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ORIGINAL ARTICLEAn integrated computer-aided decision support systemfor die stresses and dimensional accuracyof precision forging diesNecip Fazil Yilmaz therefore, steady stateconditions are not achieved due to the continuouslychanging pressure distribution. But in general it is assumedthat steady state stress conditions are present and there is auniform internal pressure along the whole length of the die23, 24. These assumptions permit calculations based on thetheory 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 andthe finite element method to provide more accuratepredictions of important parameters such as strain rates,die load, and die cavity filling when compared to the othermethods. UBET is perfect for initial stages of theoptimization algorithms, where it is necessary to reachnear-optimum solutions as quickly as possible.The stresses in dies arise mainly from the high level ofinternal pressure during forging. However, the pressure isnot constant over the whole length of the die. Since it isconcentrated in the portion of the die that is in contact withthe deforming workpiece, the pressure will vary duringforging and the length of the pressurised region will alsochange. The dimension of the forging is different from thedie because of several factors: The die insert is shrink fitted into the outer ring causingan extraction of the die cavity (Ue). In hot forging, the die may be heated prior to forgingand further heated by the hot billet during forging. Thiscauses the die insert to expand (Ut). Contraction occurs during cooling from forging tem-perature to room temperature (Uc). 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 isassumed to be equal to the original die radius R0; thus, thefinal radius of the die R4will be:R4 R0UeUtC0UcC0G3 Calculation formulae3.1 Calculation of the elastic die expansion (Ue)In order to calculate the changes in workpiece dimensionsdue to elastic deflection of the die, the elasticplasticdeformation of the workpiece has to be considered.Assuming that the workpiece is stressed uniformly by thedie and always remains cylindrical at the maximum forgingR0R1R2R3R4UeUtUcGFig. 1 Half section of a cylindrical forging of die insert 25876 Int J Adv Manuf Technol (2009) 40:875886load, 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 appliedand removed. Also, changes in workpiece dimensions occurduring ejection 25.In order to calculate the amount of expansion of the dieunder radial pressure, an initially stress-free duplex cylinderis considered. By applying the punch load on theworkpiece, two modes of deformation will occur. First,the workpiece will deform elastically and when the punchpressure becomes equal to the yield stress of the workpiecematerial, plastic deformation starts and simple compressioncontinues until the workpiece touches the die wall. Forcontinuity across the interface, the hoop (tangential) strainsfor insert and shrink ring must be equal at this point,“q1 “q2.“q1Pi1C0nb2a2C16C17b2a2C011C0ud1Ed1Pi1C0nb2a2C011ud1Ed11“q2nPic2b2C011C0ud2Ed2nPic2b2C16C17c2b2C011ud2Ed22The subscripts 1 and 2 refer to die insert and shrink ring,respectively. When the maximum load is exerted on theworkpiece, the radial stress will be greater than its yieldstrength. After reaching such a condition, if the punch loadis removed, the die will compress the workpiece plasticallyuntil the radial stress on the workpiece is reduced to twiceits shear yield stress (Sy). By using Trescas yield criterion,the total amount of radial expansion of the workpiece (U)atthe end of this stage can be calculated by:Uaaa21C0ud1b21ud1C02n2SyC02ab2PpEd1b2C0a23At the end of the forging process, the punch pressure is zeroand the radial stress (2Sy) is still acting on the workpiece.On ejection, its radius will expand elastically and theamount of recovery (s) can be calculated by assuming acylindrical state of stress (sr sq) and by placing z=0,such that:s 1C0uwEw2Sya 4where Ewand ware the Youngs modulus and Poissonsratio of the workpiece material, respectively. The totalbaTiTpFig. 2 Temperature distribution along the die radius in hot forgingDie Ring azbcabcFig. 