ORIGINAL ARTICLE
Preform and forging process designs based on geometrical
features using 2D and 3D FEM simulations
Jinn-Jong Sheu&Cheng-Hsien Yu
Received: 1 June 2008 / Accepted: 31 October 2008 / Published online: 22 November 2008 # Springer-Verlag London Limited 2008
Abstract The requirements of compact and integrated industrial products make it more difficult to produce these complicated parts. The aim of this paper attempts to propose methods of finish forging die and preform designs to produce a product consisting of a solid spur gear and cylindrical cup features. One- and two-step forming processes were proposed and evaluated using computer-aided engineering simulations. For one-step extrusion or upsetting processes, diameters and heights of billet were calculated using the product volume and the corresponding cup or gear features, respectively. For two-step forming process, Tee-shaped preform designs were proposed based on the product volume and the feature volume ratio of cup to gear; corner and fillet arcs were adopted to modify the profile of Tee and control the material flow in the finisher die. The forming processes of preform and finisher were analyzed using the two- and three-dimensional finite-element method models to predict the detail characteristics of sectional material flow and the completely three-dimensional deformation results, respectively. Experimental
tests were also carried out to validate the proposed simulation models and design methods. The forming loads, the stress and strain distributions of forged part, and the occurrences of defects were studied and a suitable preform and corresponding die designs were obtained. The proposed preform designs were verified via the numerical analyses for the feasibility study. Finally, a sound gear product had been made successfully using the proposed suitable design of preform.
Keywords Preform design . Forging die design . CAE simulation . Defect prediction
1 Introduction
Many design rules of toolsets and forging processes have been proposed to get the better accuracy and quality of forged gear parts [1]. It suggests that if the ratio of tooth width to gear diameter is large, teeth can often be formed by extrusion. One of the factors which affects the dimensions of die is the elastic expansion due to forging pressures and the accuracy of forged part increases with decreasing forging loads To obtain the better accuracy and quality of forged gear parts with a good die design, the forming analysis of forging process is essential for the evaluation of material flows and defects. Many researchers have proposed the simplified analysis methods for the forging of spur gears, gear splines, and helical gears [2–5]. Sadeghi et al. [2] have proposed a new velocity field of upper bound analysis which is capable of predicting the tooth form bulging of spur and helical gears forging. The DOI 10.1007/s00170-008-1834-5
J.-J. Sheu (*)
Department of Mold and Die Engineering,
National Kaohsiung University of Applied Sciences, 415, Chien Kuang Road,
Kaohsiung 807, Taiwan e-mail: jjsheu@cc.kuas.edu.tw C.-H. Yu
Graduate student, Department of Mold and Die Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan
tendencies of relative forging pressure with respect to the ratio of height reduction have been studied considering the different friction conditions, the tooth numbers, and the bore diameters of hollow gear. The relative forging pressure increases as the gear height reduces, and it dramatically increases during the corner filling stage. Chitakra et al. [3–5] have proposed different kinematically admissible velocity fields to do the upper bound forging analysis of external spine gears, gear coupling forms, and hollow spur gears. The proposed velocity fields have been divided into many zones to cope with to the geometrical features of the products. The optimized velocity fields are able to predict the forging loads and the deformation grids with respect to the different billet designs. Tomov and Gagov [6] have combined the slab method and the experiments of model materials to analyze the forging process of cylindrical spur gears. The statistical analysis of finite-element method (FEM) forming simulation data is used to derive the regressing equation of forging loads. Kang et al. [7] have proposed a simplified 3D FEM analysis method for the forging of a gear part with inner cam profiles. The mapping concept of equivalent area is proposed to simplify the simulation of forming process by using an arc of equivalent radius to replace the unknown free boundary of material flows in the subsequent forging steps. The re-meshing operations are accomplished using DEFORM 3D to avoid the condition of high mesh distortion.
