A study of barreling profile and effect of aspect ratio on material flow in lateral extrusion of gear-like forms

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 14, June 2007, pp A study of barreling profile and effect of aspect ratio on material flow in lateral extrusion of gear-like forms Tahir Altinbalik* Faculty of Engineering and Architecture, Trakya University, 22030, Edirne, Turkey Received 25 September 2006; accepted 2 April 2007 The aim of this study is to investigate the lateral extrusion of tapered in terms of die filling and barrel formation at the front of tooth. A series of experiments has been carried out using solid lead billets with two different billet diameters and three different billet heights of each diameter. Metal flow in the tooth region is not uniform and barreling occurs due to frictional resistance between the workpiece and the die gap surface. The barrel profile is assumed as a second order polynomial and a simple empirical relationship between the tooth dimensions and the barrel profile has been given using experimental data. Bulging profile of the tooth was measured and simulated by CAD/CAM software. Load-stroke relations and die filling ratios are obtained. In addition, Microsoft Visual Basic was coded and also magnitude and the position of the maximum stresses in the die chamber were determined by using CATIA. IPC Code: B21C Lateral extrusion is a branch of extrusion process in which a billet contained in a chamber and pressed by punch then injected radially into a die cavity. The process is characterized by combined axial and radial metal flow to fill the die cavity, which allows to produce complex component forms, particularly long shaft type components with simple and staggered flanges in a single operation. The process is called with different names in industry and literature such as injection upsetting, radial extrusion, lateral extrusion, sideway extrusion and injection forging. Lateral extrusion has several advantages, such as less load requirements, comparing to closed die forging in producing of parts with radial geometries. Studies about metal flow in lateral extrusion mostly cover the simple shaped flanges. Balendra 1-4 has studied effects of process parameters on metal flow and load requirement for complete flanges. They defined an aspect ratio of primary deformation zone (the volume occupied by the billet in the die cavity at the initiation of injection, T) for complete flanged part produced by this method. When T < 0.8 sound flow can be obtained but required force increases since metal flows into narrow die gap. Mizuno et al. 5 used the simple ideal deformation method to approximate the forming load and consequently the punch pressure. They also conducted a series of experiments to obtain the strain history, and thereby, estimated the stress. * tahira@trakya.edu.tr Recently, the FEM was also employed to simulate the lateral extrusion of solid billets for different geometries by several researchers 6-9. Ko et al. 6 used three different aspect ratios, seven different gap heights and five different die corner radii as parameters in their FEM work. Hsiang 7 studied effects of exit radius, aspect ratio of primarily deformation zone, friction factor and work-hardening coefficient by using FEM and experimentally. Lee et al. 8 and Choi et al. 9 studied the effect of punch diameter and the friction factor on the forming load by the FEM on the combination of lateral and forward or backward extrusion. Research on the lateral extrusion of the segmented flanges such as splines and gear forms are very limited in the literature. The shape of spur gears and splines, which are mostly used machine elements, is a kind of segmented flanges. Metal forming is a favourable manufacturing method of gears and gear like components due to their longer lifetime, higher fatigue strength and cost effectiveness when compared to machined gears when it is made of same material. So far, the load requirement of lateral extrusion of segmented flanges were carried out by Plancak et al. 10 and Can et al. 11 by using the Upper Bound Method. In the aforementioned research works, the barreling effect has not been considered and the deformed shape of simple flange or gear like components were almost assumed uniform from top to bottom.

