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ORIGINAL ARTICLE An integrated computer-aided decision support system for die stresses and dimensional accuracy of precision forging dies Necip Fazil Yilmaz therefore, steady state conditions are not achieved due to the continuously changing pressure distribution. But in general it is assumed that steady state stress conditions are present and there is a uniform internal pressure along the whole length of the die 23, 24. These assumptions permit calculations based on the theory of thick-walled hollow cylinders to be carried out. The upper bound elemental technique (UBET) incorpo- rates the advantages of both the upper bound theorem and the finite element method to provide more accurate predictions of important parameters such as strain rates, die load, and die cavity filling when compared to the other methods. UBET is perfect for initial stages of the optimization algorithms, where it is necessary to reach near-optimum solutions as quickly as possible. The stresses in dies arise mainly from the high level of internal pressure during forging. However, the pressure is not constant over the whole length of the die. Since it is concentrated in the portion of the die that is in contact with the deforming workpiece, the pressure will vary during forging and the length of the pressurised region will also change. The dimension of the forging is different from the die because of several factors: The die insert is shrink fitted into the outer ring causing an extraction of the die cavity (U e ). In hot forging, the die may be heated prior to forging and further heated by the hot billet during forging. This causes the die insert to expand (U t ). Contraction occurs during cooling from forging tem- perature to room temperature (U c ). In electrodischarge machining of the die components, spark gap occurs between electrode and workpiece. This decreases the die cavity size (G). As seen in Fig. 1, if the radius of the workpiece is assumed to be equal to the original die radius R 0 ; thus, the final radius of the die R 4 will be: R 4 R 0 U e U t C0U c C0G 3 Calculation formulae 3.1 Calculation of the elastic die expansion (U e ) In order to calculate the changes in workpiece dimensions due to elastic deflection of the die, the elasticplastic deformation of the workpiece has to be considered. Assuming that the workpiece is stressed uniformly by the die and always remains cylindrical at the maximum forging R0 R1 R2 R3 R4 Ue Ut Uc G Fig. 1 Half section of a cylindrical forging of die insert 25 876 Int J Adv Manuf Technol (2009) 40:875886 load, the die deflection is elastic and uniform along its axis. Ignoring the friction on workpiecedie interfaces, work- piece dimensions change when the punch load is applied and removed. Also, changes in workpiece dimensions occur during ejection 25. In order to calculate the amount of expansion of the die under radial pressure, an initially stress-free duplex cylinder is considered. By applying the punch load on the workpiece, two modes of deformation will occur. First, the workpiece will deform elastically and when the punch pressure becomes equal to the yield stress of the workpiece material, plastic deformation starts and simple compression continues until the workpiece touches the die wall. For continuity across the interface, the hoop (tangential) strains for insert and shrink ring must be equal at this point, q1 q2 . q1 P i 1C0 nb 2 a 2 C16C17 b 2 a 2 C01 1C0u d1 E d1 P i 1C0n b 2 a 2 C01 1u d1 E d1 1 q2 nP i c 2 b 2 C01 1C0u d2 E d2 nP i c 2 b 2 C16C17 c 2 b 2 C01 1u d2 E d2 2 The subscripts 1 and 2 refer to die insert and shrink ring, respectively. When the maximum load is exerted on the workpiece, the radial stress will be greater than its yield strength. After reaching such a condition, if the punch load is removed, the die will compress the workpiece plastically until the radial stress on the workpiece is reduced to twice its shear yield stress (S y ). By using Trescas yield criterion, the total amount of radial expansion of the workpiece (U)at the end of this stage can be calculated by: U a aa 2 1C0u d1 b 2 1u d1 C02n2S y C02ab 2 P p E d1 b 2 C0a 2 3 At the end of the forging process, the punch pressure is zero and the radial stress (2S y ) is still acting on the workpiece. On ejection, its radius will expand elastically and the amount of recovery (s) can be calculated by assuming a cylindrical state of stress (s r s q ) and by placing z =0, such that: s 1C0u w E w 2S y a 4 where E w and w are the Youngs modulus and Poissons ratio of the workpiece material, respectively. The total b a Ti Tp Fig. 2 Temperature distribution along the die radius in hot forging Die Ring a z b c a b c Fig. 4 Die insert and shrink ring dimensions a b 0 () 0 (+) r () To - Tp=0 Ti - Tp= Fig. 3 Radial and tangential stress distributions due to outward temperature Int J Adv Manuf Technol (2009) 40:875886 877 change in the workpiece dimensions due to elastic die expansion