Ring blank design and its effect on combined radial and axial ring rolling

Transcription

1 Int J Adv Manuf Technol (2014) 72: DOI /s ORIGINAL ARTICLE Ring blank design and its effect on combined radial and axial ring rolling Xinghui Han & Lin Hua & Xiaokai Wang & Guanghua Zhou & Bohan Lu Received: 24 September 2013 /Accepted: 16 February 2014 /Published online: 12 March 2014 # Springer-Verlag London 2014 Abstract In conventional ring rolling, it is difficult to achieve a large increase in the ring height. This paper proposes a new combined radial and axial ring rolling process, which can achieve a large increase in both the ring diameter and height. During the proposed process, the geometry of the ring blank is of great importance because it determines the distribution of the radial ring rolling process and the subsequent axial ring rolling process. Therefore, this paper is aimed to reveal the effect of the geometry of the ring blank on the combined radial and axial ring rolling process. Using the finite element (FE) method, the deformation characteristics of the ring are first investigated. Then, the effect of the geometry of the ring blank, axial height H 0, outer diameter D 0, and thickness t 0, on the geometry development and inhomogeneous deformation of the final rolled ring, is revealed. The results of this research provide an important basis for the design and optimization of the ring blank in the new combined radial and axial ring rolling process. Keywords Ring rolling. Geometry. Ring blank. Design. FE simulation 1 Introduction Ring rolling is an advanced but complicated continuous and local metal-forming process which is widely used to manufacture precise seamless rings, such as bearing races, ring X. Han: L. Hua (*) : X. Wang : G. Zhou : B. Lu School of Automotive Engineering, Hubei Key Laboratory of Advanced Technology of Automotive Parts, Wuhan University of Technology, Wuhan , China lhua@whut.edu.cn X. Han hanxinghuihlp@126.com gears, aero-engine casing, nuclear reactor parts, and various connecting flanges. Ring rolling has many advantages, such as lower level of noise and vibration, uniform quality, smooth surface, close tolerance, and considerable savings in energy and material cost. Owing to these advantages, ring rolling has wide applications in many industrial fields such as bearing, machine, automobile, petrochemicals, aeronautics, astronautics, and atomic energy. Up to now, lots of studies have been carried out on ring rolling by experimental [1 7], analytical [8 13], and simulation [14 24] methods. Summarily, the above studies are mainly concentrated on the radial ring rolling process. A typical radial ring rolling process is illustrated in Fig. 1. During the process, the driven roll rotates actively around its axis at a constant rotational speed n. Under the action of the friction force, the driven roll takes the ring to rotate together. Simultaneously, the idle roll feeds towards the ring along the radial direction. The guide roll takes translational motions and always contacts the outer surface of the ring to keep the stability of the process. Under the action of the three rolls, the ring mainly produces the deformation of thickness reduction and diameter expansion, and its axial height basically. That is to say, it is difficult for the above ring rolling process to achieve a large increase in the ring height, which greatly restricts the development and application of the ring rolling technology. On the basis of the radial ring rolling process, this paper proposes a new combined radial and axial ring rolling process, which can achieve a large increase in both the ring diameter and height. During the proposed process, the geometry of the ring blank is of great importance because it determines the distribution of the radial ring rolling process and the subsequent axial ring rolling process. In view of the importance of the geometry of the ring blank, this paper is aimed to reveal the effect of the geometry of the ring blank on the combined radial and axial ring rolling process. Using the finite element

2 1162 Int J Adv Manuf Technol (2014) 72: Axial ring rolling stage: When the outer surface of the ring completely contacts the inner surface of the constraint roll, the axial ring rolling process is established. In this stage as shown in Fig. 2c, d, the ring produces the deformation of thickness reduction, outer diameter constancy, and axial height increase. Fig. 1 Schematic diagram of the radial ring rolling process (FE) method, the deformation characteristics of the ring are first investigated. Then, the effect of the geometry of the ring blank, axial height H 0, outer diameter D 0, and thickness t 0,on the geometry development and inhomogeneous deformation of the rolled ring, is revealed. 2 Principle of the new combined radial and axial ring rolling process The principle of the new combined radial and axial ring rolling process is illustrated in Fig. 2. During the process, the constraint roll rotates actively around its axis. Under the action of the friction force, the constraint roll takes the ring to rotate together. Meanwhile, the idle roll feeds towards the ring along the radial direction. Under the action of the two rolls, the ring produces the continuous and local plastic deformation. The whole rolling process can be divided into two stages: radial ring rolling stage and axial ring rolling stage. 