Plastic Deformation Behaviors of Cold Rotary Forging under Different Contact Patterns by 3D Elastic-Plastic FE Method

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1 Materials Transactions, Vol. 50, No. 8 (2009) pp to 1958 #2009 The Japan Institute of Metals Plastic eformation Behaviors of Cold Rotary Forging under ifferent Contact Patterns by 3 Elastic-Plastic FE Method Xinghui Han and Lin Hua* School of Materials Science and Engineering, Wuhan University of Technology, Wuhan , P. R. China Cold rotary forging is an advanced but very complex incremental metal forming technology with multi-factors coupling interactive effects. The contact patterns between the upper die and workpiece have an essential effect on the cold rotary forging process. In the current work, a 3 elastic-plastic dynamic explicit FE model of cold rotary forging of a cylindrical workpiece is developed under the ABAQUS software environment and its validity has been verified by an experiment carried out on a T 200 cold rotary forging press. On the basis of this reliable 3 FE model, numerous simulation calculations have been carried out and it has been found that there are three new plastic deformation behaviors of cold rotary forging under three different contact patterns. With the first pattern, the middle part of the cylindrical workpiece is first penetrated axially from the upper surface to the lower surface by the plastic deformation zone (PZ), and then the PZ gradually develops radially towards the cylindrical surface until the entire cylindrical workpiece has become the PZ. In the second situation, the PZ gradually penetrates the axial height from the upper surface to the lower surface of the cylindrical workpiece. In the third situation, the upper region of the cylindrical workpiece is first penetrated radially from the cylindrical surface to the centre, and then the PZ gradually develops axially towards the lower surface until the entire axial height has been penetrated completely. On the basis of these behaviors, the effects of three different contact patterns on the cold rotary forging process have been comprehensively investigated. The results of this research not only provide valuable guidelines for the design, installation and adjustment of dies in the cold rotary forging process, but also help to further understand the deformation mechanism of cold rotary forging. [doi:1320/matertrans.m ] (Received April 16, 2009; Accepted May 26, 2009; Published July 8, 2009) Keywords: cold rotary forging, plastic deformation behaviors, contact patterns, cylindrical workpiece, FE modeling 1. Introduction Cold rotary forging is an advanced and innovative metal forming technology that is used to manufacture a wide variety of mechanical components such as disks, rings, flanges and gears. uring the cold rotary forging process (shown in Fig. 1), the conical upper die continuously oscillates around the vertical machine axis at a constant revolution speed n. Simultaneously, the lower die pushes the workpiece vertically at a constant feed rate v so as to cause it to be subjected to axial compression. Thus, after the workpiece is pressed repeatedly for several times, the plastic deformation will be completed perfectly. Compared with conventional forging, cold rotary forging has the following advantages: lower level of noise and vibration, uniform quality, smooth surface, close tolerance and considerable savings in energy and material costs. These significant advantages have allowed cold rotary forging to have a variety of applications in many industrial fields such as automobile, machine tool, electrical equipment, cutting tool and hardware. ue to its potential advantages and wide application prospects, many studies have been done on the cold rotary forging process. Summarily, most of these studies have concentrated primarily on measuring the pressure distribution at the contact area, 1,2) calculating and verifying the power parameters 3 7) and analyzing the metal flow 8 13) by analytical and experimental methods. Over the past few decades, the FE method has been applied to analyze the cold rotary forging process. Wang et al. 14,15) developed a 3 rigidplastic finite element code in the FORTRAN language to analyze the cold rotary forging process of a ring workpiece. Yuan et al. 16) used the 3 rigid-plastic finite element software EFORM to simulate the cold rotary forging *Corresponding author, lhuasvs@yahoo.com.cn S Machine axis γ R A B o n o γ Upper die axis process of the knuckle pin. Liu et al. 17) adopted the same software to investigate the inhomogeneous deformation of the cylindrical workpiece in the cold rotary forging process. The same software was also utilized by Sheu et al. 18) to study the cold rotary forging process of the ring gear. Recently, Hua and Han 19,20) adopted the 3 elastic-plastic dynamic explicit FE method to reveal the deformation mechanism of cold rotary forging by exploring the effects of the main C Upper die Workpiece v Contact area Pivot point Lower die Fig. 1 Schematic diagram of cold rotary forging of the cylindrical workpiec.