2 ALTINBALIK: LATERAL EXTRUSION OF GEAR-LIKE FORMS 185 However, it is seen from the experiment that barreling occurs before the metal in cavity do not touch the die wall. It is well-known that when a solid cylinder is compressed axially between two flat-faced parallel platens, the friction between the cylinder and the platens at their surfaces of contact causes nonhomogeneous deformation, which in turn produces barreling of the cylinder. The friction at the toolmaterial interface can be reduced by proper lubrication; however, it could not be completely eliminated during the forming. The barreling shape of cylinder under simple upsetting was studied by many researchers The shape of barrelling in simple upseting was proposed as arc of a circle or a circular curvature by different investigators 12-15, power law by Schey 16 and parabolic form by Kobayashi 17. Banerjee 18 and Narayanasamy et al. 19 showed theoretically that the barrel radius could be expressed as a function of axial strain and confirmed the same through experimental verification. This study aims to investigate the metal flow in the segmented flanges such as spline and spur gear form. The profile of free surface of tooth (barreling) has been investigated in the spur gear form with tapered tooth profile, as earlier done by Altinbalik 20, for spline in which tooth profile is parallel to centerline. The barreled profile in the tooth region before tooth does not touch the die wall was defined by a second degree polynomial. Then the process was simulated by a commercial CAD/CAM package. Experimental Procedure Commercially pure lead was used as experiment material due to its hot forming characteristic at the room temperature. The cylindrical billets were extruded from a cylinder of 40 mm to 20.9 mm and 22.9 mm and machined to the required length. Dies were made from DIN hot worked tool steel and hardened to 53 HRC. Two different containers with 21 mm and 23 mm inner diameters and two different lower dies with two and four teeth were used in the experiments, as shown in Figs 1 and 2 respectively. The dimensions of the gaps provided for the teeth in the lower die for two and four teethed dies are different but the volume of the die gap is the same. The height of the lower die was 15 mm and the aspect ratios of the primary deformation zone, which is ratio of flange thickness to billet diameter, were obtained as T 1 = 15/23 =0.65 and T 2 = 15/21 =0.71. It is reported that the upper limit of the range of specific flange thickness is T=1.65, but a sound flow can be Fig. 1 Lower dies used in the experiments Fig. 2 (a) Schematic illustration of lateral extrusion of taper, and ( b) Instantaneous barrel of the taper and critical dimensions Initial Height Table 1 Initial dimensions of billets Diameter d o =21 mm d o =23 mm h 01 (short) H 02 (medium) h 03 (long) obtained when T<0.8. Diameters and length of billets used in the experiments are listed in Table 1. The specimens were cleaned with acetone so as to provide a similar friction condition before deformation. Samples in the same line have same volume in Table 1. Experiments were conducted on a 150 metric ton hydraulic press with constant ram speed of 5 mm/s. Photographic views of the samples are shown in Fig. 3. Estimation of Barreled Surface Mathematical presentation of barrel of free surface of tooth before touching the die wall has been studied in the production of gear forms with two and four teeth. Tooth width, w, and tooth height, h, are the two main parameters in the barreling in tooth. The front side form of tooth profile was assumed as 2nd order

3 186 INDIAN J. ENG. MATER. SCI., JUNE 2007 polynomial function, depending on the vertical movement of the punch (stroke) and geometry of samples. The outer diameters of the tooth at various height were measured to obtain the extent of barreling, then a second order polynomial was chosen. In order to facilitate these measurements vertical lines were drawn along the tooth height by serigraphy technique. The distance between outer surface and center was measured for each specimen by means of these drawn lines. Measurements were carried out by plane view of four-teethed part a micrometer mounted on Carl-Zeiss Jena microscope. Empirical relationship between the tooth dimensions and the barrel profile was established using measured values. Then, the profile of the barreled surface and tooth dimension is given as follows: f hs= ah + as + ah+ as+ a (1) 2 2 (, ) where s and h are the stroke and height of the tooth respectively. The coefficients a 1 -a 5 are determined statistically by using the least squares of the experimental data, as given in Eq. (2). Then the sum of squares of residuals equation was differentiated with respect to each of the coefficient then five equations was obtained. Fig. 3 Photographic views of deformed parts (a) consecutive steps of part (N=4), (b) plane view of two-teethed part and (c) n i= ( ) 2 i Sr= å x- ah - as - ah- as- a (2) The coefficients of a 1 -a 5 were obtained by means of Gauss Elimination technique, then obtained coefficient were listed in Table 2. Values of correlation coefficients were given in the last column in this table. As seen from the correlation coefficients listed in Table 2, the quadratic equation represents a reasonable fit and a good agreement was found between the experimental data and predicted surface. Results and Discussion The estimated barreled surface of the tooth using the assumed equation given in Eq. (1) is plotted in Figs 4-7. Various stroke stages for three different billet height for given specimen diameter and number of teeth are seen in these figures. The numbers over Table 2 Coefficients of Eq. (1) according to billet dimensions and number of teeth A 1 a 2 a 3 a 4 a 5 (s t -s r )/s t d o =21 N=2 d o =21 N=4 d o =23 N=2 d o =23 N=4 h o1 = h o2 = h o3 = h o1 = h o2 = h o3 = h o1 = h o2 = h o3 = h o1 = h o2 = h o3 =