1. Radial ring rolling stage: In this stage as shown in Fig. 2a, b, the ring mainly produces the deformation of thickness reduction and diameter expansion, and its axial height basically. 3 Development and verification of 3D FE model of the combined radial and axial ring rolling process In this paper, the FE method is adopted to investigate the new combined radial and axial ring rolling process. The developed 3D FE model of the process is illustrated in Fig. 3. During the simulation process, the elastic plastic formulation is adopted to improve the computational accuracy, and the dynamic explicit FE procedure is used to avoid the huge computational time and convergence problem of the static implicit procedure [25]. The mass scaling technology is adopted to accelerate the calculation, and the mass scaling factor is determined to be 300. The two rolls and ring are treated as the analytical rigid bodies and deformable body, respectively. The 3D linear reduction integration continuum element with eight nodes is adopted to mesh the ring. The classical isotropic Coulomb friction model is adopted to describe the friction behavior between the two rolls and ring, and the friction coefficient under the lubricated (MoS 2 ) condition is determined to be [26]. Table 1 provides the process parameters in the simulation of the combined radial and axial ring rolling process. The ring material is 20CrMnTi alloy steel and its constitutive relationship at room temperature is expressed by Eq. (1) [27]. Its relevant mechanical properties are yield strength σ s = (a) Rolling beginning (b) Radial ring rolling (c) Axial ring rolling (d) Rolling finishing Fig. 2 Principle of the combined radial and axial ring rolling process. a Rolling beginning. b Radial ring rolling. c Axial ring rolling. d Rolling finishing

3 Int J Adv Manuf Technol (2014) 72: Axial height of the rolled ring Axial height of inner surface-simulation Axial height of outer surface-simulation Axial height of inner surface-experiment Axial height of outer surface-experiment Fig. 3 3D FE model of the combined radial and axial ring rolling process MPa, Young s modulus E= GPa, Poisson s ratio ν=0.3, and density ρ=7,800 kg/m 3. σ true ¼ 225: ε true ðmpaþ ε true 0: :33ε 0:123 þ 313; 659ðMPaÞ ε true 0: true ð1þ The experiment is conducted to validate the established 3D FE model. When the thickness reduction is 30 % in the experiment, the roundness of the rolled ring is 0.04 mm, and a ring height increase of 23 % is achievable. Figure 4 provides the comparison of the axial height of the rolled ring between the simulation and experimental results. From Fig. 4, itcanbefound that the simulation results are in good agreement with the experimental ones. The maximum relative error of the axial height of the inner and outer surface of the rolled ring is 7.82 and 7.58 %, respectively. The maximum error of the unevenness of the end surface of the rolled ring is %. Thus, the established 3D FE model of the combined radial and axial ring rolling process is reliable. Table 1 Process parameters adopted in the simulation of combined radial and axial ring rolling Parameters Values Outer diameter of the ring blank, D Inner diameter of the ring blank, d Thickness of the ring blank, t 0 5 Axial height of the ring blank, H 0 25 Thickness reduction (%) 30 Inner diameter of the constraint roll, D i 70 Diameter of the idle roll, d i 30 Feed rate of the idle roll, v (mm s 1 ) 1.0 Rotational speed of the constraint roll, n (r min 1 ) 240 Friction coefficient between the rolls and ring, μ Results and discussion Rolling time (s) Fig. 4 Comparison of the simulation and experimental results 4.1 Deformation characteristics in the combined radial and axial ring rolling process Figure 5 shows the equivalent plastic strain (PEEQ) distribution in the axial section of the rolled ring. It can be seen from Fig. 5 that during the rolling process, the plastic deformation zone gradually expands from the inner to outer surface of the ring. Because of the expanding characteristics of the plastic deformation zone, the PEEQ gradually decreases from the inner to outer surface of the ring. Therefore, the axial flow of the metal becomes less significant from the inner to outer surface of the ring, and thus, the axial section of the rolled ring exhibits a trapezium effect. Figure 6 shows the PEEQ evolution of some specific nodes in the axial section of the rolled ring. It can be seen from Fig. 6 that in the radial ring rolling process, the deformation of the ring is relatively homogeneous while it is more inhomogeneous in the axial ring rolling process. This indicates that the inhomogeneous deformation of the ring is mainly caused by the axial ring rolling process. The reason for this is that in the radial ring rolling process, the contact pressure on the inner surface is similar to that on the outer surface of the ring (shown in Fig. 6), and thus, the plastic deformation zone can penetrate the radial thickness of the ring more easily in this process. So, the ring produces a relatively homogeneous deformation. In the axial ring rolling process, the contact pressure on the inner surface is much larger than that on the outer surface of the ring (shown in Fig. 6), and thus, the deformation mainly concentrates on the inner surface of the ring. So, the ring produces an inhomogeneous deformation.