4 Die insert and shrink ring dimensionsab0 ()0 (+)r ()To - Tp=0Ti - Tp= Fig. 3 Radial and tangential stress distributions due to outwardtemperatureInt J Adv Manuf Technol (2009) 40:875886 877change in the workpiece dimensions due to elastic dieexpansion is given by:Ueaa21C0ud1b21ud1C02n2SyC02ab2PpEd1b2C0a21C0uwEw2Sya53.2 Calculation of the thermal die expansion (Ut)In hot forging, dies are preheated to prevent cracking of thedie components and to reduce the cooling rate of theworkpiece. Some heat is transferred from the workpieceduring forging which further heats the die. The combinationof these two sources of heat causes the die to expand.The temperature distribution along the radius of the diewith a preheat temperature of Tpand bore diameter of Tiisgiven in Fig. 2. The preheat temperature is assumedconstant throughout the die, but the heat transferred fromthe workpiece produces an outward heat flow with radialtemperature gradient. Assuming uniform preheating, the diewall will expand freely. The magnitude of the radialexpansion (Utp) at any radius can be determined as:Utp radTpC0TrC0C16where Tris room temperature, Tpis preheat temperature, anddis the coefficient of thermal expansion of the die material.The temperature increase on the inner surface of the dieand stress distributions are shown in Fig. 3. Thus, the radialdisplacement at any radius r due to thermal stresses can befound with:UtsC0dT3 bC0aC0 1da2b2ab1r 2dC01r21C0db3C0a3b2C0a2C20C217Total die expansion (Ut) due to temperature will then be:Ut UtpUts8Top Frame Die Geometry Forging Load Geometry Die Assembly Material Parent Frame Fig. 5 General frame structureFriction Flow Stress FORGING LOAD Contour Frame Remove Frame Region Frame DATABASELubricationGoodAveragePoorDryINFERENCE ENGINEFig. 6 Framework for forgingload frame878 Int J Adv Manuf Technol (2009) 40:8758863.3 Calculation of the thermal product contraction (Uc)Theamountofshrinkageafterhotformingoperationsdependson the working temperature and coefficient of thermalexpansion of the forged material. Assuming that shrinkagetakes place radially, and the finish forging temperature isuniform, the amount of radial contraction at any radius is:Uc rawTfC0TrC0C19where Tfis the forging temperature, wis the coefficient ofthermal expansion of the workpiece, and r is the radius of theworkpiece before contraction. In order to achieve closedimensional tolerances on forgings, die dimensions shouldbe closely controlled. From the foregoing it is apparent thatknowledge of the magnitude of the above factors should beobtained before appropriate die and electrode dimensions aredetermined.Using the above analysis, the parameters affecting forgingdimensions were calculated and for a given condition theprofileofthe die was determined. A program hasbeenwrittento perform these calculations and to create the correctedforging product dimension for die. Die insert and shrink ringdimensions (Fig. 4) are then given in Eqs. 1017.b aQ110c aQ11z b:SyE1K1C0Q21C18C1912Q Q1:Q213Q11211K1C18C19C0PPs14Q2 Q1:K1p15PP PiSydie16K1SydieSyring17Fig. 9 Friction calibration curve in terms of m 27Table 1 Aluminum ring test dataLubricated Dry (ground) Dry (rough)Do1(mm) 30 30 30Do2(mm) 37.7 38.5 38Di1(mm) 15.2 15.2 15.2Di2(mm) 14.8 13.5 11.2H1 (mm) 10 10 10H2 (mm) 5.65 5.35 5.3% H 43.5 46.5 47% D 2.63 11.18 26.3Load (ton) 25 30 35m 0.25 0.4 0.605101520051015DHP(TON)Fig. 7 Disc forging for aluminiumALUMINIUM0501001502000,00 0,10 0,20 0,30 0,40STRAIN (DH)STRESS(MPa)Fig. 8 Stressstrain curve for aluminiumInt J Adv Manuf Technol (2009) 40:875886 879where a is the die insert inner radius, b is the die insertouter radius, c is the shrink ring outer radius, z is theinterference, and Piis the inner pressure.4 General structure of the systemA general structure for building up an inference and controlengine for the decision-support expert system as well as analgorithm for finding a compromise solution for the diestress and dimensional accuracy of the product is achieved.By using an intelligent, knowledge-based object-orientedsystem, high precision manufacture of product has been putinto perspective. Knowledge representation in this workwas structured in the network representation. Parent frames(geometry, forging load, diegeometry,dieassembly,material) are connected to the top frame. Each parent framealso has child frames. General frame structure is shown inFig. 