is given by: U e aa 2 1C0u d1 b 2 1u d1 C02n2S y C02ab 2 P p E d1 b 2 C0a 2 1C0u w E w 2S y a 5 3.2 Calculation of the thermal die expansion (U t ) In hot forging, dies are preheated to prevent cracking of the die components and to reduce the cooling rate of the workpiece. Some heat is transferred from the workpiece during forging which further heats the die. The combination of these two sources of heat causes the die to expand. The temperature distribution along the radius of the die with a preheat temperature of T p and bore diameter of T i is given in Fig. 2. The preheat temperature is assumed constant throughout the die, but the heat transferred from the workpiece produces an outward heat flow with radial temperature gradient. Assuming uniform preheating, the die wall will expand freely. The magnitude of the radial expansion (U tp ) at any radius can be determined as: U tp ra d T p C0T r C0C1 6 where T r is room temperature, T p is preheat temperature, and d is the coefficient of thermal expansion of the die material. The temperature increase on the inner surface of the die and stress distributions are shown in Fig. 3. Thus, the radial displacement at any radius r due to thermal stresses can be found with: U ts C0 d T 3 bC0a C0 1 d a 2 b 2 ab 1 r 2 d C01r 2 1C0 d b 3 C0a 3 b 2 C0a 2 C20C21 7 Total die expansion (U t ) due to temperature will then be: U t U tp U ts 8 Top Frame Die Geometry Forging Load Geometry Die Assembly Material Parent Frame Fig. 5 General frame structure Friction Flow Stress FORGING LOAD Contour Frame Remove Frame Region Frame DATABASE Lubrication Good Average Poor Dry INFERENCE ENGINE Fig. 6 Framework for forging load frame 878 Int J Adv Manuf Technol (2009) 40:875886 3.3 Calculation of the thermal product contraction (U c ) Theamountofshrinkageafterhotformingoperationsdepends on the working temperature and coefficient of thermal expansion of the forged material. Assuming that shrinkage takes place radially, and the finish forging temperature is uniform, the amount of radial contraction at any radius is: U c ra w T f C0T r C0C1 9 where T f is the forging temperature, w is the coefficient of thermal expansion of the workpiece, and r is the radius of the workpiece before contraction. In order to achieve close dimensional tolerances on forgings, die dimensions should be closely controlled. From the foregoing it is apparent that knowledge of the magnitude of the above factors should be obtained before appropriate die and electrode dimensions are determined. Using the above analysis, the parameters affecting forging dimensions were calculated and for a given condition the profileofthe die was determined. A program hasbeenwritten to perform these calculations and to create the corrected forging product dimension for die. Die insert and shrink ring dimensions (Fig. 4) are then given in Eqs. 1017. b a Q 1 10 c a Q 11 z b:S y E 1 K 1 C0Q 2 1 C18C19 12 Q Q 1 :Q 2 13 Q 1 1 2 1 1 K 1 C18C19 C0PP s 14 Q 2 Q 1 : K 1 p 15 PP P i S ydie 16 K 1 S ydie S yring 17 Fig. 9 Friction calibration curve in terms of m 27 Table 1 Aluminum ring test data Lubricated Dry (ground) Dry (rough) D o1 (mm) 30 30 30 D o2 (mm) 37.7 38.5 38 D i1 (mm) 15.2 15.2 15.2 D i2 (mm) 14.8 13.5 11.2 H1 (mm) 10 10 10 H2 (mm) 5.65 5.35 5.3 % H 43.5 46.5 47 % D 2.63 11.18 26.3 Load (ton) 25 30 35 m 0.25 0.4 0.6 0 5 10 15 20 051015 DH P(TON) Fig. 7 Disc forging for aluminium ALUMINIUM 0 50 100 150 200 0,00 0,10 0,20 0,30 0,40 STRAIN (DH) STRESS(MPa) Fig. 8 Stressstrain curve for aluminium Int J Adv Manuf Technol (2009) 40:875886 879 where a is the die insert inner radius, b is the die insert outer radius, c is the shrink ring outer radius, z is the interference, and P i is the inner pressure. 4 General structure of the system A general structure for building up an inference and control engine for the decision-support expert system as well as an algorithm for finding a compromise solution for the die stress and dimensional accuracy of the product is achieved. By using an intelligent, knowledge-based object-oriented system, high precision manufacture of product has been put into perspective. Knowledge representation in this work was structured in the network representation. Parent frames (geometry, forging load, diegeometry,dieassembly, material) are connected to the top frame. Each parent frame also has child frames. General frame structure is shown in Fig. 5. Parent frames are used to describe the general class of objects. In a database, the data definition of a record specifies how the data is stored so that the database can search and sort through the data. To actually enter the values into the system, child frames and instances are formed to represent the specific objects. Prediction of forging load has vital importance for the dimensional a b c 40 17.5 30 31.1 Fig. 10 U-shaped product with different sizes of specimen 880 Int J Adv Manuf Technol (2009) 40:875886 accuracy and die life. This frame has six child frames and it is defined as