4 1164 Int J Adv Manuf Technol (2014) 72: Fig. 5 PEEQ (equivalent plastic strain) distribution in the axial section of the rolled ring. a t=0 s. b t=0.414 s. c t=0.81 s. dt=2 s (a) t=0 s (b) t=0.414 s (c) t=0.81 s (d) t=2 s 4.2 Determination of the range of the ring blank geometry Figure 7 shows the schematic diagram of the axial section of the rolled ring and ring blank in the combined radial and axial ring rolling process. D, d, H,andtare the outer diameter, inner diameter, axial height, and thickness of the rolled ring, respectively. D 0, d 0, H 0,andt 0 are the outer diameter, inner diameter, axial height, and thickness of the ring blank, respectively. Based on the principle of volume constancy, we have π 4 D2 d 2 π H ¼ 4 D2 0 d2 0 H 0 ð2þ It should be noted that the designed geometry of the rolled ring (D, d, H, andt) in the study of the effect of the ring blank geometry on the proposed process. Based on Eq. (2), the outer diameter D 0 and axial height H 0 of the ring blank can be expressed by Eqs. (3) and(4), respectively. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 2 d 2 H D 0 ¼ þ d 2 0 ð3þ H 0 process. The second one is that the outer diameter of the ring blank D 0 is equal to that of the rolled ring D. Under this condition, the entire process only includes the axial ring rolling process but not the radial ring rolling process. It is obvious that Fig. 7 (H 0 <H and D 0 <D) is the transition condition of the two extreme conditions, in which the entire process includes the radial ring rolling process and the subsequent axial ring rolling process. Based on the above description, it can be concluded that by designing different ring blank geometries, different ring rolling processes can be developed from the combined radial and axial ring rolling process, which may have a significant effect on the rolling process. According to Fig. 8, the range of the ring blank geometry can also be determined. As shown in Fig. 8a, when H 0 =H and d 0 =d i (d i is the diameter of the idle roll), the ring blank has the maximum axial height and minimum outer diameter. As shown in Fig. 8b, when D 0 =D and d 0 =d i, the ring blank has the maximum outer diameter, minimum axial height, and maximum thickness. So, the range of the ring blank geometry can be determined by Eqs. (5) (8). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 2 d 2 þ d 2 i D 0 ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 2 d 2 H þ d 2 0 D H 0 ð5þ H 0 ¼ D2 d 2 H D 2 0 d2 0 ð4þ Through a comprehensive analysis, two extreme conditions in the combined radial and axial ring rolling process can be achieved, as shown in Fig. 8. The first one is that the axial height of the ring blank H 0 is equal to that of the rolled ring H. Under this condition, the entire process only includes the radial ring rolling process but not the subsequent axial ring rolling D 2 d 2 H D 2 d 2 i t t 0 ¼ D 0 d 0 D d i 2 2 d i d 0 d H 0 ¼ D2 d 2 H D 2 0 d 2 H 0 ð6þ ð7þ ð8þ

5 Int J Adv Manuf Technol (2014) 72: Fig. 6 PEEQ evolution of some specific nodes in the axial section of the rolled ring 4.3 Effect of the ring blank geometry on the combined radial and axial ring rolling process In the design of the ring blank, four variables (D 0, d 0, H 0,and t 0 ) need to be determined. In fact, when three of them are known, the ring blank geometry can be determined. Therefore, this paper focuses on investigating the effect of H 0, D 0,andt 0 on the combined radial and axial ring rolling process. As described above, the end surface of the rolled ring is uneven, and its axial section exhibits an obvious trapezium effect, which significantly influences the geometry accuracy of the rolled ring. Therefore, the effect of the ring blank geometry on the unevenness of the end surface of the rolled ring is investigated in this study. The definition of the unevenness of the end surface of the rolled ring Δ H is illustrated in Fig. 9. It is clear that the smaller Δ H, the evener the end surface and the higher the geometry accuracy of the rolled ring and vice versa. In the combined radial and axial ring rolling process, the inhomogeneous deformation of the rolled ring may lead to the damage, and thus, investigating the inhomogeneous deformation has a great importance to improve the forming limits of the rolled ring. In this study, the standard deviation SDP of PEEQ (equivalent plastic strain) is adopted to evaluate the inhomogeneous deformation of the rolled ring. SDP is defined as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X N SDP ¼ ð PEEQ i¼1 i PEEQ a Þ 2 =N ð9þ Fig. 7 Schematic diagram of the axial section of the rolled ring and ring blank in the combined radial and axial ring rolling process where PEEQ i is the PEEQ of the node i,peeq a = N i=1 PEEQ i / N is the average PEEQ of all nodes in the ring, and N is the number of nodes in the ring. It is clear that the smaller SDP,