4 ALTINBALIK: LATERAL EXTRUSION OF GEAR-LIKE FORMS 187 Fig. 4 Calculated tooth profiles for different stroke values Fig. 6 Calculated tooth profiles for different stroke values Fig. 5 Calculated tooth profiles for different stroke values the curves show the billet diameter and amount of the vertical movement of the punch. Thus, metal flow in tooth region is represented according to proposed equation. Stroke values presented in the figures are the same as the stroke values used in the experiments and it is possible to follow advance of metal flow into tooth gap by means of Eq. (1) for any number of tooth and billet diameter. The vertical lines on the right hand side of the graphics represent the front wall of Fig. 7 Calculated tooth profiles for different stroke values the gap provided for the tooth for two and four teethed dies. The curves cover the period between the beginning of the tooth formation and the first contact to the front wall of the gap. As expected, shorter samples move horizontally to tooth gap more than longer samples. This situation is explained as a consequence of friction in the chamber. On the other hand, as seen from the photographic views of the

5 188 INDIAN J. ENG. MATER. SCI., JUNE 2007 process shown in Figs 4-7 the filling of the gaps of the teeth is not uniform from top to bottom and some barreling takes place before the complete filling has been obtained. This phenomenon was also observed by Chitkara et al. 21 for the heading of spline forging. They characterized this situation as a consequence of the difference between value of the shear stress at the top and bottom of the teeth. It is observed that metal flow is more homogeneous when samples with 23 mm diameter are used for two and four toothed cases. When the figures, which represent samples with same diameter but different tooth number, are examined it is seen that more metal flows into gaps provided for the two-toothed case for same stroke value. Increasing number of tooth causes more friction surfaces and narrower tooth gaps. Since metal flow into narrower gap is more difficult higher stroke and load values are needed to fill the gaps for four toothed dies. Variation of D/D b ratio for same lower die and different billet length, h o, is given in Figs 8 and 9. The state of billets with two different diameters at various strokes for two-toothed die is shown in Fig. 8. Figures are directly related to metal in the die gap provided for tooth, stroke values are selected as value at which die filling is obtained. Metal in the tooth gap does not touch front wall yet at these stroke values. Die filling ratios are almost same in the experiment groups which are denoted by same line, bold or weak. Thus, movement of billets with same initial volumes but different h 0 /d 0 ratios in the die was observed. As expected, billets with diameter of 23 mm reach the die filling ratio of billets with diameter of 21 mm at lower stroke values. Although metal flow seems to be more homogeneous when h o /d o increases this result is misleading. Since the aim of this type forming is to extrude more metal into die gaps at lower strokes, better die filling is obtained due to shorter initial length, h o, consequently decreasing friction along the chamber. The die filling ratios of data presented by bold lines are same and this is also valid for data presented by weak lines. Since more die filling is obtained for smaller billet height (h 0 ) and consequently friction resistance increases due to bigger surface. Therefore, D and D/D b values decrease. So, when the metal touches the front wall of the gap provided for tooth, there will be more unfilled zone left at the lower part of tooth for the small values of D/D b ratio. This situation is compensated by increasing the stroke at the end forcing the metal to flow into this zone. Fig. 8 D/D b ratios for different h 0 /d 0 values Fig. 9 D/D b ratios for different h 0 /d 0 values As it is seen from Fig. 8, more homogeneous tooth is formed when h o /d o ratio is increased. The size of unfilled region under the tooth is not bigger due to higher values of D/D b when metal touches the front wall of the die. In addition, better die filling ratios are obtained at lower stroke values. Thus, it is suggested to use a billet having bigger diameter to obtain near or near net shape in lateral extrusion. But the disadvantages of using bigger diametered billet are that it needs slightly higher forming loads when compared to smaller diametered billets. On the other hand, required load to fill the unfilled corners is 3-10 times higher than used load 22. Therefore, it is useful to examine the graphics of load and die filling. The state of billets with two different diameters at various strokes for four-toothed die is shown in Fig. 9. The effect billet diameter and billet length is similar to that for two-toothed die. More homogeneous flow is also observed for the billets diameter of 23 mm and die filling ratios of similar to that obtained with billets diameter of 21 mm. Load-stroke graphics of billets with three different heights for both groups are given in Figs 10 and 11. Since the root diameter of lower die is 25 mm, free bulging occurs for both diameters and recording of load values was started when the metal just entered

