International Syposiu on Material, Energy and Environent Enginee (ISM3E 2015) Optiu Design of Assebled Cavity Dies for Precision Forging Process Jun-song Jin1 and Xin-yun Wang1,* 1 State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China Abstract. For a given three-layer assebled die of cold precision forging gear, the optiu design was ipleented based on the elastic solution of the thick-wall cylinder under the adissible tensile stress. A non-unifor interference fit structure was eployed, and the iniu tangential tensile stress in the cavity was defined as the objective function. The inner radius r2 and radius r3 of the inner shrink, and the interference fit agnitude of atching faces between different layers were defined as variables of the objective function. These variables were optiized with MATLAB software package. The optiized results were verified with elastic-plastic finite eleent analysis (FEA). Then, forging experients were conducted according to the calculated data with MATLAB and FEA results. Copared to conventional design ethods, the optiized die structure with non-unifor interference fit is effective in prolonging the service life of gear dies ore than ten ties. and the upper section and botto section have the sae agnitude of interference fit [2-4]. Most of the copression effect induced by this unifor interference fit will be borne by the lower section since the lower section has stiffness higher than that of the upper section. The effect of shrink will be lowered, and the prestress will be insufficient at the upper section. For a conventional structure that has the unifor interference fit, cracking ay occur at the corner of cavity dies early because of insufficient pre-stress. There are two possible ways to solve this proble. One is to increase the radius at the corner to reduce stress concentration, but this ethod contributes little to the production because the diensional change of a precise workpiece is unallowable. The second way is to iprove the pre-stress by increasing the agnitude of an interference fit. However, it is liited by the allowable stress of die aterials. Further ore, a greater agnitude of interference fit will lead to difficult assebly. The present paper proposed a three-layer assebled die structure with a non-unifor interference fit to iprove the effect of shrink, and extend the life of dies. As a contrast, a conventional three-layer assebled die with unifor interference fit was analysed (see Fig. 1). The proposed structure with non-unifor interference fit is shown in Fig. 2, and the value of interference fit between the upper section and the inner is bigger than that between the lower section and the inner, which are arked with circles and crosses, respectively. Paraeters of assebled dies were optiized and verified with FEA. Finally, experients were conducted in a gear factory according to the analysed results. 1 Introduction Pre-stressing a forging die by shrinking a over the outside is a coon ethod to iprove the service life of dies and is frequently used in industry. However, the residual copressive and circuferential stresses are introduced into the die du pre-stressing. These residual stresses can significantly reduce the agnitude of circuferential tensile stresses that are aroused in the etal working. Kutuk et al. studied a cylindrical approach for shrink-fit precision cylinder gear forging dies via finite eleent analysis (FEA) [1]. Fu and Shang analysed the stress of bevel gear forging dies and optiized by the boundary-eleent ethod [2]. Song and I studied the closed-die forging of bevel gears process by FEA. The radius of the shrink was set to be three ties over the axiu radius of the gear according to epirical equations [3]. Zhang designed a double-layer die for cold and war bevel gear forging experients [4]. All of the dies used in these studies were designed as one shrink. However, pre-stressing of double-layer assebled die is insufficient due to the stress concentration on soe occasions, so a three-layer assebled die is required. The optiu design of three-layer assebled backward and/or forward extrusion dies was studied [6-8]. No tensile stress or iniu tensile stress was defined as the target functions. Die sets with