6 1166 Int J Adv Manuf Technol (2014) 72: Fig. 8 Geometrical relationship of the ring blank, rolled ring, and idle roll in the extreme conditions. a H 0 =H and d 0 =d i. b D 0 =D and d 0 =d i (a) H0 H and d0 d i (b) 0 D Dand d0 di the more homogeneous the deformation of the rolled ring and vice versa. calculation conditions are adopted to investigate the effect of H 0 on the proposed process Effect of the axial height of the ring blank H 0 on the combined radial and axial ring rolling process In the study of the effect of the ring blank geometry on the proposed process, the designed geometry of the rolled ring (D, d, H, andt). This indicates that when H 0 changes, D 0 or t 0 has to change accordingly so as to guarantee the volume constancy of the ring blank. Therefore, two Calculation condition 1: Calculation condition 2: Change H 0 by D 0 but t 0 remains unchanged. Select H 0 ={22, 23, 25, 27, 29}, t 0 =5 mm, and the corresponding D 0 ={70, 67.18, 62.22, 57.99, 54.31}. Change H 0 by t 0 but D 0 remains unchanged. Select H 0 ={22, 23, 25, 27, 29}, D 0 = mm, and the corresponding t 0 ={5.76, 5.48, 5, 4.60, 4.26}. Fig. 9 Definition of the unevenness of the end surface of the rolled ring Δ H. ΔH ¼ H inner Houter H 100%. H inner and H outer are the axial height of the inner and outer surface of the rolled ring, respectively Effect of the axial height of the ring blank H 0 on the geometry development of the rolled ring Figure 10 shows the effect of H 0 on the axial height of the rolled ring. It can be seen from Fig. 10a that under calculation condition 1 (Change H 0 by D 0 but t 0 ), with increasing H 0, the inner surface of the rolled ring gradually decreases while the outer surface of the rolled ring gradually increases in the axial height, i.e., with increasing H 0, the unevenness of the end surface of the rolled ring gradually decreases and the end surface quality becomes better, as shown in Fig. 11. The reason is as follows: when H 0 is smaller, D 0 becomes larger (t 0 ) and thus the axial ring rolling process becomes dominant, as shown in the schematic diagram in Fig. 10a. As described above, it is difficult for the plastic deformation zone to penetrate the radial thickness from the inner to outer surface of the ring in the axial ring rolling process. Therefore, the metal on the inner surface produces much larger axial deformation while the metal on the outer surface produces much smaller axial deformation, resulting in a more uneven end surface of the rolled ring. With increasing

7 Int J Adv Manuf Technol (2014) 72: H 0, the radial ring rolling process gradually becomes dominant, and thus, the plastic deformation zone can penetrate the radial thickness from the inner to outer surface of the ring more easily. Therefore, the metal on the inner and outer surface produces more homogeneous axial deformation, resulting in an evener end surface of the rolled ring. It can be seen from Fig. 10b that under calculation condition 2 (Change H 0 by t 0 but D 0 ), with increasing H 0, the inner surface of the rolled ring gradually decreases while the outer surface of the rolled ring gradually increases in the axial height, i.e., with increasing H 0, the unevenness of the end surface of the rolled ring gradually decreases and the end surface quality becomes better, as shown in Fig. 11. The reason is as follows: On one hand, as H 0 increases, t 0 gradually decreases (D 0 ). On the other hand, as H 0 increases, the radial ring rolling process gradually becomes dominant, as shown in the schematic diagram in Fig. 10b. Under the above two conditions, the plastic deformation zone