required. As shown in Fig. 6, the final filled zone is the corner formed by roller, spindles and work-piece, in the forming process. A small sector body with a thickness of one unit is analyzed to calculate the feeding force with the main stress method. According to Fig. 6, the force equilibrium equation of the small sector body in direction is (2 + h)d × 1 + ( + d )h × 1 − h × 1 = 0
By substituting the boundary condition = 1 , = 0 plasticity condition − r = s = 2, and integrating r along the cylinder face, the mean feeding force f on the body with thickness of one unit can be expressed as:
f =
Table 2 Values of die dimension.
1
r cos d = s
m m m m1 + · sin 1 − sin 1 − · sin 1 − · cos 1 2 2 2 2
0
Step no.
a
b1
c1
c2
r1
r2
1 2 3 4
1.5 1.5 1.5 1.5
4.00 5.34 7.12 9.50
4 4 4 4
5 5 5 5
0.5 0.5 0.5 0.5
1.5 2.0 2.6 0
d 21 16.5 12.5 9
(5)
(6)
a2 + b2 , = (w − where m = −(2 + h)/h, 1 = tan−1 (a/b), h = a)h/a. h is the width of the sector body in a radial direction, and r are stresses in tangential and radial directions, respectively. s is the tensile, is the shear yield stresses.
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Fig. 6. Sketch of main stress on sector unit body.
Fig. 7 shows the compressed zone of the work-piece, the total feeding force F can be expressed as:
F=
l
fdt = s
m m m m1 + · sin 1 − sin 1 − · sin 1 − · cos 1 l 2 2 2 2
(7)
0
where Rr and Rw are the radius of the roller groove and final workpiece, respectively. The radii of the work-piece before the last circle is Rw + , the length of contacted zone is l ≈ Rb ˇ. The angle of compressed zone, ˇ, can be expressed as: ˇ = 180 − cos−1
2(Rw − )(Rw − Rr ) + 2 2Rw (Rr − Rw ) + 2Rw 2
(8)
4. Finite element analysis (FEA)
same size as the spindles. A solid brick element with reduced integration points was employed to divide the work-piece into elements, and the ALE adaptive mesh method was adopted to remesh the large deformed area during the process (Huang et al., 2008). The initial thickness of the blank is 3 mm, and the outer diameter is 326 mm. The material parameters of ANSI 1045 steel were obtained from the results of the testing experiment carried out on the GLEEBLE 3500 material testing machine at room temperature. The compressed strain rate is 0.1/s, 0.5/s and 2/s and the Young’s modulus is 2.1 × 105 MPa. The difference in the stress–strain curve at different strain rate is slight, so the effect of strain rate was ignored. The parameters of the unified constitutive equation = C ε¯ n are C = 1019.7 MPa and n = 0.11, respectively. The roller shape and dimension is shown in Fig. 5 and Table 2.
4.1. Elastic–plastic FEA model 4.2. Boundary conditions The commercial software Abaqus/explicit was used to analyze the proposed rotary forming process. The finite element analysis model was constructed as shown in Fig. 8. The toolings were set as analytical rigid bodies, and the work-piece was set as an elasticplastic body. Considering that no deformation was allowed for in the center portion of the work-piece where it was clamped by the spindles, the blank was modeled to be a ring to reduce the simulation time. The inner diameter of the ring is 272 mm, the
As shown in Fig. 8, the reference point C1 of the work-piece and the two spindles were fixed. The ring roller center, C2 rotated around point C1 with angular velocity ω = 6.28 rad/s and translated −−−→ in C1 C2 direction with a velocity v = 0.05 mm/s to maintain the roller center moving along a path described by Eq. (3). The translational freedoms in the z direction and rotational freedoms about coordinate x-axis and y-axis were constrained for point C2 . The
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Fig. 9. The work-piece in each step.
a capacity of 2000 kN. The tooling action was controlled by a PLC unit. The groove of the ring roller was heat-treated to a hardness of HRC 58-62, and polished to a surface roughness of 0.4 m. A center hole was pre-punched in the sheet blank to be in position with the ejector. The clamping force was set to be 500 kN during the rotary forming process. Graphite emulsion was used as a lubricant and for cooling. Fig. 7. Sketch of compressed zone.
6. Results and discussion Coulomb law with a friction coefficient of 0.12 was used to describe the frictional behaviors among the work-piece and toolings. 5. Experimental setup Using the FEA results, a four-step forming experiment was performed on the rotary forming apparatus mentioned previously with
Fig. 8. Finite element model and schematic movement of the objects.