2 1950 X. Han and L. Hua n φ =γ θ n φ =γ n φ = γ +θ γ θ γ θ γ Pivot point v v v (c) Fig. 2 The three contact patterns between the upper die and the cylindrical workpiece. Only the pivot point of the upper die contacts the upper surface of the cylindrical workpiece at the beginning of the process. The generatrix of the upper die is in complete contact with the upper surface of the cylindrical workpiece at the beginning of the process. (c) Only one point on the generatrix of the upper die contacts the edge of the upper surface of the cylindrical workpiece at the beginning of the process. processing parameters on the process. All of these analytical results provided a significant basis for better understanding the deformation characteristics and mechanism of the cold rotary forging process. However, many problems are still not clear because cold rotary forging is a very complex metal forming technology under coupled effects with multi-factors. Therefore, it is still difficult to select the proper processing parameters so as to precisely control the cold rotary forging process. In the current study, in order to reveal the deformation mechanism of cold rotary forging under different contact patterns, numerous numerical simulation calculations have been carried out based on the reasonable 3 elastic-plastic dynamic explicit FE model developed under the ABAQUS software environment. Through these simulations, three new plastic deformation behaviors of cold rotary forging have been found under three different contact patterns. Moreover, the effects of these three different contact patterns on the cold rotary forging process have been also comprehensively explored. 2. Contact Patterns between the Upper ie and the Cylindrical Workpiece In practical production, many rotary forged parts can be obtained from a cylindrical workpiece. Therefore, this study focuses on studying the cold rotary forging process of the cylindrical workpiece. In the installation and adjustment of the upper die, there are three different contact patterns between the upper die and the cylindrical workpiece, as shown in Fig. 2. In the first, only the pivot point of the upper die contacts the upper surface of the cylindrical workpiece at the beginning of the process, so that there is an angle between the upper die and the upper surface of the cylindrical workpiece, as shown in Fig. 2. Obviously, the angle between the machine axis and the upper die axis can be expressed by eq. (1) according to the geometric relationship shown in Fig. 2 ¼ ð >Þ ð1þ where is the inclination angle of the upper die. In the second situation, the generatrix of the upper die is in complete contact with the upper surface of the cylindrical workpiece at the beginning of the process, so that the angle between the machine axis and the upper die axis can be expressed by eq. (2), as shown in Fig. 2. ¼ ð ¼ 0Þ ð2þ In the last situation, only one point on the generatrix of the upper die contacts the edge of the upper surface of the cylindrical workpiece at the beginning of the process, so that the angle between the machine axis and the upper die axis can be given by eq. (3), as shown in Fig. 2(c). ¼ þ ð3þ It can be seen from Fig. 2 that the three contact patterns between the upper die and the cylindrical workpiece are obviously different, thus resulting in different deformation characteristics and mechanisms in the cold rotary forging process FE Modeling of Cold Rotary Forging of the Cylindrical Workpiece Based on the forming characteristics, a reasonable 3 FE model of cold rotary forging of a cylindrical workpiece is developed under the ABAQUS/Explicit environment, as shown in Fig. 3. Summarily, the proposed 3 FE model has the following features: (1) Because the elastic deformation that occurs in the cylindrical workpiece has an important effect on the cold rotary forging process, the elastic-plastic FE method is adopted to improve the computational accuracy. (2) The dynamic explicit FE procedure is used to avoid the huge computation time and convergence problem of the static implicit procedure. (3) The upper die and lower die are defined as 3 analytical rigid bodies while the cylindrical workpiece is defined as a 3 deformable solid body. Contact pairs are defined between the dies and the cylindrical workpiece and the contact type is defined as surface-to-surface. The finite sliding formulation is adopted to account for the relative

3 Plastic eformation Behaviors of Cold Rotary Forging under ifferent Contact Patterns by 3 Elastic-Plastic FE Method 1951 Table 1 Processing parameters adopted in the simulation and experiment. Fig. 3 Upper die Global coordinate system Cylindrical workpiece Lower die 3 FE model of cold rotary forging of the cylindrical workpiece. Parameters Values Initial radius of the cylindrical workpiece R 0 /mm 20 Initial height of the cylindrical workpiece H 0 /mm 15 Height reduction H=H 0 /% 20 Feed rate of the lower die v/mm s 1 1 Rotational speed of the upper die n/r min Feed amount per revolution S/mm r 1 Inclination angle of the upper die / 2 Friction coefficient between the dies and workpiece Þ Motion orbit of the upper die Circle line motion of two surfaces. In addition, the relative sliding that exists between the dies and workpiece contributes to describe the friction condition of the contact pairs with Coulomb friction model. (4) The rigid motion of the rigid bodies in all degrees of freedom can be represented by a reference point (RP), as shown in Fig. 3. The upper die is constrained to rotate only around the global 2-axis, while the lower die is constrained to translate only along the global 2-axis. In order to guarantee the successful performance of the process, the constraint type distributing coupling is adopted to constrain the rotation and translation of the cylindrical workpiece caused by the oscillation of the upper die. (5) The 3 linear reduction integration continuum element with eight nodes (C38R) is used to discretise the cylindrical workpiece. The number of elements in the cylindrical workpiece is determined by its size and the computational efficiency and precision. Meanwhile, the adaptive mesh technology is employed to reduce the distortion of the elements. (6) Mass scaling technology is adopted in the simulation process. Appropriate mass scaling factors are selected to improve the computational efficiency, while the computational accuracy is also satisfied. 