can penetrate the radial thickness from the inner to outer surface of the ring more easily. Therefore, the metal on the inner and outer surface produces more homogeneous axial deformation, leading to an evener end surface of the rolled ring. It can be seen from Fig. 11 that the effect of H 0 by changing D 0 on the unevenness of the end surface of the rolled ring is different from that by changing t 0. D 0 curve (Change H 0 by D 0 but t 0 ) and t 0 curve (Change H 0 by t 0 but D 0 ) have the same Δ H at H 0 =25 mm, where they corresponds to the same geometry of the ring blank (H 0 =25 mm, D 0 =62.22 mm, t 0 =5 mm). When H 0 is larger than 25 mm, t 0 curve has smaller Δ H than D 0 curve. When H 0 is smaller than 25 mm, D 0 curve has smaller Δ H than 32.0 Axial height of the inner surface of the rolled ring Axial height of the outer surface of the rolled ring Axial height of the rolled ring Axial height of the ring bank H 0 (a) Effect of H 0 on the axial height of the rolled ring (Change H 0 by D 0 but t 0 ) 32.0 Axial height of the inner surface of the rolled ring Axial height of the outer surface of the rolled ring Axial height of the rolled ring Axial height of the ring bank H 0 (b) Effect of H 0 on the axial height of the rolled ring (Change H 0 by t 0 but D 0 ) Fig. 10 Effect of H 0 on the axial height of the rolled ring. a Effect of H 0 on the axial height of the rolled ring (Change H 0 by D 0 but t 0 remains unchanged). b Effect of H 0 on the axial height of the rolled ring (Change H 0 by t 0 but D 0 )

8 1168 Int J Adv Manuf Technol (2014) 72: Unevenness of the end surface of the rolled ring H (%) Change H 0 by D 0 but t 0 Change H 0 by t 0 but D Axial height of the ring bank H 0 Fig. 11 Effect of H 0 on the unevenness of the end surface of the rolled ring t 0 curve. Therefore, in order to make the end surface evener so as to improve the end surface quality of the rolled ring, increasing H 0 by t 0 is superior to increasing H 0 by D 0,while decreasing H 0 by D 0 is superior to decreasing H 0 by t 0.Itcan be also seen from Fig. 11 that when H 0 ranges from 22 to 29 mm, t 0 curve corresponds to a larger range of Δ H than D 0 curve. This indicates that changing H 0 by t 0 is more effective to control the unevenness of the end surface of the rolled ring than changing H 0 by D 0. Effect of the axial height of the ring blank H 0 on the inhomogeneous deformation of the rolled ring As described above, under the two calculation conditions, it is much easier for the plastic deformation zone to penetrate the radial thickness from the inner to outer surface of the ring as H 0 increases. Therefore, SDP gradually decreases and the deformation of Inhomogeneous deformation of the rolled ring SDP Change H 0 by D 0 but t 0 Change H 0 by t 0 but D Axial height of the ring blank H 0 Fig. 12 Effect of H 0 on the inhomogeneous deformation of the rolled ring the rolled ring becomes more homogeneous as H 0 increases, as shown in Fig. 12. It can be seen from Fig. 12 that D 0 curve and t 0 curve have the same SDP at H 0 =25 mm, where they correspond to the same geometry of the ring blank (H 0 = 25 mm, D 0 =62.22 mm, t 0 =5 mm). When H 0 is larger than 25 mm, t 0 curve has smaller SDP than D 0 curve. When H 0 is smaller than 25 mm, D 0 curve has smaller SDP than t 0 curve. Therefore, in order to make the deformation of the rolled ring more homogeneous so as to improve its forming limit, increasing H 0 by t 0 is more effective than increasing H 0 by D 0, while decreasing H 0 by D 0 is more effective than decreasing H 0 by t 0. From Fig. 12, it can be also seen that when H 0 ranges from 22 to 29 mm, t 0 curve corresponds to a larger range of SDP than D 0 curve. This indicates that changing H 0 by t 0 is more effective to control the inhomogeneous deformation of therolledringthanchangingh 0 by D Effect of the outer diameter of the ring blank D 0 on the combined radial and axial ring rolling process Calculation condition 1: Calculation condition 2: Change D 0 by H 0 but t 0 remains unchanged. Select D 0 ={54.31, 57.99, 62.22, 67.18, 70}, t 0 =5 mm, and the corresponding H 0 ={29, 27, 25, 23, 22}. Change D 0 by t 0 but H 0 remains unchanged. Select D 0 ={54.31, 57.99, 62.22, 67.18, 70} mm, H 0 =25 mm, and the