6.1. Forming process Fig. 9 shows the formed work-pieces at each step. In the position shown in Fig. 6, the simulated forming process and comparison of the final shape between FEA and experiments in each step are shown in Fig. 10. According to Fig. 10, both step one and step two can be divided into two forming stages. In the first stage, the blank rim was compressed by the roller in a radial direction until its lateral surface was fully in contact with the groove bottom as shown in Fig. 10b and f, respectively. In the second stage, the rim was thickened gradually from the lateral side to the inner side, as shown in Fig. 10c and g, respectively. Comparing Fig. 10d with q, and Fig. 10h with r, the rim width and thickness of the final section shapes of the simulation showed significant agreement with those in the experiments. The only difference between the simulated data and experimental results is that during the experiments, a small flash formed in the gaps between the spindles and ring roller (shown in enlarged views I and II of Fig. 10). However, no flash occurred in the simulation. According to Fig. 10, both step three and step four can be divided into three forming stages. The deformation of stage one is similar to that of the first stage in the former two steps. In the second stage, the rim was thickened until its upper surface contacted the groove wall, as indicated in Fig. 10k and o. In the third stage, the lower surface of the rim contacted the groove wall gradually, from the lateral side to the inner side. The final section shapes are shown in Fig. 10l and p, respectively. Comparing Fig. 10l with s, and Fig. 10p with t, the rim width and thickness of the final section shapes in the simulation showed significant agreement with those in the experiments. In these two steps, flashes were formed in both experiments (shown in enlarged views VI and VI of Fig. 10) and simulation results (shown in enlarged views III and V of Fig. 10).
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Fig. 10. The forming process in FEA and the sectional results of experiments.
According to the forming results of the FEA and experiments, it proves that the proposed new process and the design rule based on Eq. (4) in Section 3.1 is feasible to thicken the rim of disk-like parts.
6.2. Feeding force Fig. 11 shows the simulated force–displacement curves during the rotary forming process. Meanwhile, the triangles mark the experimental force in each step, and the quadrangles indicate the calculated force from Eq. (7), whose parameters a = 1.7 and b = 1.8, in step three, and a = 1.1 and b = 1.2, in step four, are illustrated in an enlarged views of VIII and IX of Fig. 10, respectively. The curves
of step one and step two can be divided into two stages, according to the slope, which corresponds to the two forming stages of step one and step two in Fig. 10. The curves of step three and step four can also be divided into three stages, according to the slope, which corresponds to the three forming stages of step three and step four in Fig. 10. According to Fig. 11, the final feeding force of the experiment is 8.55% higher than that of the simulation in step one, 4.96% higher than that of the simulation in step two, 5.22% higher in step three, and 4.33% higher in step four. The feeding force, in step three and step four, calculated by Eq. (7) were 41.8 kN and 119.4 kN, respectively. The calculated value is only 46.1% of the experimental value and 48.5% of the simulation in step three, and 101.2%
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3) A design rule for multi-step thickening for disc-like parts was proposed, which can provide an initial experimental process design. FEA and experimental results showed that the rim of a disc-like part can be thickened successfully by using the proposed rule. Acknowledgments The research was supported by the NCET-11-0185 and ‘the Fundamental Research funds for the Central Universities’ (HUST: No. 2010MS095). The authors gratefully extend their acknowledgements to Hubei Tri-ring metal forming equipment Co. Ltd. for manufacturing the equipment. References Fig. 11. Feeding force versus displacement.
of the experimental value and 105.6% of the simulation in step four. In step one and step two, no small corner was finally formed (see Fig. 10q and r), which does not match the assumptive conditions of Eq. (7), therefore the feeding force could not be calculated. In step three, due to the formation of a big round corner as shown in Fig. 10s, the principle stress assumptions of the main stress method were not satisfied. Therefore the feeding force showed a large difference between the experimental and FEA results when calculated by Eq. (7). In step four, the calculated feeding force is nearly the same as that shown by experiment and simulation. It indicates that Eq. (7) can be reasonably used to calculate the final feeding force. The key point in using this equation is to obtain the values of a and b. In fact, we could assume that a equals b, and set the value to be the allowable radii of the required parts. For example, in step four in this experiment, the final allowable radii is 1.2 mm, so there is a = b = 1.2. The force calculated by Eq. (7) was 114.3 kN, which is only 4.3% lower than that calculated with a = 1.1 and b = 1.2. Based on the results and analysis above, the calculated feeding force by Eq. (7) shows significant agreement with that of the FEA and experiment, when the small corner is formed on the workpiece. The equation is therefore reasonable. 7. Conclusions 1) A new rotary forming process used to thicken the rim portion of a disc-like part was proposed, and the corresponding apparatus was also designed and manufactured. The presented rotary forming process was tested by experiment and FEA. 2) A formula for calculating the feeding force was deduced and FEA and experimental results proved the rationality in the prediction of the feeding force according to the given assumptions.
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