Explanation of the mushroom effect in the rotary forging of a cylinder

Journal of Materials Processing Technology 151 (2004) 178182 Explanation of the mushroom effect in the rotary forging of a cylinder G. Liu , S.J. Yuan, Z.R. Wang, D.C. Zhou School of Materials Science and Engineering, Harbin Institute of Technology, P.O. Box 435, Harbin 150001, PR China Abstract Rotary forging is an incremental forging process and is available to form various axisymmetrical parts from cylindrical billets. However, under certain conditions, a cylindrical billet is liable to be formed into a mushroom-shape after rotary forging, but not a drum shape in upsetting. A 3D rigidplastic finite element method is used to simulate the rotary forging process to reveal the deformation mechanism of the mushroom shape workpiece. The stress, strain rate and strain distributions at different positions of the workpiece and at different times during the process are presented, and then the deformation zones are presented in detail for analyzing the deforming patterns. The reasons why the part with H 0 /D = 0.51.0 (ratio of initial height to diameter) is formed into a mushroom shape are analyzed and it is concluded that these are non-uniform deformation under the effect of the eccentric loading and the different deforming degrees along the tangential direction at various heights of the workpiece. However, this kind of effect can be used to manufacture a part with a flange from a cylinder, instead of being regarded as a defect. 2004 Elsevier B.V. All rights reserved. Keywords: Finite element method; Rotary forging; Mushroom effect; Deformation non-uniformity 1. Introduction Rotary forging has an outstanding advantage of decreas- ing the forming load because a part can be formed by a ro- tary die incrementally 1, especially various axisymmetric parts formed from cylindrical billets 2. However, it is well known that there is severe deformational non-uniformity in the rotary forging process 35. In the process of rotary forging of a cylinder with the condition of H/D = 0.51.0 (ratio of initial height to diameter), a workpiece with mush- room shape is easy to formed, as shown in Fig. 1. This phenomenon is called “mushroom effect” 6, and is ob- viously different from cylinder upsetting between two flat dies, although the workpiece also has flat top and bottom surfaces. For the upsetting of similar workpieces, because of the effect of friction, the deformation on the top surface and bottom surface (zone I in Fig. 2) is usually more difficult than that of the middle position (zones II and III), so that the final part often looks like a drum with a bigger diameter at the middle section. For understanding the interesting de- formation feature and mechanism, the deformation process is simulated by a commercial FEM code DEFORM TM 3D. Corresponding author. E-mail address: (G. Liu). According to the results of stress and strain rate, the defor- mation pattern of rotary forging is drawn and analyzed. 2. Finite element model of rotary forging of a cylinder The finite element model of rotary forging of a cylinder is shown in Fig. 3, in which the dies are assumed as rigid bodies and the workpiece is modeled as rigidplastic incompress- ible material without temperature effects. The mechanical behavior of the simulation material is modeled according to that of pure Plumbum billet. The constant shear friction fac- tor model is adopted in this simulation with a friction factor of 0.3. The motion of the rotary die with an inclination angle of 3 can be described as the combination of a rotation ( ) around the machine axis and a rotation ( ) around the rotary die axis, which coincides with the real rotary machine used in the experiments. The lower die has a upward translational motion () along the machine axis. The angular velocity ( ) of the rotary die rotating around the machine axis is 31.21 rad/s, with a feed per revolution (S) of 0.65 mm. The dimensions of the workpiece are 60 mm 40 mm (H 0 /D = 0.67), so that the relative feed per revolution is S/H 0 = 0.0163. In the experiments, the final shape of this workpiece is a mushroom shape, as shown in Fig. 1. 0924-0136/$ see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.035 G. Liu et al. / Journal of Materials Processing Technology 151 (2004) 178182 179 Fig. 1. Mushroom-shaped workpiece of rotary forging. Fig. 2. Drum shape after upsetting: (I) dead metal; (II) mild deformation metal; (III) severe deformation metal. Fig. 3. FEM model of the rotary forging of a cylinder billet. 