unifor agnitudes of interference fit were designed, and infinite length thick-wall cylinder with unifor inner pressure was assued in the analysis. The assuption was acceptable according to the experiental results due to the unifor cross-section of inner cavity die along die syetrical axis. A typical characteristic of cavity die of bevel gear is that the cross-section along the die syetrical axis is not unifor. The upper section is a cavity used to pattern bevel gear, and the lower section, naed as the thick botto, with a hole is used to press the blank and eject the forged gear. All of the entioned papers designed this type of thick botto dies with a double-layer structure, 2015. The authors - Published by Atlantis Press 613
r1 r4 r3 Figure 1. Conventional design of three-layer assebled gear cavity dies. r4 r3 r2 r1 r2 2.2 Stress analysis for three-layer die Fig. 4 shows the paraeters and pressures in a three-layer assebled die between each layer. According to Equation (2), the tangential stress σ θ3 at radius r 3 of the can be expressed as: ( r4 r3 ) p3 3 r4 r3 (3) r4 r3 p3 3 ( r4 r3 ) (4) where p 3 is the interface pressure between the inner and, r 3 is the interface radius between the inner and and r 4 is the radius of the. Meanwhile, the tangential stress of the inner shrink can be expressed as: 2 p2( r2 r3 ) 2p3r3 2 r3 r2 (5) 2 2( r3 r2 ) 2p3r3 p2 (6) r r 2 3 ro Figure 2. Bevel gear die with a non-unifor interference fit. 2 Elastic solution odel of assebled thick-wall cylinder p o p i ri For assebled cold foring dies, the failure of shrink s is usually aroused by the tangential cracks caused by tensile stress. Since nearly no plastic deforation occurs because of high hardness, the die can be considered as elastic odel. When the two shrink s reach the adissible tensile stress, the axiu copression pre-stress on the die can be obtained. 2.1 Elastic solutions for single-layer thick-wall cylinder Fig. 3 shows a single-layer thick-wall cylinder with inner pressure p i and pressure p o, the distribution of tangential stress σ θ and radial stress σ r can be expressed as: rr i o ( po pi) 1 pr i i pr o o r 2 ro ri r ro ri (1) rr i o ( po pi) 1 pr i i pr o o 2 ro ri r ro ri (2) where r i and r o are the inner radius and radius, respectively, r varies between r i and r o. Figure 3. A single-layer thick-wall cylinder with inner pressure p i and pressure p o. r4 p i r3 r1 Figure 4. Paraeters for three-layer assebled cavity die. r2 where σ θ2 is the adissible tensile stress for the inner, p 2 is the interface pressure between the inner and p 2 p 3 614
cavity die, and r 2 is the interface radius between the cavity die and inner. The tangential stress σ θ=r1 at the equivalent inner face of the cavity die can be expressed with inner pressure p i and pressure p 2 as: 2 p r p( r r ) r1 2 22 i 2 1 r2 r1 (7) The radial stress σ r=r2 at r=r 2 pressure p i is pr r r p 1 r r r r r r r2 2 i 1 1 4 i 2 4 1 4 1 2 led by the inner (13) 3 Interference agnitude calculation The agnitudes of interference fit of a three-layer assebled die are derived fro a sipler double layer shrink. Fig. 5 shows an assebled double-layer thick-wall cylinder with no inner pressure and pressure, the assebled pressure p on interface can be expressed as [9]: E ( r r )( r r ) p r r r r i1 o1 2 2 ( o1 i1 ) 2 r ( r r ) p E( r r )( r r ) 3 o1 i1 i1 o1 Where, δ is the agnitude of an interference fit, r il is the inner radius of inner cylinder, r o1 is the radius of the cylinder, and r is the interface radius between the two assebled cylinders. The interface pressure aroused by shrinking between the cavity die and inner is naed as p 2, while p 3 is that between the inner and. These two pressures are used to calculate the interference agnitudes of a three-layer assebled die as displayed in Fig. 4. The radial stress σ r=r3 at r=r 3 led by p 2 is (8) (9) p p rr2 rr2 (14) According to Equation (9), the interference agnitudes at r=r 2 and r=r 3 are expressed as: 2 r ( r r ) p ( )( ) 3 2 4 1 2 2 E r2 r1 r4 r2 2 r ( r r ) p ( )( ) 3 3 4 1 3 3 E r3 r1 r4 r3 p Figure 5. Model for the assebled double-layer thick-wall cylinder. ri1 r ro1 (15) (16) p2r2 r4 r r (1 ) 3 2 r4 r2 r3 (10) p p 3 3 r r 3 The radial stress σ r=r2 at r=r 2 led by p 3 