Lee et al. [8] have adopted a rigid-plastic FEM program to analyze the forging process of a bevel gear part and proposed a better die design which is able to avoid the unfilled defects using a central pin installed at the lower die. The key concept of this design is to force the materials flow out to the corner areas with the pushing of central pin. Song et al. [9] have developed an in-house FE program named CAMPform 3D to investigate the die filling of gear teeth in the cold forward extrusion process. The area ratios of the filled gear teeth to the whole gear part are introduced to evaluate the forming process. The results have revealed that the gears with or without a mandrel can be simulated with reliability using different shear friction factors. Petruska et al. [10] have adopted the compression tests of
cylindrical specimens with surface notch to evaluate the various ductile fracture criteria. The compression tests of low alloy steel 50CrV4 are carried out to verify the criteria proposed by Cockroft and Latham and Freundenthal et al. The explicit FEM code LS-DYNA3D has been adopted to obtain the critical values of the above-mentioned fracture criteria. A cubic stress–strain equation is proposed to model the material flow. Cai et al. [11] have proposed the alternative die design of a near-net shape gear forging, and the analysis of forming process has been accomplished using the Explicit Abaqus software. The shapes of counterpunch and the fixing methods of die are chosen in the existing alternatives of the tool design in accordance to the geometry of forged parts. Yeo et al. [12] have designed a prestressed cold extrusion die with stress rings using the rigid and the elastic FEM methods, respectively, for the analyses of the forming process and the die stress. A suitable prestressed ring design is helpful to reduce the hoop and the radial stresses of the extrusion dies. A simulation-based approach of die design and assessment has been presented by Fu et al. [13] considering the fatigue analysis methods of the stress life and the strain life. The relationship between the plastic strain and the fatigue life proposed by Coffin [14] and Mansion [15] has been adopted for the fatigue analysis of strain life. The forging processes are simulated by using DEFORM to obtain the stresses and the strains of die components. To save the time-consuming process of FEM simulations, the artificial neural networks (ANN)and the genetic algorithms (GA) has been adopted to predict the spring-back of a sheet metal bending or to search the optimal extrusion die design [16,
17]. The integration of ANN and GA makes the simulation process less costly and maximizes the utilization of the analysis data of forming processes.
The preform design of a multipass forming process is another issue of forging analysis. Design of intermediate preform is generally carried out using empirical production experience. Lapovok [18] has proposed a method of optimal preform design that consists of the preform parameter choosing step and the mathematical experiment step. The die life has been presented by the accumulated
Tooth number: 30 Module: 0.75 Pressure angle: 20 Addendum dia.:24mm Pitch circle dia.:22.5mm Root dia.:
Fig. 1 Geometry, dimensions of the forged gear part
equivalent plastic strain and chosen as the criterion of optimal preform design. Kang et al. [19] have proposed an iteration algorithm for the preform design of H-shaped plane strain components using FEM simulation. Rectangular stocks with different height to width ratios have been adopted for the blocker die designs, which consist of line and arc segment profiles. Deformed geometries and the total effective strains have been examined to evaluate the ability of die filling and the feasibility of material flows. The proposed method is only a feasible design, yet the optimi-zation is still a problem in this study. To improve the time-consuming preform design task, Chang and Bramley [20] have proposed a reverse simulation approach based on the upper bound method with the finite-element procedure. A measure of the material distribution has been proposed to evaluate the geometrical complexity of the rectangular and the circular sections for the preform designs of two-dimensional plane strain examples. Multiplication of the second moments of area about the x-axis, Ix, and about the y-axis, Iy, is considered as a measure of geometrical complexity. The target of preform profile in the reverse simulation process is to find a value of IxIy as close to the value of the deformed workpiece as possible. Tomov [21] has mentioned a criterion called shape complexity factor (SCF) proposed by G. P. Teterin et al. [22] to judge the need of preform design. The SCFs of the forged part and the billet are defined by Eqs.1and 2, respectively,