4. Verification of the eveloped 3 FE Model of Cold Rotary Forging After finishing the 3 FE model of the cold rotary forging process, its validity has to be evaluated experimentally. For experimental convenience, the second contact pattern shown in Fig. 2 is adopted to validate the proposed 3 FE model. The experiment has been carried out on a T 200 cold rotary forging press at Hubei Automobile Axle Co., Ltd in China. This press is hydraulically driven and has a maximum capacity of 200 tons. Four types of motion orbits for the upper die can be selected on the T 200 cold rotary press: circle, straight, spiral and rosette line. The circle line is chosen as the motion orbit of the upper die for experimental control convenience. The forging conditions in the experiment are translated to suitable parameters for the FE simulation, as shown in Table 1. The workpiece material used in the model is AISI1020 and its mechanical properties are shown in Table 2. MoS 2 is used as the lubricant in the experiment. In order to quantitatively evaluate the validity of the proposed 3 FE model, the variations in the upper surface diameter of the cylindrical workpiece during the forming process have been compared between the simulation and Table 2 Mechanical properties of the cylindrical worpiece. Material AISI1020 ensity /kg m Young s modulus E/GPa 210 Poisson s ratio 0.3 Constitutive equation ¼ 850" 0:25 Upper surface diameter of the cylindrical workpiece(mm) Fig Height reduction, H/H 0 / % experiment, as shown in Fig. 4. It can be found from Fig. 4 that the simulation results are in good agreement with the experimental ones and that the maximum relative error is 3.76%. Therefore, the 3 elastic-plastic dynamic explicit FE model of cold rotary forging is proved to be reliable experimentally and further investigation can be done using the developed 3 FE model. 5. Results and iscussion Simulation results Experimental results Comparison of simulation results with experimental ones. 5.1 Calculation conditions In order to quantitatively reveal the effect laws of three different contact patterns on the cold rotary forging process, it is regulated that the value of angle between the upper die and the upper surface of the cylindrical workpiece is negative under the first contact pattern, the value of is zero under the second contact pattern and it is positive under the third contact pattern. Besides the contact patterns between the upper die and the cylindrical workpiece, the feed amount per revolution S and the inclination angle of the upper die are also key factors and have an essential effect on the cold rotary forging process. 19) So their interactive effect on the forming

4 1952 X. Han and L. Hua Contact area between the dies and workpiece (m 2 ) [ 10-3 ] Contact area between the upper die and workpiece Contact area between the lower die and workpiece Time, t / s Contact area between the dies and workpiece (m 2 ) [ 10-3 ] Contact area between the upper die and workpiece Contact area between the lower die and workpiece Time, t / s Contact area between the dies and workpiece (m 2 ) [ 10-3 ] Contact area between the upper die and workpiece Contact area between the lower die and workpiece Time, t / s (c) Fig. 5 Variation curves of contact area between the dies and the cylindrical workpiece under three different contact patterns. Contact area histories under the first contact pattern (S ¼ 0:2 mm r 1, ¼ 7, ¼ 6 ). Contact area histories under the second contact pattern (S ¼ 0:2 mm r 1, ¼ 7, ¼ 0 ). (c) Contact area histories under the third contact pattern (S ¼ 0:2 mm r 1, ¼ 7, ¼ 7 ). process is studied. The calculation conditions adopted in this study are as follows: In order to reveal the interactive effect of and the feed amount per revolution S on the cold rotary forging process, select ¼f 1; 0; 1; 3; 5; 7g ( ), S ¼f0:04; 0:2; 0:8g (mm r 1 ), ¼ 2 (under the first contact pattern, and have to satisfy the relation >jj), while keeping the other processing parameters listed in Tables 1 and 2 unchanged. In order to reveal the interactive effect of and inclination angle of the upper die on the cold rotary forging process, select ¼f0; 1; 3; 5; 7g ( ), S ¼ 0:2 mm r 1, ¼ 0:5 ; Select ¼f 1; 0; 1; 3; 5; 7g ( ), S ¼ 0:2 mm r 1, ¼ 2 ; and select ¼f 6; 3; 1; 0; 1; 3; 5; 7g ( ), S ¼ 0:2 mm r 1, ¼ 7. The other processing parameters listed in Tables 1 and 2 are kept unchanged. 