corresponding t 0 ={5.91, 5.44, 5, 4.57, 4.36}. Effect of the outer diameter of the ring blank D 0 on the geometry development of the rolled ring Figure 13 shows the effect of D 0 on the axial height of the rolled ring. It can be seen from Fig. 13a that under calculation condition 1 (Change D 0 by H 0 but t 0 ), with increasing D 0, the inner surface of the rolled ring gradually increases while the outer surface of the rolled ring gradually decreases in the axial height, i.e., with increasing D 0, the unevenness of the end surface of the rolled ring gradually increases and the end surface quality becomes worse, as shown in Fig. 14. The reason for this is the same as the effect of H 0 on the axial height of the rolled ring. With increasing D 0, H 0 gradually decreases (t 0 ) and thus the axial ring rolling process gradually becomes dominant, as shown in the schematic diagram in Fig. 13a. Under this circumstance, it is difficult for the plastic deformation zone to penetrate the radial thickness from the inner to outer surface of the ring. Therefore, the metal on the inner surface produces much larger axial deformation while the metal on the outer surface produces much smaller axial deformation, resulting in a more

9 Int J Adv Manuf Technol (2014) 72: Axial height of the rolled ring Axial height of the inner surface of the rolled ring Axial height of the outer surface of the rolled ring Outer diameter of the ring blank D 0 (a) Effect of D 0 on the axial height of the rolled ring (Change D 0 by H 0 but t 0 ) 32.0 Axial height of the rolled ring Axial height of the inner surface of the rolled ring Axial height of the outer surface of the rolled ring Outer diameter of the ring blank D 0 (b) Effect of D 0 on the axial height of the rolled ring (Change D 0 by t 0 but H 0 ) Fig. 13 Effect of D 0 on the axial height of the rolled ring. a Effect of D 0 on the axial height of the rolled ring (Change D 0 by H 0 but t 0 remains unchanged). b Effect of D 0 on the axial height of the rolled ring (Change D 0 by t 0 but H 0 ) uneven end surface of the rolled ring. It can be seen from Fig. 13b that under calculation condition 2 (Change D 0 by t 0 but H 0 ), with increasing D 0, the inner surface of the rolled ring gradually decreases while the outer surface of the rolled ring gradually increases in the axial height, i.e., with increasing D 0, the unevenness of the end surface of the rolled ring gradually decreases and the end surface quality becomes better, as shown in Fig. 14. The reason is that with increasing D 0, t 0 gradually decreases (H 0 ), and thus, it is much easier for the plastic deformation zone to penetrate the radial thickness from the inner to outer surface of the ring. Therefore, the metal on the inner and outer surface produces more homogeneous axial deformation, resulting in an evener end surface of the rolled ring. It can be seen from Fig. 14 that H 0 curve (Change D 0 by H 0 but t 0 ) and t 0 curve (Change D 0 by t 0 but H 0 ) have the same Δ H at D 0 =62.22 mm, where they correspond to the same geometry of the ring blank (H 0 =25 mm, D 0 =62.22 mm, t 0 =5 mm). When D 0 is larger than mm, t 0 curve has smaller Δ H than H 0 curve. When D 0 is smaller than mm, H 0 curve has smaller Δ H than t 0 curve. Therefore, in order to make the end surface evener so as to improve the end surface quality of the rolled ring, increasing D 0 by t 0 is superior to increasing D 0 by H 0, while decreasing D 0 by H 0 is superior to decreasing D 0 by t 0. Effect of the outer diameter of the ring blank D 0 on the inhomogeneous deformation of the rolled ring Based on the above analysis, under calculation condition 1, it is more