SCF ð ÞF ¼ P2 A F . P2A C h i 2RGF ð Þ=RGC ½ ð1Þ SCF ð Þ0¼ P2 A 0 . P2A C0 h i 2RC0 ð Þ=R0 ½ ð2Þ
where P, A, and R are perimeters, areas of the vertical sections of the forged component and circumscribed cylinder and radii of the gravity centers of the forged component (with subscript GF) and circumscribed cylinder (with subscript GC). The indexes F, C, and 0 refer to the forging component, circumscribed cylinder, and the slug dimensions, respectively. If the ratio of SCFF to SCF0 is
larger than one, a preform impression will be required in the sequence of forging. This factor is the result of an expert assessment and usually requires more preform impressions. Zhao et al. [23] have adopted the above-mentioned complexity factor to do the preform forging analysis using the rigid viscoplastic FEM formulation. An integrated blade and rotor turbine disk forging has been adopted to demonstrate the forward simulation of an empirical preform design and the preform design method-ology based on the backward simulation. The occurrence of incomplete die filling has been observed in the case of the empirical preform design, but it did not happen when using the preform design based on the backward simulation. In our research, the softwares DEFORM 2D and 3D are both adopted to simulate the two- and three-dimensional forging processes, respectively, for the evaluations of the sectional material flows and the complete deformation behaviors of billet. A systematic algorithm of preform design is proposed considering the product features.
2 Forging process and preform designs
The closed forging process without flash was adopted in the finisher die design to produce the coupled gear product. cup gear Extrusion flow Upsetting flow Intersection zone
Fig. 2 Illustration of geometrical features (left) and flow patterns (right)
Rb
Rt
Ht
Hb
T T-ArcD1 T-ArcD2 T-ArcD3
Ts Ts-ArcD2 Ts-FilletR2 Extrusion Upsetting
Removed volume
Fig. 3 Illustration of one-step billets (upper) and two-step preforms (middle and lower)
The preform designs were proposed to obtain better material distributions and die filling in the finisher forging. The forging process and preform designs were proposed based on the geometrical features of the product and the observation of the material flow patterns. The shape complexity factor [21,22] of the forged part was calculated using the simplified geometrical features of the product vertical cross sections. The shape complexity factors of the divided upper and lower features of the product cross sections were calculated and averaged. The abruptly geometrical change at the intersection zone raises complex material flow during the forming process and needs to be considered carefully.
2.1 The features of the forging product geometry
The product material of this study is AISI-4115. A full annealing heat treatment had been carried out after the preforming operation. The annealed preforms were cold-forged to make the products with lubricant of forming oil using the tools made of SKD-11. The geometrical features, the main dimensions, and the specifications of the product are depicted in Fig. 1. There are two major features as shown in the section view of the product (Fig. 1)—cup
section and rod (gear) section, respectively. The corre-sponding billet diameters of the featured sections were assumed to be equal to those of the rod (gear addendum) and the cup outer profile. The shape complexity factors calculated using Eqs.1 and 2 give 1.0 and 2.1 for the rod
(gear) and the cup sections, respectively. The averaged shape complexity factor (1.55) is high (>1.0), which implies a preform design should be added in the forging sequence. The irregular material flows might be expected in the axial direction based on the calculated SCF and the observation of product geometrical features.