6 ALTINBALIK: LATERAL EXTRUSION OF GEAR-LIKE FORMS 189 into tooth gaps. The measured load differences are almost equal to each other as increases in the height of the billets are equal. But, the difference between load values gets bigger at the end of experiment. Die filling values of longer specimens are higher than that of the billets with short and medium height. This situation causes the better corner filling and higher load values at the same stroke. It is easily seen from these figures that load value increase with increasing billet diameter and height. The main reason for this is that surface area with contacts to chamber increases. Higher stroke value is necessary for two-toothed die and d 0 =21 mm billet although it requires lower load values. These group billets requires 50% higher stroke than that with d 0 = 23 mm. The same situation also valid for die gaps with four-toothed. Better die filling is obtained for these experiment groups at 50% higher strokes. The load difference for the longest billets is about 14% for both diameters of 21 and 23 mm. Thus, die filling graphics may help to follow the required ways to obtain similar forms. Die filling ratios with increasing stroke for different diameters and heights are shown in Figs 12 and 13. It is seen from these figures that short and medium height billets renders better die filling compared to Fig. 12 Die filling ratio versus punch stroke for d 0 =21 (a) N=2 toothed taper form (b) N=4 toothed taper form Fig. 10 Forging load versus punch stroke diagram for d 0 =21 (a) N=2 toothed taper form and (b) N=4 toothed taper form Fig. 11 Forging load versus punch stroke diagram for d 0 =23 (a) N=2 toothed taper form and (b) N=4 toothed taper form Fig. 13 Die filling ratio versus punch stroke for d 0 =23 (a) N=2 toothed taper form and (b) N=4 toothed taper form

7 190 INDIAN J. ENG. MATER. SCI., JUNE 2007 longest billets due to effect of friction. However, die filling ratios after 75% of total stroke are constant and do not shown any discrepancy for short and medium height billets for both diameters and tooth numbers. At this stage, die filling is about 97% for all groups. For d 0 = 21 mm, the die filling ratio for longest billets for both tooth numbers is 98.5%. But the die filling is 100% for both tooth numbers when d 0 = 23 mm. When Figs 8 and 9 are examined together, D/D b ratio of samples with d 0 = 23 mm is higher and capacity of die filling is better. The other interesting point observed from the experiments is that the difference between die filling ratios for longest and shortest samples given any tooth number and diameter varies 1.5% to 3%. When die and billet aspect ratio (h 0 /d 0 ) are optimized, it must be considered that load value and die filling decrease and required stroke increases when smaller diametered and shorter billets are used. The process was simulated by using commercial 3D CAD/CAM system called CATIA which has ability to solid modeling. Selecting the two different billet diameter, metal flow has been observed. Figures show phase of deformation steps of process for two different diameter billets at given Fig. 14 (a) Solid model simulation, (b) visual basic screen of deformed billets and (c) FEM analysis of container for given max. load (d 0 =21, N=2)

8 ALTINBALIK: LATERAL EXTRUSION OF GEAR-LIKE FORMS 191 Fig. 15 (a) Solid model simulation, (b) visual basic screen of deformed billets and (c) FEM analysis of container for given max. load (d 0 =21, N=4) Fig. 16 (a) Solid model simulation, (b) visual basic screen of deformed billets and (c) FEM analysis of container for given max. load Fig. 17 (a) Solid model simulation, (b) visual basic screen of deformed billets and (c) FEM analysis of container for given max. load (d 0 =23, N=2) different stroke values. As seen, more material enters into gaps provided for tooth for shorter billet length is used for given stroke value at the (a) of the figures. In addition, a programme in Microsoft Visual Basic was coded. The programme has a window in which the diameters of billet and number of tooth are chosen. All the experimentally obtained data were located in this programme. h and l values of barreling and measured load depending on the stroke values and coefficients of the equation given Eq. (1) are shown on this window at the (b) of the figures. Thus, all values of the process at any stage can be monitored. In (c) of the figures, the magnitude and position of maximum stress obtained according to Von-Mises which correspondence to measured highest load value are shown as coloured scale. Chamber has been