5.2 Contact area between the dies and cylindrical workpiece under three different contact patterns uring the cold rotary forging process, the contact area between the dies and the cylindrical workpiece changes with time due to the oscillation of the upper die, resulting in the plastic deformation zone (PZ) that is very complicated and changeable. Therefore, the contact area has a significant effect on the cold rotary forging process. Figure 5 shows the variation curves of contact area between the dies and the cylindrical workpiece under three different contact patterns. Under the first and third contact patterns, the contact between the upper die and the cylindrical workpiece is a point of contact at the beginning of the process, thus resulting in the contact area between them gradually increasing from zero to the maximum value quasi-linearly with time, as shown in Fig. 5 and Fig. 5(c). Under the second contact pattern, the contact between the upper die and the cylindrical workpiece is a line of contact at the beginning of the process, so the contact area between them increases rapidly from zero to a certain value. After that, the deformation of the cylindrical workpiece has entered the steady stage, so that the contact area between them increases slowly until it reaches the maximum value, as shown in Fig. 5. It can be also seen from Fig. 6 that the contact area between the lower die and the cylindrical workpiece has the same variation trends under three different contact patterns. At the beginning of the t=56s t=1.254s (c) t=1.881s (d) t=3.8s Fig. 6 PEEQ distribution in the axial section of the deforming cylindrical workpiece under the first contact pattern. process, the lower die cannot contact the cylindrical workpiece completely under the action of the eccentric load imposed by the upper die, so the contact area between them decreases significantly. After that, the contact area between them gradually increases until t ¼ 3 s. After t ¼ 3 s, the lower die stops the axial feed while the upper die still oscillates so as to make the upper surface of the cylindrical workpiece become a smooth surface, so the contact area between the dies and the cylindrical workpiece decreases

5 Plastic eformation Behaviors of Cold Rotary Forging under ifferent Contact Patterns by 3 Elastic-Plastic FE Method 1953 t=0.513s t=0.798s t=1.007s t=1.501s (c) t=2.508s (c) t=2.622s (d) t=3.8s Fig. 7 PEEQ distribution in the axial section of the deforming cylindrical workpiece under the second contact pattern. rapidly. By comparing the contact area histories, it can be found that under any contact pattern, the contact area between the upper die and the cylindrical workpiece is smaller than that between the lower die and the cylindrical workpiece at any time during the process. Therefore, the axial unit pressure on the upper region of the cylindrical workpiece is larger than that on the lower region. That is to say, it is easier for the metal near the upper die to satisfy the yield condition and enter the plastic deformation state. 5.3 Plastic deformation behaviors under three different contact patterns In order to obtain proper information about the plastic deformation behaviors of cold rotary forging, the distribution of the PEEQ (equivalent plastic strain) of the cylindrical workpiece in the forming process is selected to analyze the development of the PZ. Figs. 6 8 show the PEEQ distribution in the axial section of the deforming cylindrical workpiece under three different contact patterns. From Figs. 6 8, it can be found that the development of the PZ has the following characteristics: (1) As described above, it is easier for the metal near the upper die to satisfy the yield condition for entering the plastic deformation state. Meanwhile, under the first contact pattern, only the pivot point of the upper die contacts the upper surface of the cylindrical workpiece at the beginning of the process. So the PZ is formed first in the middle part of the upper region of the cylindrical workpiece, as shown in (d) t=3.8s Fig. 8 PEEQ distribution in the axial section of the deforming cylindrical workpiece under the third contact pattern. Fig. 6. As the forming process continues, the PZ gradually expands axially towards the lower surface and radially towards the cylindrical surface, as shown in Fig. 6. Obviously, the PZ first penetrates the axial height of the cylindrical workpiece, as shown in Fig. 6(c). After that, the PZ continues to develop radially towards the cylindrical surface until the entire cylindrical workpiece has entered the plastic deformation state, as shown in Fig. 6(d). (2) Under the second contact pattern, the generatrix of the upper die is in complete contact with the upper surface of the cylindrical workpiece at the beginning of the process. Thus, the upper region of the cylindrical workpiece first enters the plastic deformation state under the action of the oscillation of the upper die, as shown in Fig. 7. With increasing the forming time, the PZ gradually expands axially towards the lower surface of the cylindrical workpiece, as shown in Fig. 7. As the lower die feeds and the upper die oscillates continuously, the PZ gradually penetrates the entire height of the cylindrical workpiece, as shown in Fig. 7(c) and Fig. 7(d). From the above analysis, it can be concluded that, just like a type of wave, the PEEQ distribution exhibits a transfer characteristic from the upper surface to the lower surface of the cylindrical workpiece under the second contact pattern. (3) Under the third contact pattern, only one point on the generatrix of the upper die contacts the edge of the upper surface of the cylindrical workpiece at the beginning of the process. Therefore, the corner zone of the upper region of the