2.2 Features of the material flow at the finishing stage To explain the backward and the forward extrusion flow characteristics of the product geometrical features, the velocity vectors in the axial and the lateral directions are illustrated in Fig. 2. The materials are moving not only in the axial direction but also in the lateral direction simultaneously. Different designs of preform will strongly affect the relationships of these different material flows. If the downward extrusion flows of cup area meet the upsetting flows of the gear section at the intersection zone (Fig. 2), the contact of free surfaces of the workpiece will cause a folding defect. A systematical design method of preforms based on the features of product geometry and material flow was developed. The material flow could be Table 1 The volumes and volume ratios of the different preform designs
V Product T-Type Preform Ts-Type Preform
V.P mm3 Ratio to V.A mm3 Ratio to V.A Ratio to V.P mm3 Ratio to V.A Ratio to V.P
V.C (U) 3,170 0.51 4,926 0.69 1.55 3,695 0.57 1.17
V.G (L) 3,057 0.49 2,199 0.31 0.72 2,827 0.43 0.92
V.A 6,227 1.00 7,125 1.00 1.14 6,522 1.00 1.05
V.C/V.G=1.04 V.U/V.L=2.24 V.U/V.L=1.31
V volume, A all, P product, C cup, G gear, U upper, L lower
Table 2 The major dimensions of billets and preforms
Billet of one step Preform of two step Extrusion Upsetting T type Ts type
Rt 14 10 14 14 Rb None None 10 10 Ht 11 21 8 6 Hb None None 7 9 Punch holder Punch Fitting ring Upper die Die holder Ejector Lower die
controlled mainly by the geometries of the preform designs proposed in this study
2.3 Design rules of the forging process and the preform To establish the material flow patterns, one-step processes of extrusion or upsetting with different sizes of cylindrical billet designs are suitable initial trials. The cross section of the forged part is similar to a big tee, and the T-shape preform is a most intuitive deign. Seven preform designs were proposed for the two-step forming process and categorized into T-type and Ts-type groups. Ts-type pre-forms have a smaller volume and less flash materials allowed. The illustrations of the proposed preforms are depicted in Fig.3as well as the legends of dimension and the codes of design. To determine the radii and heights of the billet and the preforms, the billet–product volume ratio was adopted. The proposed dimension calculation algo-rithms of the billet and the preforms are given as follows.
For one-step extrusion and upsetting approaches, the billet radius Rtis calculated referring to the dimensions of the cup and the gear features as given in Eqs. 3 and 4, respectively:
Rt¼ INT outer radius of cup þ inner radius of cupðð Þ=2Þ ¼ 14 ð3Þ Rt¼ INT root diameter of gear=2ð Þ ¼ 10 ð4Þ
where INT( ) is a truncation function for finding the nearest smaller integer of the input variables to guarantee that the billet can be put into the die cavity easily and smoothly. The height (length) of the one-step billets, Ht, is calculated using the volume of product, Vproduct, and the volume ratio of flash,η:
Ht¼ INT Vproduct 1 þ hð Þ p R2t
: ð5Þ
The adopted volume ratio of flash for extrusion and upsetting processes are 9% and 6%, respectively.
For two-step forging approaches, the proposed algorithm of Tee-shaped preform design is given as follows:
Step 1 Determine the large and the small radii, Rt and Rb, using Eqs.3and 4, respectively.
Step 2 Chose the volume ratio of flash, 14% and 5% for T- and Ts-types preform designs, respectively. Step 3 Guess an initial volume ratio of the upper and the
lower sections of the Tee-shaped preform using the volumes of cup and gear parts, respectively. Step 4 Calculate the corresponding Htand Hbvalues. Step 5 Adjust the Htand Hbto the nearest integer with the
stroke constraint of the preform forging process. Deddendum model
Addendum model FEM model
Deddendum section Addendum section Punch Workpiece Lower die Ejector
Fig. 5 2D CAD and FEM models at addendum and dedendum sections
Product
3D
CAE
model
Billet mesh
Preform mesh
Forged product
Fig. 6 3D CAD and FEM meshes of billet, preform, and forged partTable 1 lists the volumes and the volume ratios of geometrical features for the product, the T-type preform, and the Ts-type preform, respectively. Considering that the volume ratio of the cup and the gear features is about 1 and the shape complex factors of the cup and the gear features are 1.5 and 1, respectively, the initial guess of volume ratios of preform was set to 1.5 and 2.0 for Ts- and T-type designs, respectively. The constraint of step 5 was applied and iterated steps 3 to 5 to obtain the final volume ratios 1.3 and 2.2, respectively. Table 2shows the calculated dimensions of the billet and the preform designs using the proposed algorithms. Corer arcs and fillets were designed at the intersection of Tee-shaped preform to control the inter-Exp.3 Exp.2 Exp.1 Fitting 0 0.6 True strain 800 600 400 200 0
True stress (MPa)
0.2452 2
706.19
1
R
σ
=
=
ε
Fig. 7 The power law–plastic material flow stress model
Preform forging finisher forging finisher forging
T-ArcD2 : Dedendum section Addendum section
Ts-ArcD2 : Dedendum section Addendum section :
Ts-FilletR2: Dedendum section Addendum section Fig. 8 The 2D flow patterns
of preforming and finishing operations
ference of material flow. The notations D1, D2, D3, and R2 were given to represent the corner designs of the tee-shaped preform; D and R denotes the semi-circle and the fillet designs, respectively; the subscripts are the radii.