is pr r (1 ) r r r r r2 3 3 1 2 3 1 2 (11) (12) 4 Paraeter optiization procedure The equivalent radius of a cavity die is a constant and arked with r 1, while r 2 and r 3 are variables, Equation (7) is defined as the target function and the target is to get the iniu value of σ θ=r1. Since Equation (7) is a higher order equation, it is very difficult to give its analytic solution by partial derivative ethods, so coputer prograing ethod was used and MATLAB software was eployed as a prograing tool. Fig.6 briefly shows the flow diagra of searching algorith for optiization procedure. The algorith of the optiization procedure for target value is as follows: Stage 1. Input the iniu value of design variable r 2, and initialize design variable r 3, where r 2 <r 3 <r 4. 615
Stage 2. Calculate the value of the objective function (7), if the value reaches the iniu, go to the next stage, otherwise update r 3 with an increent Δr 3 until r 3 = r 4. Stage 3. If the value reaches the iniu for r 2, go to the next stage, otherwise update r 2 with an increent Δr 2 and go to Stage 2. If r 2 = r 4, go to next stage. Stage 4. If r 2 =r 4, a single layer die is designed; else if r 2 =r 3 r 4 or r 2 r 3 =r 4, a double layer die is designed, output the target value and the corresponding values of r 2 and r 3, and calculating δ 2 and δ 3 by Equations (8)-(16); Else, output the target value and the corresponding values r 2 and r 3 and calculating δ 2 and δ 3 by Equations (8)-(16). Table 1. Material paraeters for each layer. Nae Material Adissible stress Hardness (MPa) (HRC) Cavity die 65Nb 2400 60 Inner 5CrNiMo 1200 40-45 Outer 5CrNiMo 1200 >35 Table 2. Magnitudes of interference fit. Method δ 2 δ 3 Traditional ethod 0.533 0.391 Optiized ethod 0.465 0.412 Table 3. Geoetry paraeters and corresponding stress. Method Traditional ethods optiized ethods r 1 () r 2 () r 3 () r 4 () σ θ=r1 (MPa) 30 51 87 300 543 30 43.5 81 300 411 6 FEA of the dies 6.1 FEA odel To verify the results, FEA was carried on with Ansys soft package. Elastic-plastic dies were considered in siulation, conside the high hardness and sall teperature variation. The Young s odules of the cavity die and s were set to 2.07E5 MPa and 2.10E5 MPa, respectively. The stress-strain curves of the aterials at roo teperature were illustrated in Figs. 7 and 8 [11, 12]. Figure 6. Scheatic of the calculation flow in MATLAB. 5 Optiized paraeters and conventionally designed paraeters The aterial paraeters of assebled dies are shown in Table 1. The geoetry paraeters and agnitudes of an interference fit between each layer designed with the conventional ethod [10] and proposed ethod are shown in Tables 2 and 3, respectively. The inner pressure p i was 2500 MPa. The increent values of Δr 2 and Δr 3 were set to 0.1. An optiu value was obtained after 353197 steps of iteration. Stress(GPa) 4 3.75 3.5 3.25 3 2.75 2.5 2.25 2 1.75 1.5 1.25 1 0.75 0.5 0.25 0 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 Strain(%) Figure 7. Stress-strain curve of 65Nb. 616
Stress(GPa) 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 1011121314 Strain(%) variables (such as stress, strain and displaceent) du the siulations at pre-defined points. For the, Path 1 was defined in the inner surface along the axial direction shown in Fig. 10, and the circuferential stress distribution on the path is shown in Fig. 11. Fig. 12 shows the Path 2 definition on the inner surface of the inner. Figs. 13 and 14 show the circuferential stress and radial stress along the path. Fig. 15 shows the Path 3 definition along the cavity die corner. The distributions of the first principle stress, von stress and strain along the path are shown in Figs.16, 17, and 18, respectively. Figure 8. Stress-strain curve of 5CrNiMo. Figure 9. The FEA odel. Figure 10. Definition of Path 1 at the. Three types of die structures were odelled in siulations. The first one was odelled with unifor interference fit shown in Fig. 1 with conventional geoetry paraeters and interference agnitude, the second die set was odelled with a unifor interference fit shown in Fig. 1 and optiized paraeters, and the third one was odelled with a non-unifor interference and optiized paraeters shown in Fig. 2. The contact pair