10 1170 Int J Adv Manuf Technol (2014) 72: Fig. 14 Effect of D 0 on the unevenness of the end surface of the rolled ring Unevenness of the end surface of the rolled ring H (%) 10 Change D 0 by H 0 but t 0 9 Change D 0 by t 0 but H Outer diameter of the ring blank D 0 difficult for the plastic deformation zone to penetrate the radial thickness from the inner to outer surface of the ring with increasing D 0. Therefore, SDP gradually increases and the deformation of the rolled ring becomes more inhomogeneous with increasing D 0, as shown in Fig. 15. Under calculation condition 2, it is much easier for the plastic deformation zone to penetrate the radial thickness from the inner to outer surface of the ring with increasing D 0. Therefore, SDP gradually decreases and the deformation of the rolled ring becomes more homogeneous with increasing D 0, as shown in Fig. 15. It can be also seen from Fig. 15 that in order to make the deformation of the rolled ring more homogeneous so as to improve its forming limit, increasing D 0 by t 0 is superior to Inhomogeneous deformation of the rolled ring SDP Change D 0 by H 0 but t 0 Change D 0 by t 0 but H Outer diameter of the ring blank D 0 Fig. 15 Effect of D 0 on the inhomogeneous deformation of the rolled ring increasing D 0 by H 0, while decreasing D 0 by H 0 is superior to decreasing D 0 by t Effect of the thickness of the ring blank t 0 on the combined radial and axial ring rolling process Calculation condition 1: Calculation condition 2: Change t 0 by H 0 but D 0 remains unchanged. Select t 0 ={4.26, 4.60, 5, 5.48, 5.76}, D 0 = mm, and the corresponding H 0 ={29, 27, 25, 23, 22}. Change t 0 by D 0 but H 0 remains unchanged. Select t 0 ={4.26, 4.60, 5, 5.48, 5.76}, H 0 =25 mm, and the corresponding D 0 ={69.96, 66.77, 62.22, 57.67, 55.41}. Effect of the thickness of the ring blank t 0 on the geometry development of the rolled ring Figure 16 shows the effect of t 0 on the axial height of the rolled ring. It can be seen from Fig. 16 that under the two calculation conditions, with increasing t 0, the inner surface of the rolled ring gradually increases while the outer surface of the rolled ring gradually decreases in the axial height, i.e., as t 0 increases, the unevenness of the end surface of the rolled ring gradually increases and the end surface quality becomes worse, as shown in Fig. 17. The reason is that as t 0 increases, it is more difficult for the plastic deformation zone to penetrate the radial thickness from the inner to outer surface of the ring. Therefore, the metal on the inner surface produces much larger axial deformation while

11 Int J Adv Manuf Technol (2014) 72: Axial height of the inner surface of the rolled ring Axial height of the outer surface of the rolled ring Axial height of the rolled ring Thickness of the ring blank t 0 (a) Effect of t 0 on the axial height of the rolled ring (Change t 0 by H 0 but D 0 ) 32.0 Axial height of the rolled ring Axial height of the inner surface of the rolled ring Axial height of the outer surface of the rolled ring Thickness of the ring blank t 0 (b) Effect of t 0 on the axial height of the rolled ring (Change t 0 by D 0 but H 0 ) Fig. 16 Effect of t 0 on the axial height of the rolled ring. a Effect of t 0 on the axial height of the rolled ring (Change t 0 by H 0 but D 0 ). b Effect of t 0 on the axial height of the rolled ring (Change t 0 by D 0 but H 0 ) the metal on the outer surface produces much smaller axial deformation, resulting in a more uneven end surface of the rolled ring. It can be seen from Fig. 17 that in order to make the end surface evener so as to improve the end surface quality of the rolled ring, increasing t 0 by D 0 is superior to increasing t 0 by H 0, while decreasing t 0 by H 0 is superior to decreasing t 0 by D 0. It can be also seen from Fig. 17 that changing t 0 by H 0 is more effective to control the unevenness of the end surface of therolledringthanchangingt 0 by D 0. Effect of the thickness of the ring blank t 0 on the inhomogeneous deformation of the rolled ring According to the above analysis, under the two calculation conditions, it is more difficult for the plastic deformation zone to penetrate the radial thickness from the inner to outer surface of the ring as t 0 increases. Therefore, SDP gradually increases and the deformation of the rolled ring becomes more inhomogeneous as t 0 increases, as shown in Fig. 18. It can be seen from Fig. 18 that in order to make the deformation of the rolled ring more homogeneous so as to improve its forming limit, increasing t 0 by D 0 is more effective than increasing t 0 by H 0,while decreasing t 0 by H 0 is more effective than decreasing t 0 by D 0. From Fig. 18, it can be also seen that changing t 0 by H 0 is more effective to control the inhomogeneous deformation of therolledringthanchangingt 0 by D 0.