3 Forging die design and process simulation 3.1 Design of finisher die
Figure 4 represents the section view of the assembled toolset for the finisher forging. The gear teeth were manufactured in the lower die cavity. A gear-shaped ejector was inserted to the lower die which is adjustable to control the extruded length of the gear part. A fitting ring was also designed to prestress the die insert and reduce the hoop stress of die during forging process.
3.2 Numerical simulation models of the forging process The DEFORM 2D (version 8.1) and 3D (version 5.0) softwares were adopted to predict the sectional material flows and the three-dimensional deformation behaviors, respectively. The two- and three-dimensional computer-aided design (CAD) and FEM models are shown in Figs.5
and6, respectively. The section cuts of the 2D simulations (Fig.5) were made at the addendum and the dedendum of gear feature, respectively. The element number of the billet mesh is 5,000 for the 2D preform forming simulation and increased nearly to 10,000 at the end of forging due to the automatic mesh operations. The 2D preforms with re-meshed elements were transferred into the finisher die for the finish forming simulation, yet the states of the stress and the strain data of meshes were set to zero to reflect the fully annealing heat treatment. For the 3D FEM simulations, the CAD models of preforms were adopted and meshed using 26,000 to 30,000 elements directly for the finish forging simulation. Because the annealing heat treatment was applied before the finisher forging, no preform forming simulations were taken in 3D FEM models. The preform
forming simulation of 3D models was carried out only for a special case which the sound production was obtained. In such case, the 3D billet was meshed using 20,000 elements and increased to about 30,000 at the end of preform forging. A constant shear friction factor 0.12 [24] was assigned for all simulation models, because the cold forging was done using the die material of SKD-11. The flow stress model of AISI-4115 workpiece was obtained from the cylindrical upsetting tests and put into the simulation softwares.
4 Results and discussion
4.1 Upsetting tests and flow stress model
The upsetting tests of cylindrical specimens were carried out to obtain the flow stress model of the workpiece. The cylindrical specimens were well lubricated with the sprayed MoS2and Teflon liquid to minimize the effects of frictions. Figure 7 presents the results of tested data and a fitting curve of flow stress. The power law flow stress model obtained from the curve fitting was adopted in the simulations only at the medium true strain range (<0.6). A perfect plasticity model was assumed for the larger strain (≥0.6) range because the upsetting experiment can be conducted without barreling only up to 50% reduction in height (natural strain 0.693) and very often it is sufficient to specify an average value of flow stress for prediction the forming loads [25].