6 1954 X. Han and L. Hua cylindrical workpiece first produces the plastic deformation, as shown in Fig. 8. As the forming process continues, the PZ gradually develops towards the centre of the cylindrical workpiece along the radial direction and towards the lower surface along the axial direction, as shown in Fig. 8. It is obviously observed from Fig. 8(c) that the upper region of the cylindrical workpiece is first penetrated in the radial direction. After that, the PZ continues to expand towards the lower surface of the cylindrical workpiece until the entire axial height is completely penetrated, as shown in Fig. 8(d). From the above analysis, it can be seen that the development of the PZ in the deforming cylindrical workpiece takes place in obviously different ways under three different contact patterns. Through a comprehensive analysis and summary, it has been found that there are three kinds of new plastic deformation behaviors of cold rotary forging under three different contact patterns, as described in the following. (1) Under the first contact pattern, the middle part of the cylindrical workpiece is first penetrated axially from the upper surface to the lower surface by the PZ, and then the PZ gradually develops radially towards the cylindrical surface until the entire cylindrical workpiece has entered the plastic deformation state. (2) Under the second contact pattern, the PZ gradually penetrates the axial height from the upper surface to the lower surface of the cylindrical workpiece. (3) Under the third contact pattern, the upper region of the cylindrical workpiece is first penetrated radially from the cylindrical surface to the centre by the PZ, and then the PZ gradually develops axially towards the lower surface until the entire axial height has been penetrated completely. 5.4 Effects of three different contact patterns on the mushroom effect of the deformed cylindrical workpiece Based on the above analysis, it can be found that the three new plastic deformation behaviors of cold rotary forging under different contact patterns have a point in common: the PZ always penetrates the axial height of the cylindrical workpiece from the upper surface to the lower surface. Under this circumstance, the plastic deformation of the upper region of the deforming cylindrical workpiece is always larger than that of the lower region. Consequently, the deformed cylindrical workpiece exhibits the mushroom effect under any of three different contact patterns (shown in Figs. 6 8), which is the main deformation characteristic of cold rotary forging. From the above analysis, it can be concluded that the axial plastic penetrating state of the cylindrical workpiece has a decisive effect on the mushroom effect. That is to say, if the PZ can penetrate the axial height of the cylindrical workpiece more easily from the upper surface to the lower surface, the metal of both the upper and lower regions produces the large plastic deformation, thus resulting in the less obvious mushroom effect of the deformed cylindrical workpiece. Inversely, when it is difficult for the PZ to penetrate the axial height of the cylindrical workpiece from the upper surface to the lower surface, the upper region produces the large plastic deformation while the lower region is in elastic or small plastic deformation state, thus resulting in the more obvious mushroom effect. Under the first contact pattern (corresponding to the first plastic deformation behavior), the middle part of the cylindrical workpiece is first penetrated axially from the upper surface to the lower surface by the PZ and then the PZ gradually develops radially towards the cylindrical surface until the entire cylindrical workpiece has entered the plastic deformation state. Obviously, this kind of plastic deformation behavior is favorable to the axial plastic penetrating of the cylindrical workpiece. Therefore, the metal of both the upper region and lower region of the cylindrical workpiece produces the large plastic deformation. Consequently, the diameter of the upper surface and lower surface expands homogeneously, thus leading to the less obvious mushroom effect. Under the second contact pattern (corresponding to the second plastic deformation behavior), the PZ gradually penetrates the axial height from the upper surface to the lower surface of the cylindrical workpiece. So the upper region of the cylindrical workpiece is in large plastic deformation state while the lower region produces the relatively smaller plastic deformation, thus resulting in the obvious mushroom effect. Under the third contact pattern (corresponding to the third plastic deformation behavior), the upper region of the cylindrical workpiece is first penetrated radially from the cylindrical surface to the centre by the PZ, and then the PZ gradually develops axially towards the lower surface until the entire axial height has been penetrated completely. It is obvious that this kind of plastic deformation behavior is unfavorable to the axial plastic penetrating of the cylindrical workpiece. That is to say, the PZ mainly develops radially from the cylindrical surface to the centre in the upper region of the cylindrical workpiece. So the upper region is in large plastic deformation state while the lower region is in elastic or small plastic deformation state, thus leading to the more obvious mushroom effect. In order to quantitatively describe the mushroom effect, the roughness of the cylindrical surface of the deformed cylindrical wokpiece is put forward based on the deformation characteristics of cold rotary forging, as shown in Fig. 9. Obviously, larger values for lead to the more obvious mushroom effect of the deformed cylindrical workpiece, and vice versa. Figure 10 shows the effect of on the roughness of the cylindrical surface under different S and. It can be seen from Fig. 10 that the curves