5.Parent frames are used to describe the general class ofobjects. In a database, the data definition of a recordspecifies how the data is stored so that the database cansearch and sort through the data. To actually enter thevalues into the system, child frames and instances areformed to represent the specific objects. Prediction offorging load has vital importance for the dimensionala b c 4017.53031.1Fig. 10 U-shaped product withdifferent sizes of specimen880 Int J Adv Manuf Technol (2009) 40:875886accuracy and die life. This frame has six child frames and itis defined as one of the main frames of the developedsystem (Fig. 6).Contour frame This is the child frame of forging loadparent frame. This frame takes its knowledge from thegeometry parent frame. In order to determine the forgingload, 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 theentities found are inclined line or arc.Remove frame This is the child frame of forging loadparent frame. In this frame, removed entities are stored inthe database. There are two instances. One of them containsthe knowledge about inclined lines and the other containsarcs.Region frame This frame is the child frame of forging loadparent frame. The geometry decomposition is made by theknowledge taken from this frame. Vertical and horizontallines 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 thematerial, die, or punch. Therefore, each side must bechecked and friction factor must be determined. This frameis used for the determination of sides, whether it contactsthe material, die, or punch.c 2050ab4012.53022.2Fig. 11 T-shaped product withdifferent sizes of specimenInt J Adv Manuf Technol (2009) 40:875886 881Lubrication frame This frame takes its knowledge fromfriction frame and adds its own knowledge. This frame hasfour slots: good lubrication, average lubrication, poorlubrication, and no lubrication (dry). These slots arerequired from the user. The entered values are used forthe determination of friction factor for each side of theregion and therefore for all forging products.Flow stress frame Deformation characteristics of eachmaterial are different from the other materials. The flowstress value changes for all deformation conditions.Therefore, this property of the material must be in hand.5 ExperimentationIn the experiments a hydraulic press which has a capacityof 600 kN was used. A graphitewater based lubricant wasused as a lubricant. Great care was taken to ensure that allthe working surfaces were completely and evenly lubricat-ed. As a die insert material, AISI A10 air hardeningmedium alloy cold worked tool steel was used. The tool setcomprised essentially a container, punch, ejector, andbolster.U-shaped, T-shaped, and taper shaped aluminium prod-ucts were forged. Experiments were carried out at roomtemperature. Three different sizes of cylindrical aluminiumbillets were used. Products which have a dimension of40 mm in outside diameter and 20 mm in height wereobtained from stock bars and hollow bars.5.1 Disc forgingA disc forging compression test was carried out to determinethe stress-strain curveforaluminium.To thisaim,incrementalcompression was performed and after each loading, reductionof area and corresponding load were calculated and recorded.40123022.32532.1a b cFig. 12 Taper shaped productwith different sizes of specimen882 Int J Adv Manuf Technol (2009) 40:875886A 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 ringcompression test has been carried out. A flat ring specimenis plastically compressed between two platens. Increasingfriction results in an inward flow of the material anddecreasing friction results in an outward flow of thematerial. For a given percentage of high reduction duringcompression test, the corresponding measurement of theinternal diameter of the test specimen provides a quantita-tive knowledge of the magnitude of the prevailing frictioncoefficient at the die and workpiece interface 26, 27.From this perspective, ring compression test data foraluminum are presented in Table 1.%H and %D valuesFig. 13 a Die stress calculationscreen. b Corrected diedimensionsInt J Adv Manuf Technol (2009) 40:875886 883are obtained by the following equations and frictioncoefficient m is found from Fig. 9.