definition in both the conventional structure and the proposed structure were shown in Figs. 1 and 2. All the contact pairs were defined as face-to-face. A contact face and a target face were defined in each contact pair. Eleent types of contact 170 and 174 were utilized to define the contact face and target face, respectively. The definition contact type is very iportant in the siulation. Copared with other contact types, the face-to-face contact pair has any advantages, such as supporting lower order and higher order eleents, coplex contact surface, saller disk space, and CPU tie requireent, etc. To reduce the calculating tie, a single-tooth cavitydie odel was constructed, and syetrical boundary condition was eployed (see Fig. 9). Figure 11. Stress distribution on Path 1 (1. first odel; 2. second odel; 3. third odel). 6.2 FEA results The path tool was eployed to investigate the stress distribution. This tool can collect the output values of the 617
Figure 12. Definition of Path 2 at the inner. Figure 15. Definition of Path 3 at the cavity die. Figure 13. Circuferential-stress distribution on Path 2 (1. first odel; 2. second odel; 3. third odel). Figure 16. First principle stress distribution on Path 3 (1. first odel; 2. second odel; 3. third odel). Figure 17. Von stress distribution on Path 3 (1. first odel; 2. second odel; 3. third odel). Figure 14. Radial-stress distribution on Path 2 (1. first odel; 2. second odel; 3. third odel ). 618
third FEA odel. Die structure and corresponding die set are shown in Fig. 20. 7.3 Experients results The forged bevel gear was shown in Fig. 21. By using the die set of a unifor interference fit, a foring load L of 3700 kn was needed to fill the teeth cavities. Within 1000 forging cycles, the botto corner of the second die set cracked (see Fig. 22). However, the botto corner of the die set with non-unifor interference fit didn t crack until 10000 ties of forging. Figure 18. Strain distribution on Path 3 in three odels (1E, 2E, 3E: elastic strain; 1P, 2P, 3P: plastic strain ). pitch diaeter 7 Experient and application 7.1 Experient conditions Tip angle pitch cone angle Root cone angel An involute bevel gear was chosen as the objective part, with its paraeters shown in Table 4 and Fig. 19, respectively. Table 4. Paraeters of investigated bevel gear. Paraeter Value Nuber of teeth 16 Module 3.869 Pressure angle 24 o Pitch diaeter 61.904 Pitch cone angle 57.995 o Root cone angel 50.734 o Tip angle 63.317 o Tooth addendu 2.850 Tooth dedendu 4.640 Back sphere diaeter 76.850 Circular tooth thickness at big end 5.693 Figure 19. Paraeters of the bevel gear. The gear aterial used in this research was 20CrMo. It was annealed at 770 C to a hardness of HB 140. The blank was a cylinder of 32 in diaeter and 37 in height. Surface phosphate treatent was undertaken, and MoS2-oil ixture was used for better lubrication. 65Nb steel was eployed for the cavity die. The die cavity was illed and polished to a roughness of 0.2 µ after heat treatent to get a hardness of HRC 60.5. Forging was carried on a Y-28-400/400 double-action hydraulic press. A 3000 KN claping force F was applied on dies based on previous experience. 7.2 Die set According to the calculated results with MATLAB and FEA data with Ansys. Two types of die sets were designed, one was a three-layer assebled cavity die which was the sae as the first FEA odel, and the other was an assebled cavity die which was siilar to the 619
8 Discussion Figure 20. Illustration of the die structure (a) and experient die set (b). Figure 21. A forged bevel gear. Table 2 reveals that the two agnitudes of an interference fit between each layer are uch different, the value of δ 2 is 0.142 larger than that of δ 3 in conventional design ethod. However, the two values are only 0.053 in difference with the optiized ethod. Table 3 reveals that r 2 and r 3 designed by the optiized ethod are 7.5 and 6, which are saller than those by a the conventional ethod, respectively. The tangential tensile stress at the equivalent cylindrical face of the cavity die is reduced about 24.3%, fro 543 MPa to 411 MPa. Fig. 11 shows that the circuferential stress in the inner face of the out along Path 1 in the second odel is lower than that in