have a similar variation trend for all cases of S and. Under the same S or,as increases, first increases rapidly and then increases slowly when is larger than 3. That is to say, the mushroom effect of the deformed cylindrical workpiece becomes more obvious with increasing. According to the above analysis, when is a smaller value (corresponding to the first plastic deformation behavior), it is favorable to the axial plastic penetrating of the cylindrical workpiece, thus resulting in the less obvious mushroom effect. When is a larger value (corresponding to the third plastic deformation behavior), it is unfavorable to the axial plastic penetrating of the cylindrical workpiece and thus the more obvious mushroom effect occurs. Therefore, with the increase of, the plastic deformation behavior transforms from the first case to the third, thus resulting in the

7 Plastic eformation Behaviors of Cold Rotary Forging under ifferent Contact Patterns by 3 Elastic-Plastic FE Method 1955 max 0 min efinition of φ under the first contact pattern max Roughness of cylindrical surface of the cylindrical workpiece φ (%) S =4 mm r -1 2 S = mm r -1 S = mm r min efinition of φ under the second pattern max 0 Roughness of cylindrical surface of the cylindrical workpiece φ (%) γ =0.5 γ =2 γ = min (c) efinition of φ under the third contact pattern φ = max Fig. 9 efinition of the roughness of the cylindrical surface of the deformed cylindrical workpiece. 0 is the initial diameter of the cylindrical workpiece. max and min are the maximum and minimum diameter of the cylindrical surface of the deformed cylindrical workpiece, respectively. more obvious mushroom effect. The effect laws of on can also be explained from the view of the contact area between the upper die and the cylindrical workpiece, as shown in Fig. 11. It can be observed from Fig. 11 that with a fixed S or, the contact area between the upper die and the cylindrical workpiece gradually decreases as increases, resulting in a decrease in the PZ (located in the contact area between the upper die and the cylindrical workpiece). As a result, it is more difficult for the PZ to penetrate the entire axial height, thus leading to the more obvious mushroom effect. It can also be found from Fig. 11 that the contact area decreases slowly when is larger than 3. Thus, the effect of on becomes less significant as exceeds 3. Further study of Fig. 10 reveals that with increasing S or decreasing, the mushroom effect of the deformed cylindrical workpiece becomes less obvious, which is consistent with the results of Ref. 19). Therefore, the three different contact patterns between the upper die and the cylindrical workpiece (corresponding to three new plastic deformation behaviors) have significant 0 min Fig. 10 Effect of on the roughness of the cylindrical surface under different S and. Effect of on the roughness of the cylindrical surface under different S ( ¼ 2 ). Effect of on the roughness of the cylindrical surface under different (S ¼ 0:2 mm r 1 ). effects on the metal flow in the cold rotary forging process. That is to say, controlling the three different contact patterns can effectively control the mushroom effect of the deformed cylindrical workpiece. 5.5 Effects of three different contact patterns on the degree of inhomogeneous deformation In the metal forming process, the degree of inhomogeneous deformation of the workpiece has a critical effect on the quality of the final products. In this study, the difference between the maximum and minimum PEEQ is adopted to represent the degree of inhomogeneous deformation of the deformed cylindrical workpiece, namely id ¼ " max " min. The larger id is, the more inhomogeneous the deformation of the cylindrical workpiece is, and vice versa. Figure 12 illustrates the PEEQ distribution of the cylindrical surface along the axial direction under different. It can be seen from Fig. 12 that with increasing, the upper region of the cylindrical workpiece gradually increases while the lower region approximately remains unchanged in the PEEQ, thus leading to the more inhomogeneous deformation. Figure 13 provides the effect of on the degree of inhomogeneous deformation under different S and. From Fig. 13, it can be found that the degree of inhomogeneous deformation has an identical variation trend for all cases of S and. With fixed S and, the degree of inhomogeneous deformation increases

8 1956 X. Han and L. Hua Contact area between upper die and workpiece (m 2 ) Contact area between upper die and workpiece (m 2 ) [ 10-3 ] S =4 mm r -1 S = mm r -1 S = mm r [ 10-3 ] γ =0.5 γ =2 γ = Fig. 11 Effect of on the contact area between the upper die and the cylindrical workpiece under different S and. Effect of on the contact area between the upper die and the cylindrical workpiece under different S ( ¼ 2 ). Effect of on the contact area between the upper die and the cylindrical workpiece under different (S ¼ 0:2 mm r 1 ). PEEQ (Equivalent plastic strain) θ = 6 θ = 3 θ = 1 θ =0 θ =1 θ =3 θ = istance along the axial direction from the upper to lower surface of the cylindrical workpiece, H / mm Fig. 12 PEEQ distribution of the cylindrical surface along the axial direction under different. significantly when is smaller than 3, but increases slowly as exceeds 3. That is to say, the deformation of the cylindrical workpiece becomes more inhomogeneous with the increase of. This can also be explained by the three new plastic deformation behaviors of cold rotary forging under three different contact patterns. Under the first contact egree of inhomogeneous deformation of the cylindrical workpiece