one of the main frames of the developed system (Fig. 6). Contour frame This is the child frame of forging load parent frame. This frame takes its knowledge from the geometry parent frame. In order to determine the forging load, the contour frame is the first frame that is to be fired. The entities are searched to find the inclined lines and arcs. During this process, related rules are fired so that the entities found are inclined line or arc. Remove frame This is the child frame of forging load parent frame. In this frame, removed entities are stored in the database. There are two instances. One of them contains the knowledge about inclined lines and the other contains arcs. Region frame This frame is the child frame of forging load parent frame. The geometry decomposition is made by the knowledge taken from this frame. Vertical and horizontal lines are drawn from the corners to the corresponding line. In this way, rectangular regions are obtained. The knowl- edge about the regions are stored in the database. Friction frame One side of the region contacts one of the material, die, or punch. Therefore, each side must be checked and friction factor must be determined. This frame is used for the determination of sides, whether it contacts the material, die, or punch. c 20 50 a b 40 12.5 30 22.2 Fig. 11 T-shaped product with different sizes of specimen Int J Adv Manuf Technol (2009) 40:875886 881 Lubrication frame This frame takes its knowledge from friction frame and adds its own knowledge. This frame has four slots: good lubrication, average lubrication, poor lubrication, and no lubrication (dry). These slots are required from the user. The entered values are used for the determination of friction factor for each side of the region and therefore for all forging products. Flow stress frame Deformation characteristics of each material are different from the other materials. The flow stress value changes for all deformation conditions. Therefore, this property of the material must be in hand. 5 Experimentation In the experiments a hydraulic press which has a capacity of 600 kN was used. A graphitewater based lubricant was used as a lubricant. Great care was taken to ensure that all the working surfaces were completely and evenly lubricat- ed. As a die insert material, AISI A10 air hardening medium alloy cold worked tool steel was used. The tool set comprised essentially a container, punch, ejector, and bolster. U-shaped, T-shaped, and taper shaped aluminium prod- ucts were forged. Experiments were carried out at room temperature. Three different sizes of cylindrical aluminium billets were used. Products which have a dimension of 40 mm in outside diameter and 20 mm in height were obtained from stock bars and hollow bars. 5.1 Disc forging A disc forging compression test was carried out to determine the stress-strain curveforaluminium.To thisaim,incremental compression was performed and after each loading, reduction of area and corresponding load were calculated and recorded. 40 12 30 22.3 25 32.1 a b c Fig. 12 Taper shaped product with different sizes of specimen 882 Int J Adv Manuf Technol (2009) 40:875886 A reduction in height versus load graphic is shown in Fig. 7, and a stressstrain curve is shown in Fig. 8. In order to determine the friction factor (m), the ring compression test has been carried out. A flat ring specimen is plastically compressed between two platens. Increasing friction results in an inward flow of the material and decreasing friction results in an outward flow of the material. For a given percentage of high reduction during compression test, the corresponding measurement of the internal diameter of the test specimen provides a quantita- tive knowledge of the magnitude of the prevailing friction coefficient at the die and workpiece interface 26, 27. From this perspective, ring compression test data for aluminum are presented in Table 1.%H and %D values Fig. 13 a Die stress calculation screen. b Corrected die dimensions Int J Adv Manuf Technol (2009) 40:875886 883 are obtained by the following equations and friction coefficient m is found from Fig. 9. %H H 1 C0H 2 H 1 *100 %D D i1 C0D i2 D i1 *100 5.2 U-shaped forging Inprecisionforgingoftheproducts,completefillingofthedie is regarded as the most important criterion for improving the dimensional accuracy of the forged part. The volume of the preform should be carefully controlled, otherwise underfilling or overloading of the tools may occur. It can generally be said that metal does not flow easily through the corners. Complete filling can be satisfactorily achieved by using appropriate initial billet geometry. Figure 10 shows the dimensions of the U-shaped forging produced from three different sizes of billets by keeping their volume constant. The first one was forged from solid cylindrical bar and the product was obtained with 26 tons of load. The second one (Fig. 10b) was subjected to 55 tons of load, but the inner side of the specimen could not be filled. In