4.2 Observations of flow patterns using FEM simulations The complete 2D simulations of the two-step forming process can be finished in about 6 h with the element size ranging from 0.3 to 0.5 mm. The 3D simulations required twice the time of the 2D model with similar element size Effective stress of billet Punch fracturing marks
13000 8600 4700 700 0 MPa
Fig. 9 Effective stress distribution of billet and cracked marks on punch surface
Table 3 The simulation results for different preform designs Designs Defect Punch
loads Damage value Max. eff. strain Max. eff. stress Extrusion Yes 201 0.236 2.44 941 Upsetting Yes 185 0.336 2.59 940 T-Type Yes 202 0.100 2.03 940 T-ArcD1 Yes 208 0.150 1.55 940 T-ArcD2 Yes 198 0.167 2.28 940 T-ArcD3 Yes 195 0.240 2.37 940 Ts-Type Yes 193 0.197 2.04 942 Ts-ArcD2 Yes 191 0.110 1.93 941 Ts-FilletR2 No 198 0.145 1.93 940
and the stress and strain data of deformation prediction are converged to the same levels. The simulation time of 2D model increased to about the same level of 3D model if smaller element size ranging from 0.05 to 0.1 mm are adopted in 2D and element size ranging from 0.3 to 0.5 mm are adopted in 3D. The simulations were done using a Pentium® Dual CPU 3.2-GHz PC with the installation of 2-GB RAM. Figure 8 shows the two-dimensional flow patterns of the three selected preform designs, T-ArcD2, Ts-ArcD2, and Ts-FilletR2. The meshes of billet after preform forging were smooth and only a few dense elements were presented. The refined meshes of severe deformations were shown mainly at the upper-right part of the cup feature in the finisher forging. There were no defects observed on the dedendum section cut of gear for all preform designs in the filling stage of finisher forging. On the contrary, the occurrence of folding defects appeared on the addendum section cut of gear for all preform designs except the case of Ts-FilletR2design. The observation of sectional material flows may conclude two findings. First, the deformation of preform forging is not significant and smooth meshes are reserved. Second, the different preform designs show a strong influence on the occurrences of forming defects especially on the addendum section of gear which a larger lateral deformation is required.
4.3 Observations and experiments of the one-step forming The die stress analyses were carried out to examine the die life based on the maximum effective stresses. The maxi-mum stress levels of 2,540 and 2,490 MPa were found for the extrusion and the upsetting punches, respectively. The high level of die stress gives the poor die life. A cylindrical billet 28 mm in diameter and 11 mm in height was adopted for the one-step forging tests on a 600-ton mechanical press. Figure 9 illustrates the very high effective stress distribution of the billet (left) and the fractured punch (right) of the one-step extrusion test. The cracked marks of the punch were induced by the high effective stress of billet and similar to the distribution of stress. Figure9reveals that the severe deformation of billet is the cause of high die stress and makes the one-step forming infeasible.
4.4 Observations of the different designs of process and preform
Table3summarizes the simulation results of the occurrence of forming defects, the punch loads, the maximum effective strains and stresses, and the normalized Cockroft-Lathan damage values for different process and preform designs. The damage values are smaller than the critical value (0.45) of carbon steels for all designs, which reveals that no fracturing defects of billets will be observed. The required forming loads of all processes are lower than of 200 tons; which means the forging experiments are able to be done on a 600-ton mechanical press. The process using the Ts-FilletR2preform design gives the lower damage value and effective strain and stress levels and shows no defects. The comparison of the listed data in Table3 concludes that the
2D FEM (Addendum) Experiment 3D FEM
Fig. 10 Numerical and experi-mental folding defects observa-tion using T-ArcD3preform
design
preform design is very significant to the control of material flow and the prevention of forming defects.
4.5 Observation of the two-step forming with defects The forming results using preform design T-ArcD3 were observed using numerical simulations and experimental tests. Figure10shows the deformation grids of the 2D (left) and 3D (right) FEM simulations and the forged specimen (middle). The folding defects were predicted by both of the computer-aided engineering simulations and the forging experiment. The reason of the observed folding defects is that the upsetting and the extrusion material flows meet each other at the intersection zone of cup and gear features in the period of die filling. As a result, the free surfaces
contact with each others and form a folding defect on the gear face as the experimental specimen shown in Fig. 10. Figure 11 depicts the three-dimensional velocity distribu-tion when the final finisher forging is completed, which shows that the lateral upsetting and the downward extrusion flows interfered with each other at the intersected corner of cup and gear features.