egree of inhomogeneous deformation of the cylindrical workpiece S =4 mm r -1 S = mm r -1 S = mm r γ =0.5 γ =2 γ = Fig. 13 Effect of on the degree of inhomogeneous deformation under different S and. Effect of on the degree of inhomogeneous deformation under different S ( ¼ 2 ). Effect of on the degree of inhomogeneous deformation under different (S ¼ 0:2 mm r 1 ). pattern, the PZ can penetrate the axial height of the cylindrical workpiece more easily. So more metal will participate in the plastic deformation and the cylindrical workpiece will produce the more homogeneous deformation. As increases, the plastic deformation behavior gradually transforms from the first behavior to the third, and thus it is unfavorable to the axial plastic penetrating of the cylindrical workpiece. Consequently, more metal is in elastic or small plastic deformation state and less metal participates in the plastic deformation. Therefore, the deformation of the cylindrical workpiece becomes more inhomogeneous. From the above analysis, it can also be concluded that the effect laws and mechanism of on the metal flow are the same as that on the degree of inhomogeneous deformation. Further investigation of Fig. 13 reveals that as S increases or decreases, the deformation of the cylindrical workpiece becomes more homogeneous, which is in accordance with the results of Ref. 19). Based on the above analysis, it can be concluded that it is the inhomogeneous deformation that leads to the mushroom effect of the deformed cylindrical workpiece. In the practical production of some rotary forged parts, the first contact pattern is preferred in order to reduce the mushroom effect and make the deformation more homogeneous. However, the mushroom effect has the duality and it has the wide application in the riveting process. When the mushroom effect is obvious, the head of the rivet produces the large plastic deformation while the rod of the

9 Plastic eformation Behaviors of Cold Rotary Forging under ifferent Contact Patterns by 3 Elastic-Plastic FE Method Axial forging force (KN) Forging moment (N m) θ = 6 θ =0 θ = θ = 6 θ =0 θ =7 Time, t / s Time, t / s Fig. 14 Axial forging force and forging moment histories under different contact patterns. Axial forging force histories under different contact patterns (S ¼ 0:2 mm r 1, ¼ 7 ). Forging moment histories under different contact patterns (S ¼ 0:2 mm r 1, ¼ 7 ). rivet is in elastic or small plastic deformation state, allowing loose riveting to be achieved. Inversely, when the mushroom effect is not so obvious, both the head and rod of the rivet produce large plastic deformations, and thus tight riveting can be achieved. Therefore, the first contact pattern is a good choice to achieve tight riveting in the riveting process and the third one is preferred to achieve loose riveting. 5.6 Effects of three different contact patterns on the force and power parameters In order to provide a valuable guideline for selecting the proper cold rotary forging press, the force and power parameters in the cold rotary forging process have been investigated in detail. Figure 14 provides axial forging force and forging moment histories under three different contact patterns. It is obvious that the variation trends of the axial forging force and forging moment histories are the same as that of the contact area histories. Under the first and third contact patterns, the contact between the upper die and the cylindrical workpiece is a point of contact at the beginning of the process, thus the force and power parameters gradually increase from zero to the maximum value with time. Under the second contact pattern, the contact between the upper die and the cylindrical workpiece is a line of contact at the beginning of the process, so the force and power parameters first increase rapidly from zero to a certain value. After that, the cylindrical workpiece has entered the steady deformation stage, and the force and power parameters increase slowly up to their maximum values. After t ¼ 3 s, the lower die stops the axial feed while the upper die still oscillates so as to make the upper surface of the cylindrical workpiece become a smooth surface. Therefore, the force and power parameters decrease significantly. Figure 15 shows the effect of on the maximum axial forging force and forging moment under different S and. It can be found from Fig. 15 that the maximum axial forging force and forging moment have the similar variation trends for all cases of S and. With fixed S or, the maximum axial forging force and forging moment first decrease sharply as increases, and then decrease slowly when is larger than 3. The reason for this can also be explained by the three new plastic deformation behaviors under three different contact patterns. Under the first contact pattern, it is much easier for the PZ to penetrate the axial height of the cylindrical workpiece. So more metal will participate in the plastic deformation and more energy is needed to produce the plastic deformation. With increasing, the plastic deformation behavior gradually transforms from the first behavior to the third, and thus it is unfavorable to the axial plastic penetrating of the cylindrical workpiece. Under this circumstance, more metal is in elastic or small plastic deformation state and less metal will participate in the plastic deformation, thus resulting in the consumption of less energy to produce the plastic deformation. When is larger than 3, the effect of on the contact area between the upper die and the cylindrical workpiece and the degree of inhomogeneous deformation become less