%H H1C0H2H1*100%D Di1C0Di2Di1*1005.2 U-shaped forgingInprecisionforgingoftheproducts,completefillingofthedieis regarded as the most important criterion for improving thedimensional accuracy of the forged part. The volume of thepreform should be carefully controlled, otherwise underfillingor overloading of the tools may occur. It can generally be saidthat metal does not flow easily through the corners. Completefilling can be satisfactorily achieved by using appropriateinitial billet geometry.Figure 10 shows the dimensions of the U-shaped forgingproduced from three different sizes of billets by keepingtheir volume constant. The first one was forged from solidcylindrical bar and the product was obtained with 26 tons ofload. The second one (Fig. 10b) was subjected to 55 tons ofload, but the inner side of the specimen could not be filled.In the third one (Fig. 10c) both upsetting and extrusion typemetal deformation exists. In this case the product isobtained with 40 tons of load.5.3 T-shaped forgingT-shaped forging is shown in Fig. 11. Forging of thisproduct was approached with three different sizes ofspecimens by keeping their volume constant.Figure 11 shows the dimensions of the T-shaped forgingproduced from three different sizes of billets. Although 55tons of load was applied, Fig. 11a shows that the T-shapedproduct could not be obtained and the die cavity could not befilled completely. But the second one was subjected to 40tons of load and the die cavity was almost filled. The thirdspecimen has the same diameter in the smaller part of theshape and 26 tons of load was enough to obtain this product.5.4 Taper-shaped forgingTaper shaped forging is shown in Fig. 12. This product useddifferent sizes of specimens while keeping their volumeconstant. Figure 12 shows the dimensions of the tapershaped forging produced from three different sizes of billets.Figure 12a shows that taper shaped product could not beobtained by 55 tons of load since the preform is completelysubjected to the extrusion mode of deformation. But in thesecond trial 30 mm diameter of billet was used and theproduct was obtained with 35 tons of load (Fig. 12b). Inthis forging, the top of the taper could not be formedFig. 14 Print screen ofExcel sheetTable 2 Corrected die geometry dimensions (mm)U shape T shape Taper shapeUe0.03563 0.03563 0.04667Final workpiece radius 19.96437 19.96437 19.95333Final die radius 20.03563 20.03563 20.04667b 28.78528 28.78528 27.66765c 41.42962 41.42962 38.27494z 0.02978 0.02978 0.02642w1 9.98815 10.0456 7.51274w2 10.0456 9.98815 7.5110884 Int J Adv Manuf Technol (2009) 40:875886completely. The third specimen, having a diameter of25 mm, was subjected to 24 tons of load and the requiredproduct was obtained in almost its desired dimensions.These experiments show that the product can beobtained in different forging loads depending on the initialbillet geometry due to the fin formation, upsetting orextrusion mode of deformation, and friction effect.5.5 Dimensional accuracy analysisSince the die for precision forging experiences very highradial pressure during the process, it considerably deformsin the radial direction. Therefore this radial deformation ofthe die becomes an important factor influencing thedimensional accuracy of the product. In order to obtain aproduct with accurate dimension, it is essential to evaluatethe elastic deformation (Ue) of the die and the product.Using the above analysis, the parameters affecting forgingdimensions,i.e.elasticdieexpansion(Ue), were calculated byusing Eq. 5 and for a given condition the dimension of thedie was determined. The stress calculation screen and thecorrected die dimensions for U-shaped forging, as anexample, are shown in Figs. 13a and b, respectively.The results and calculations obtained were also verifiedin the Excel sheet shown in Fig. 14.According to the die stress and dimensional accuracycalculations, U-shaped, T-shaped, and taper-shaped diecavities are tabulated in Table 2 and the resulting forgedprofiles are given in Fig. 15.The die design considerations for taper-shaped products areshown in Fig. 16. The punch is shown as a single unit anddetail of the punch is not given. The punch forms the topsurface of a cavity and is attached to the moving ram of aforging machine. The ejector is used to r