4.6 Observation of the two-step forming without defects The proposed preform design, Ts-FilletR2, is the best one from the viewpoints of smooth material flow and defect prevention. Figure12shows the results of 2D (left) and 3D
2D FEM (Addendum) Experiment 3D FEM
Fig. 12 Numerical and experi-mental folding defects observa-tion using Ts-FilletR2preform
design
Fig. 13 Velocity vectors of die filling using Ts-FilletR2 preform
design T-ArcD3 (0.466-2.37) B C D E F H B A C D G G A=0.239 (white) B=0.633 C=0.867 D=1.100 E=1.330 F=1.570 G=1.80 H=2.030 I=2.270 J=2.500 One-step extrusion (0.484-2.44) G H B A C DE F B C D E F I Ts-FilletR2 (0.418-1.93) B C D E A B CD E FG
Fig. 14 Effective strain distributions for one- and two-step forming process designs
(right) simulations and the forged specimen (middle). No occurrences of defects are observed numerically or experi-mentally. The tee-shaped preform design with a 2-mm fillet radius is able to prevent the folding defects because the downward material flows of the cup feature are reduced in the period of final die filling. Figure13 illustrates the 3D velocity vectors in the final die filling stage using the Ts-FilletR2preform design, which shows that the lateral flows in the gear feature region are obviously smaller than those of the T-ArcD3design. As expected, the interference of the extrusion and the upsetting material flows was decreased dramatically and the die cavities of gear features were filled smoothly.
4.7 The comparison of the effective strain distributions Figure 14 summarizes the effective strain distributions of the one-step extrusion and the two-step processes (with preform designs T-ArcD3and Ts-FilletR2). The Ts-FilletR2 preform design had achieved a lower maximum strain (1.93) than the other designs and, as a result, the smoother material flows can be expected. The denser contours of effective strain observed at the intersection corner of cup and gear features for one-step extrusion and two-step forming with T-ArcD3 preform revealed that the turbulent material flows might occur here. A smoother material flow (more uniform contours and lower levels of effective strain) obtained for the two-step process using Ts-FilletR2preform design is the reason why the folding defects can be prevented.
5 Conclusions
In this paper, the feasibility of a coupled gear part forging using one-step and two-step forming processes were studied numerically and experimentally. The proposed intuitive preform design methodology based on the geo-metrical section features and dimensions of product was able to obtain the preform geometry successfully. Tee-shaped preforms with corner and fillet features had shown a significant effect on the material flow control and the defect prevention. The 2D and the 3D FEM models were applied to simulate the sectional material flow and the deformation attributes successfully. The smaller element size can be adopted for the 2D simulation within a reasonable CPU time no longer than the 3D FEM model with a bigger element size. The folding defects on the gear addendum faces had been observed precisely and successfully in both of the 2D and 3D numerical simulations, as well as in the experimental tests. The velocity vectors intersected at the corner of cup and gear features represent interference of the extrusion and the upsetting material flows and explain
the occurrences of folding defects. The proposed two-step process with the Ts-FilletR2 preform design was able to make a sound product without defects and in good agreement with the experimental works.
Acknowledgments Financial support for this work was provided by the National Science Council Taiwan, R.O.C, under the contract NSC 95-2622-E-151-016-CC3. The manpower and facility supports of the New Kailung Gear and Machinery Co., Ltd. are specially thanked.