significant, indicating that the metal participating in the plastic deformation decreases slowly. Thus, the effect of on the maximum axial forging force and forging moment becomes less significant as exceeds 3. Further study of Fig. 15 reveals that with the increase of S or the decrease of, the maximum forging force and forging moment gradually increase, which is also in accordance with the results of Ref. 19). From the above analysis, it can be found that a contradiction occurs between the force and power parameters and the degree of inhomogeneous deformation. On one hand, increasing is favorable to reduce the force and power parameters. On the other hand, the deformation of the cylindrical workpiece becomes more inhomogeneous as increases. Thus, the contact patterns between the upper die and the cylindrical workpiece should be carefully considered in order to balance the homogeneous deformation and the force and power parameters. 6. Conclusions In this paper, a reliable 3 elastic-plastic dynamic explicit FE model of cold rotary forging of a cylindrical workpiece is developed under the ABAQUS software environment. Based on this valid 3 FE model, the effects of three different contact patterns between the upper die and the cylindrical workpiece on the cold rotary forging process have been comprehensively explored. The results of this research show the following: (1) There exist three kinds of new plastic deformation behaviors of cold rotary forging under three different contact

10 1958 X. Han and L. Hua Maximum axial forging force(kn) S =4 mm r -1 S = mm r -1 S = mm r Maximum axial forging force(kn) γ =0.5 γ =2 γ = (c) Maximum forging moment(n m) S =4 mm r -1 S = mm r -1 S = mm r (d) 900 Maximum forging moment(n m) γ =0.5 γ =2 γ = Fig. 15 Effects of on the maximum axial forging force and forging moment under different S and. Effect of on the maximum axial forging force under different S ( ¼ 2 ). Effect of on the maximum axial forging force under different (S ¼ 0:2 mm r 1 ). (c) Effect of on the maximum forging moment under different S ( ¼ 2 ). (d) Effect of on the maximum forging moment under different (S ¼ 0:2 mm r 1 ). patterns: Under the first contact pattern, the middle part of the cylindrical workpiece is first penetrated axially from the upper surface to the lower surface by the PZ, and then the PZ gradually develops radially towards the cylindrical surface until the whole cylindrical workpiece has entered the plastic deformation state. Under the second contact pattern, the PZ gradually penetrates the axial height from the upper surface to the lower surface of the cylindrical workpiece. (c) Under the third contact pattern, the upper region of the cylindrical workpiece is first penetrated radially from the cylindrical surface to the centre by the PZ, and then the PZ gradually develops axially towards the lower surface until the entire axial height has been penetrated completely. (2) The three different contact patterns have significant effects on the cold rotary forging process. With increasing the angle between the upper die and the upper surface of the cylindrical workpiece (the contact pattern gradually transforms from the first one to the third), the mushroom effect of the deformed cylindrical workpiece becomes more obvious and the deformation becomes more inhomogeneous, while the maximum axial forging force and forging moment gradually decrease. Therefore, the contact pattern should be carefully considered in order to balance the homogeneous deformation and the force and power parameters. (3) The results of this research thoroughly reveal the effect laws of the contact patterns on the cold rotary forging process. They not only provide valuable guidelines for the design, installation and adjustment of dies in the cold rotary forging process, but also help to better understand the deformation mechanism of cold rotary forging. Acknowledgment The authors would like to thank the Natural Science Foundation of China for istinguished Young Scholars (No ) for the support given to this research. REFERENCES 1) J. B. Hawkyard, C. K. S. Gurnani and W. Johnson: J. Mech. Eng. Sci. 19 (1977) ) X. H. Pei,. C. Zhou and Z. R. Wang: Proc. 2nd Int. Conf. on rotary metalworking processes, (IFS Ltd., UK, 1982) pp ) M. Zhang: Proc. 3rd Int. Conf. on rotary metalworking processes, ed, by M. Kobayashi, (Kyoto, Japan, 1984) pp ) J. Oudin, Y. Ravalard, G. Verwaerde and J. C. Gelin: Int. J. Mech. Sci. 27 (1985) ) J. B. Hawkyard and C. P. Smith: Int. J. Mech. Sci. 30 (1988) ) S. Choi, K. H. Na and J. H. Kim: J. Mater. Process. Technol. 67 (1997) ) T. Canta,. Frunza,. Sabadus and C. Tintelecan: J. Mater. Process. Technol (1998) ) P. M. Standring, J. R. Moon and E. Appleton: Met. Technol. 7 (1980) ). C. Zhou, Y.. Han and Z. R. Wang: J. Mater. Process. Technol. 31 (1992) ). C. Zhou, S. J. Yuan, Z. R. Wang and Z. R. Xiao: J. Mater. Process. Technol. 32 (1992) ) H. K. Oh and S. Choi: J. Mater. Process. Technol. 68 (1997) ) T. Nakane, M. Kobayashi and K. Nakamura: Proc. 2nd Int. Conf. on rotary metalworking processes, (IFS Ltd., UK, 1982) pp ) G. C. Wang, J. Guan and G. Q. Zhao: J. Mater. Process. Technol. 169 (2005) ) G. C. Wang and G. Q. Zhao: J. Mater. Process. Technol. 95 (1999) ) G. C. Wang and G. Q. Zhao: Finite. Elem. Anal. es. 38 (2002) ) S. J. Yuan, X. H. Wang, G. Liu and. C. Zhou: J. Mater. Process. Technol. 86 (1998) ) G. Liu, S. J. Yuan, Z. R. Wang and. C. Zhou: J. Mater. Process. Technol. 151 (2004) ) J. J. Sheu and C. H. Yu: Proc. 35th Int. MATAOR Conf., (2007) pp ) L. Hua and X. H. Han: Mater. es. 30 (2009) ) X. H. Han and L. Hua: Mater. es. 30 (2009)