3. Analysis of the forming mechanism of the mushroom shape 3.1. Simulation results After 15 cycles of rotary forging by the rotary die, when the axial compression rate is 25%, the FEM mesh of the workpiece is formed into a mushroom shape with a bigger top and a smaller bottom, as shown in Fig. 4, which is similar to Fig. 1 due to employing the same initial conditions. From simulation, the stresses and strain rates in the work- piece during rotary forging can be calculated and used to analyze the forming mechanism of the process. For analyzing the deformation pattern in the workpiece, the three typical meridional sections shown in Fig. 5 are regarded as the analyzed objects. The shaded area is the Fig. 4. Mushroom shape resulting from simulation. Fig. 5. Positions of the meridional sections: (AB) exit position of contact area; (CD) middle position of contact area; (EF) entrance position of contact area. contact area between the rotary die and the workpiece. Three directions, the tangential (), radial () and axial (z) direction (see Fig. 6(a) are assumed as the principal directions of stress and strain rate. Therefore, the three stresses along 2 2 1 1 2 2 3 3 1 1 3 3I II I II z (a) 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 I I II III II III (b) . . . . . . . . . . . . . . . 1 2 1 II 3 2 I 3 I II 2 1 3 3 1 2 (c) . . . . . . Fig. 6. Stress and strain rate state in three meridional sections through the contact area: (a) section AB; (b) section CD; (c) section EF. 180 G. Liu et al. / Journal of Materials Processing Technology 151 (2004) 178182 these principal directions at any points can be ordered as 1 2 3 by their algebraic values, whilst the strain rate order is 1 2 3 . Because of the clockwise rolling movement of the rotary die ( represents the angular velocity of movement), the line AB represents the exit-section position of the contact area, line CD represents the middle-section, and line EF represents the entrance-section. As number of the revolutions of the rotary die is 4, ac- cording to the stress order and the strain rate order, the de- formation pattern in the three meridional sections can be zoned as shown in Fig. 6. On the other hand, in the top and bottom surface of the workpiece, the deformation area can be divided into four zones as shown in Fig. 7(a), and two zones as shown in Fig. 7(b). 3.2. Analysis of the deformation patterns in the plastic forming zones From Fig. 6, it can be seen that the deformation area in the workpieces looks like a mushroom, and that there is a cone-shaped dead zone in the lower part of the workpiece. In the exit section (AB), according to Fig. 6(a), zones I and II are the major deforming zones with 3D compressive stress (viz. axial, radial and tangential direction), but differ- ent stress orders in different zones. In zone I, the absolute value of radial stress is higher than that in the tangential direction, and both of them are very small because this sec- 3 2 1 2 z 1 3 2 2 3 3 1 1 1 1 2 2 2 1 3 3 2 1 III II I IV I II III IV 3 3 (a) 3 1 2 1 II I 2 I 2 II 1 3 3 2 3 1 (b) . . . . . . . . . . . . . . . . . . . . Fig. 7. Stress and strain rate state in the top and bottom surface of the workpiece: (a) top surface; (b) bottom surface. tion is located at the exit of the contact area. In zone II the absolute value of tangential stress is higher than that of ra- dial stress. The strain rates have coincident orders with the stress and the material in the deformation zones is shortened along the axial direction, but elongated along the radial and tangential directions. As the exit-section, the strain rates in zones I and II are smaller than those in the other sections, so that they do not play a main role on the deformation result. In the middle section (CD) of the contact area, the de- formation is most severe. In zones I and II (Fig. 6(b) the material is affected by 3D compressive stress. Because the absolute value of the tangential compressive stress is greater than that of radial stress, the main deformation in zone I is radial elongation, which is contrary to that of zone II. Un- usually, tangential tensile stress appears in zone III because of the tangential elongation of material in zone II. In the entrance section (EF), zone I is also a 3D com- pressive stress zone, but the elongation in the tangential direction is the main deformation pattern. In zone II, the material sustains two tensile stresses along radial and tan- gential directions. In sections CD and EF, from top to bottom, the absolute values of stress and strain rate decrease clearly, where the maximum value on the bottom is about 10% of the value on the top. From the deformation in meridional sections, it can be seen that the main deformation of the workpiece occurs on the contact area of the top end, and that the main deforma- tion pattern is tangential elongation. According to Fig. 7(a), the deformation pattern on the top