9 192 INDIAN J. ENG. MATER. SCI., JUNE 2007 assumed as thick walled pipe due to its geometry. The required inner pressure values (p i ) were obtained using the reported formulas 23 for thick walled pipes. Then, the problem was simulated by using CATIA. As expected, the highest stress occurred in inner side. The dies used in the experiments are designed for lead and soft aluminium alloys so the existing stress could be blocked up by the dies. The difference between the values of analytical calculation and obtained form CATIA analysis is about 3.6%. Conclusions It is concluded from the experimental work that the shape of the tooth profile is not straight and the barreling occurs. Degree of barreling increases with number of teeth due to increasing the frictional resistance and barreling form is presented by 2 nd order polynomial. A Visual Basic programme developed according to offered equation. Thus, material flow has been observed for similar geometrical parts and different materials at varying stroke values. On the other hand, it is indicated that convenient parts can be produced to its final dimensions by injection upsetting which can be thought as pre-shaping process. Bigger billet diameter and long billet height offer sound metal flow and good die filling ratio but required high forming load compared to smaller billet diameter. However, the difference between die filling ratio values are not higher, it is possible to apply machining process to obtain finish dimensions instead of filling the unfilled zone under the tooth by applying higher load to obtain final dimension of the parts. Additionally the amount and position of the existing stress in the die chamber also obtained by using CATIA. Nomenclature d 0 = billet diameter, mm h 0 = initial height of billet, mm h = height of tooth, mm a 1 -a 5 = coefficients of the suggested equation D = contact (bottom) diameter of taper, mm D b = maximum diameter of barrel, mm l, L = horizontal displacement of tooth, mm N = number of teeth s = vertical stroke of the ram, mm References 1 Balendra R, Int J Mach Tool Des Res, 25 (1985) Balendra R & Qin Y, Int J Mach Tools Manuf, 34 (8) (1994) Balendra R, Int J Processd Res, 25 (6) (1987) Balendra R, Int J Mach Tools Manuf, 33 (6) (1993) Mizuno T, Mizuno T & Kitamura K, J Mater Process Technol, 96 (1999) Ko B D, Kim D J, Lee S H & Hwang B B, J Mater Process Technol, 113 (2001) Hsiang S H & Ho H L, Int J Adv Manuf Technol, 23 (2004) Lee Y S, Hwang S K, Chang Y S & Hwang B B, J Mater Process Technol, 113 (2001) Choi H J, Choi J H & Hwang B B, J Mater Process Technol, 113 (2001) Plancak M, Bramley A N & Osman F, J Mater Process Technol, 34 (1992) Can Y, Altinbalik T & Akata H E, J Mater Process Technol, 166 (2005) Kulkarni K M & Kalpakjian S, ASME J Eng Ind, 91 (1969) Gupta N K & Shah C B, Int J Mach Tool Des Res, 26 (2) (1985) Tseng A A, Horsky J, Raundesky M & Kotrbacek P, Mater Design, 22 (2001) Narayansamy R, Murthy R S N, Viswanathan K & Chary G R, J Mech Weld Technol, 16 (1988) Schey J A, Venner T R & Takomana S L, Trans Am Soc Mech Eng Ser B, J Eng Ind, 104 (1982) Kobayashi S, J Eng Forge Ind, 92 (2) (1970) Banerjee J K, J Eng Mater Technol, 107 (1985) Narayanasamy R & Pandey K S, J Mater Process Technol, 70 (1997) Altinbalik T & Can Y, Mater & Design, 27 (9) (2006) Chitkara N R & Bhutta M A, Int J Mech Sci, 43 (7) (2001) O Connell M, Painter B, Maul G & Altan T, J Mater Process Technol, 59 (1996) Black P H & Adams O E, Jr., Machine Design, (Mc-Graw- Hill Book Company), 1968.