12 1172 Int J Adv Manuf Technol (2014) 72: Unevenness of the end surface of the rolled ring (%) 12 Change t 0 by H 0 but D Conclusions Change t 0 by D 0 but H Thickness of the ring blank t 0 Fig. 17 Effect of t 0 on the unevenness of the end surface of the rolled ring On the basis of the radial ring rolling process, this paper proposes a new combined radial and axial ring rolling process, which can achieve a large increase in both the ring diameter and height. In view of the importance of the geometry of the ring blank, this paper reveals the effect of the geometry of the ring blank on the combined radial and axial ring rolling process using the FE method. The results of this research show the following: 1. The combined radial and axial ring rolling process includes two stages: radial ring rolling stage and axial ring rolling stage. In radial ring rolling, the plastic deformation zone can penetrate the radial thickness from the inner to outer surface of the ring more easily. In axial ring rolling, it is more difficult for the plastic deformation zone to Inhomogeneous deformation of the rolled ring SDP Change t 0 by H 0 but D 0 Change t 0 by D 0 but H Thickness of the ring blank t 0 Fig. 18 Effect of t 0 on the inhomogeneous deformation of the rolled ring penetrate the radial thickness from the inner to outer surface of the ring. 2. By designing different ring blank geometries, two kinds of extreme ring rolling processes, i.e., only radial ring rolling process and only axial ring rolling process, can be developed from the combined radial and axial ring rolling process, which may change the distribution of the radial ring rolling process and the subsequent axial ring rolling process. Moreover, the range of the ring blank geometry is determined in this study. 3. Under the two calculation conditions (Change H 0 by t 0 and Change H 0 by D 0 ), with increasing H 0,theend surface quality becomes better and the deformation of the rolled ring becomes more homogeneous. In order to make the end surface evener and the deformation more homogeneous, increasing H 0 by t 0 is superior to increasing H 0 by D 0, while decreasing H 0 by D 0 is superior to decreasing H 0 by t 0. Moreover, changing H 0 by t 0 is more effective to control the unevenness of the end surface and the inhomogeneous deformation of the rolled ring than changing H 0 by D Under calculation condition 1 (Change D 0 by H 0 but t 0 ), with increasing D 0, the end surface quality becomes worse and the deformation of the rolled ring becomes more inhomogeneous. Under calculation condition 2 (Change D 0 by t 0 but H 0 ), with increasing D 0, the end surface quality becomes better and the deformation of the rolled ring becomes more homogeneous. In order to make the end surface evener and the deformation more homogeneous, increasing D 0 by t 0 is superior to increasing D 0 by H 0, while decreasing D 0 by H 0 is superior to decreasing D 0 by t Under the two calculation conditions (Change t 0 by H 0 and Change t 0 by D 0 ), with increasing t 0,theendsurface quality becomes worse and the deformation of the rolled ring becomes more inhomogeneous. In order to make the end surface evener and the deformation more homogeneous, increasing t 0 by D 0 is superior to increasing t 0 by H 0, while decreasing t 0 by H 0 is superior to decreasing t 0 by D 0. Moreover, changing t 0 by H 0 is more effective to control the unevenness of the end surface and the inhomogeneous deformation of the rolled ring than changing t 0 by D 0. Acknowledgments The authors would like to thank the National Basic Research Program of China (No. 2011CB706605), Innovative Research Team Development Program of Ministry of Education of China (No. IRT13087), Innovative Research Groups of the Natural Science Foundation of Hubei Province (No. 2011CDA12), National Natural Science Foundation for Young Scholars (No ), and the Fundamental Research Funds for the Central Universities (No IV-014) for the support given to this research.

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