the first odel. The corresponding stress in the third one is uch lower than that in the forer two. That eans the of the third die is safer than the others. According to Fig. 13, the second odel has the highest circuferential stress along Path 2, and the third one has the lowest value. Especially, at a distance about 18, the circuferential stress in the third one changes fro tensile state to copressive state. It indicates that the inner of the third die has the least risk of failure. At the distance of 2 to 18 on the path, the third odel has uch bigger radial copressive stress, indicating the pre-stress applied on cavity die is safer (see Fig. 14). The distributions of the first principle stress and von stress along Path 3 are shown in Figs.16 and 17. Fro the distance of 8 to 17 on Path 3, the first principle stress becoes negative, which eans the cavity die is in a purely copressive stress state (see Fig. 16). The axiu value of the von stress occurs in the first odel according to Fig. 17. The higher von stress leads to the higher possibility of crack, and a cracked die designed in the first odel is shown in Fig. 22. No plastic deforation occurs in other place except at the corner on the Path 3 (see Fig. 15). According to Fig. 18, the axiu plastic strain is 0.45% in the first odel, 0.35% in the second odel and only 0.2% in the third odel. The plastic deforation distributes little to the whole odel, so the odel can be assued to be elastic. A little different can be found between the FEA results and the calculate values fro MATLAB prograing. The reason is that the shape of cavity die is not taken into consideration in MATLAB prograing. However, they show the sae variation tendency. Both the FEA and experient results prove that the optiized die set with non-unifor interference fit is a better way to increase the service life of die with the non-unifor cavity and thick botto. Mass production in Dongfeng Autoobile Finished Gear Co. proves that the service life of die designed with the optiized ethod is over ten ties longer than that of the die designed with the conventional ethod. Figure 22. Failure of the die. 9 Conclusions In this paper, a die structure with non-unifor interference fit was designed to iprove the life of dies. 620
The value of interference fit between the upper section and the inner was bigger than that between the lower section and the inner. The objective of optiization was to iniize the tensile stress by axiizing the prestress of shrink s. A ethod that cobined coputer prograing and thick-wall cylinder elastic solutions was eployed to optiize the radius r 2 and r 3, and calculate the agnitudes of an interference fit. Based on the calculated results, FEA and experients were conducted. Both FEA and experient results proved that the structure of non-unifor interference fit can increase the service life of assebled cavity dies effectively. Acknowledgeents We would like to express our deep gratitude to the National Key Technology Research & Developent Progra of China (Grant No. 2006BAF04B06) and Hubei Provincial Technology Research & Developent Progra Of China (Grant No. 2005AA101B19) for financial support and Dongfeng Finished Gear Plant for experient support of this project. References [1] Kutuk M.A., Proceedings of the Institution of Mechanical Engineers, 217(2003) [2] Fu M.W. and Shang B.Z., Journal of Materials Processing Technology, 53(1995) [3] Song J. H. and I Y. T., Journal of Materials Processing Technology, 192(2007) [4] Zhang H. and Sun W., Forging & Staping Technology, 30(2005) [5] Xu X.B., Metal Foring Technology, 21(2003) [6] Lou H.W. and Gao, J.Z., Journal of Jiangsu Machine Building & Autoation, 1(2003) [7] Luo Z.H. and Zhang Z.L., Journal of Plasticity Enginee, 36(2002) [8] Zhang C.E., (Shandong University, Shandong, 2007) [9] Xu B.Y. and Huang Y., Elastic-Plastic Mechanics and Application (Mechanical Industry Press, Peking, 1994) [10] Li S.J., Datu for Forging Process and Die Design (Mechanical Industry Press, Beijing, 1991) [11] Xia J.C., China Die & Mould Design Canon (Jiangxi Science & Technology Press, Jiangxi, 2003) [12] Editorial Board of Operative Mould Technology, Mould Materials and Service Lives (Mechanical Industry, Beijing, 2004) 621