References
1. Dean TA (2000) The net-shape forming of gears. Mater Des 21:271–278
2. Sadeghi MH (2003) Gear forging: mathematical modeling and experimental validation. J Manuf Sci Eng 125:753–762 doi:10.1115/1.1616952
3. Chitkara NR, Bhutta MA (1999) Forging and heading of hollow spur gear forms: an analysis and some experiments. Int J Mech Sci 41:1159–1189 doi:10.1016/S0020-7403(98)00092-7
4. Chitkara NR, Kim Y (1996) An analysis of external spline gear forming by an upper bound energy method. Int J Mech Sci 38 (7):777–789 doi:10.1016/0020-7403(95)00084-4
5. Chitkara NR, Kim Y (1996) Upper bound analysis of near-net shaped forging of gear coupling form. Int J Mech Sci 38(7):791– 803 doi:10.1016/0020-7403(95)00085-2
6. Tomov BI, Gagov VI (1999) Modelling and description of the near-net-shape forging of cylindrical spur gears. J Mater Process Technol 92:444–449 doi:10.1016/S0924-0136(99)00169-7
7. Kang GJ, Song WJ, Kim J, Kang BS, Park HJ (2005) Numerical approach to forging process of a gear with inner cam profile using FEM. J Mater Process Technol 164–165:1212–1217 doi:10.1016/ j.jmatprotec.2005.02.137
8. Lee YK, Lee SR, Lee CH, Yang DY (2001) Process modification of bevel gear forging using three-dimensional finite element analysis. J Mater Process Technol 113:59–63 doi: 10.1016/S0924-0136(01)00701-4
9. Song JH, Im YT (2004) Determination of a major design parameter for forward extrusion of spur gears. J Manuf Sci Eng 126:255–263 doi:10.1115/1.1688379
10. Petruska J, Janicek L (1998) Computationally-experimental workability determination of compressed cylindrical specimen with surface defect. J Mater Process Technol 80-81:572–578 doi:10.1016/S0924-0136(98)00164-2
11. Cai J, Dean TA, Hu ZM (2004) Alternative die designs in net-shape forging of gears. J Mater Process Technol 150:48–55 doi:10.1016/j.jmatprotec.2004.01.019
12. Yeo HT, Choi Y, Hur KD (2001) Analysis and design of the prestressed cold extrusion die. Int J Adv Manuf Technol 18:54–61 doi:10.1007/s001700170094
13. Fu MW, Yong MS, Muramatsu T (2008) Die fatigue life design and assessment via CAE simulation. Int J Adv Manuf Technol 35:843–851 doi:10.1007/s00170-006-0762-5
14. Coffin LF (1954) A study of the effects of cyclic thermal stresses on a ductile metal. Trans ASME 76:931–950
15. Mansion SS (1953) Behavior of materials under conditions of thermal stress. Heat Transfer Symposium, University of Michigan Engineering Research Institute, pp 9–75
16. Wu CY, Hsu YC (2002) Optimal shape design of an extrusion-forging die using a polynomial network and a genetic algorithm. Int J Adv Manuf Technol 20:128–137 doi:10.1007/s001700200134
17. Lin JC, Tai CC (1999) The application of neural networks in the prediction of spring-back in an L-shaped bend. Int J Adv Manuf Technol 15:163–170 doi:10.1007/s001700050053
18. Lapovok R (1998) Improvement of die life by minimisation of damage accumulation and optimisation of preform design. J Mater Process Technol 80–81:608–612 doi:10.1016/S0924-0136(98) 00213-1
19. Kang RS, Lee JH, Kim BM, Choi JC (1995) Process design in fleshless forging of rib/web-shaped plane-strain components by the finite element method. J Mater Process Technol 47:291–309 doi:10.1016/0924-0136(95)85005-8
20. Chang CC, Bramley AN (2000) Forging preform design using a reverse simulation approach with the upper bound finite element procedure. Proceedings of the Institution of Mechanical Engineers, Part C. J Mech Eng Sci 214(1):127–136
21. Tomov B (2007) Hot closed die forging—state-of-art and future development. J Achievements Mater Manuf Eng 24 (1):443–449
22. Teterin GP, Tarnovskij IJ, Chechik AA (1966) A shape complexity criterion. Kuznecno– shtampovochnoe, proizwodstvo 7. pp 6–9 (in Russian)
23. Zhao Q, Wright ED, Grandhi RV (1995) Forging preform design with shape complexity control in simulating backward deforma-tion. Int J Mach Tools Manuf 35(9):1225–1239 doi: 10.1016/0890-6955(94)00117-3
24. Altan T, Kobayashi S, Oh SI (1989) Metal forming and the finite element method. Oxford University Press, New York, p 32 25. Altan T, Ngaile G, Shen G (2005) Cold and hot forging
fundamentals and applications. American Society for Metals, Schaumberg, pp 27–40