surface of the workpiece can be zoned into four parts. It can be seen that the state of the stressstrain rate in the top surface is very complex. In zone I, tensile stresses are exerted along the radial and tangential directions and the main deformation is tangential elongation. In zones II and III, under the 3D compressive stresses, the main deformation in zone II is radial elongation, whereas in zone III, it is the tangential elongation that is playing a major role. In zone IV on the edge, the material is tensioned in the tangential direction and compressed in the radial direction with lower absolute values of stress than for the other three zones. From Fig. 7(b), the deformation pattern in the bottom sur- face is simpler than that in the top surface. Moreover, the plastic deformation area and the absolute values of strain rate in the bottom surface of the workpiece are much smaller than those in the top surface. Over the whole plastic area, the three principal stresses are all compressive stress. In zone I, the radial elongation is greater than that in the tangen- tial direction, whilst in contrast, the tangential strain rate is slightly bigger than the radial strain rate in zone II. 3.3. Analysis on strain change at typical positions The tangential and radial strains at six typical points on a meridional section are extracted to describe the deformation G. Liu et al. / Journal of Materials Processing Technology 151 (2004) 178182 181 Fig. 8. Typical points on the meridional section of the workpiece. 0.00 0.08 0.16 0.24 0.32 0.40 04812162 Revolution number of rotary die n (r) Radial strain e r 24 1 2 3 4 5 6 Fig. 9. Radial strain at typical points. process and result quantitatively. The positions of the six points are shown in Fig. 8. From the changing process of the radial strain shown in Fig. 9, it can be seen that at point 1 is much higher than that at other points, and that at point 5 has the lower value. The values of at other points are almost the same and increase slowly. Thus, the more severe radial elongation of the center metal on the top surface is one of the reasons for the mushroom effect. From the changing process of the tangential strain shown in Fig. 10, it can be seen that at points 1 and 2 is much greater than that at the other points, and at points 5 and 6 are minimum all along. From top to bottom, the values of decrease gradually, thus the tangential strain on the 0.00 0.06 0.12 0.18 0.24 0.30 0.36 0481216202 Revolution number of rotary die n (r) Tangential strain e q 4 1 2 3 4 5 6 Fig. 10. Tangential strain at typical points. Fig. 11. Tangential strain in the meridional section after 23 cycles of rotary forging. top surface is greater than that at the bottom: then the more severe tangential elongation plays an important role in the forming of a mushroom-shaped workpiece. In general, because of the partial loading exerted on the workpiece top by a rotary die with a conical surface along the rotary direction, plastic deformation occurs easily in the contact area of the top surface, but not so easily in the bottom material. From top to bottom, the material area under stress increases gradually so that the absolute values of the stresses in various directions decrease, and then the main plastic de- formation area minifies from top to bottom. In the middle of the contact area, the radial elongation is the first principal strain, however, in most of the plastic area, the tangential elongation plays the main role because of the rolling effect of a rotary die with a conical surface. Finally, after 23 cycles of rotary forging, the diameter of the top surface is bigger than that of the bottom, so that the shape of the workpiece is like that of a mushroom, and then the tangential strain in the top surface is much greater than that in the bottom (see Fig. 11). In a sense, the deformation non-uniformity is a kind of defect, however, this phenomenon also can be used to manufacture a flange from a cylindrical billet 7,8. Thus, the mushroom effect in rotary forging should be regarded as a special advantage of the rotary forging process. 4. Conclusions When the ratio of H/D is in the range from 0.5 to 1.0, it is easy to form a mushroom-shape workpiece. Because of the partial loading exerted on the workpiece top by a rotary die, the contact area on the bottom is much bigger than that on the top, so that the material on the bottom is more difficult to deform. From top to bottom, the material area under stress in- creases gradually so that the absolute values of the stresses in the various directions decrease, and then the main plastic deformation area minifies from top to bottom. Es- pecially, there is a dead zone in the lower end of the workpiece. In mo