the third one (Fig. 10c) both upsetting and extrusion type metal deformation exists. In this case the product is obtained with 40 tons of load. 5.3 T-shaped forging T-shaped forging is shown in Fig. 11. Forging of this product was approached with three different sizes of specimens by keeping their volume constant. Figure 11 shows the dimensions of the T-shaped forging produced from three different sizes of billets. Although 55 tons of load was applied, Fig. 11a shows that the T-shaped product could not be obtained and the die cavity could not be filled completely. But the second one was subjected to 40 tons of load and the die cavity was almost filled. The third specimen has the same diameter in the smaller part of the shape and 26 tons of load was enough to obtain this product. 5.4 Taper-shaped forging Taper shaped forging is shown in Fig. 12. This product used different sizes of specimens while keeping their volume constant. Figure 12 shows the dimensions of the taper shaped forging produced from three different sizes of billets. Figure 12a shows that taper shaped product could not be obtained by 55 tons of load since the preform is completely subjected to the extrusion mode of deformation. But in the second trial 30 mm diameter of billet was used and the product was obtained with 35 tons of load (Fig. 12b). In this forging, the top of the taper could not be formed Fig. 14 Print screen of Excel sheet Table 2 Corrected die geometry dimensions (mm) U shape T shape Taper shape U e 0.03563 0.03563 0.04667 Final workpiece radius 19.96437 19.96437 19.95333 Final die radius 20.03563 20.03563 20.04667 b 28.78528 28.78528 27.66765 c 41.42962 41.42962 38.27494 z 0.02978 0.02978 0.02642 w1 9.98815 10.0456 7.51274 w2 10.0456 9.98815 7.5110 884 Int J Adv Manuf Technol (2009) 40:875886 completely. The third specimen, having a diameter of 25 mm, was subjected to 24 tons of load and the required product was obtained in almost its desired dimensions. These experiments show that the product can be obtained in different forging loads depending on the initial billet geometry due to the fin formation, upsetting or extrusion mode of deformation, and friction effect. 5.5 Dimensional accuracy analysis Since the die for precision forging experiences very high radial pressure during the process, it considerably deforms in the radial direction. Therefore this radial deformation of the die becomes an important factor influencing the dimensional accuracy of the product. In order to obtain a product with accurate dimension, it is essential to evaluate the elastic deformation (U e ) of the die and the product. Using the above analysis, the parameters affecting forging dimensions,i.e.elasticdieexpansion(U e ), were calculated by using Eq. 5 and for a given condition the dimension of the die was determined. The stress calculation screen and the corrected die dimensions for U-shaped forging, as an example, are shown in Figs. 13a and b, respectively. The results and calculations obtained were also verified in the Excel sheet shown in Fig. 14. According to the die stress and dimensional accuracy calculations, U-shaped, T-shaped, and taper-shaped die cavities are tabulated in Table 2 and the resulting forged profiles are given in Fig. 15. The die design considerations for taper-shaped products are shown in Fig. 16. The punch is shown as a single unit and detail of the punch is not given. The punch forms the top surface of a cavity and is attached to the moving ram of a forging machine. The ejector is used to remove the product from the die without imposing deformation. The ejector is also used to give the shape to the bottom side of the product. The die insert forms the inner side of the die (die cavity). Since the die insert is subjected to forging load, friction load, and temperature,itsmaterialmustbechosensothatitisrobustin all required conditions. In order to increase the resistance against internal pressure, it is usual to make an insert shrink fitted into one or more shrink rings. The compressive stress imposed by the shrink ring has a cumulative effect at the bore of the die insert. Therefore, resultant tensile stress on the bore, caused by the forging loads transmitted through the forging part, can be substantially reduced. Actual Forging Product Profile Corrected Die Dimensions Fig. 15 U-, T-, and taper-shaped die cavities and the resulting product profiles 1 2 3 4 5 6 7 8 9 10 1. Punch 2. Product 3. Die 4. Shrink ring 5. Bolt 6. Die clamp ring 7. Bolster 8. Ejector 9. Ejector seat 10. Ejector rod Fig. 16 General assembly of die shape Int J Adv Manuf Technol (2009) 40:875886 885 6 Conclusion Computer-aided determination of forging design holds great importance for preserving the gradually disappearing know- how for the forging industry. The developed decision support system has wide applicability since the forging shapes, which are partly presented in this work, represent a large proportion of the total industrial parts. It is assumed that i