Closed Die Forging of Powder Preforms
A K Gupta, Associate A K Jha, Member
The present study is concerned with an upper bound solution constructed for determining the die load during completely closed die forging of metal powder preform under axi-symmetric condition. In the analysis, an appropriate interfacial friction law and yield criterion for porous material have been used. At the final stage of closed-die forging a product, the unfilled corners require huge working loads to fill them complete, and in some cases, this cannot be realized within the limits of the tool strength. The filling of corners in completely closed die forging of porous cylindrical shape is also considered for analysis. The results so obtained are analyzed and discussed to explain the interaction of various processing parameters involved and are presented graphically.
Keywords : Closed-die sinter forging; Corner filling; Powder preform; Densification; Die load; Simulation
NOTATION a h hm J′
: optimization parameter : vertical unfilled length of top and bottom corner : sticking zone height for billet : second invariant of deviatoric stress : constant (= 2) : instantaneous billet height touch with workpiece-container interface : constant quantity (> unity) : pressure : sticking zone radius for billet : container bore : instantaneous billet radius touch with workpiece-punch interface : Punch velocity : radial, circumferential and axial velocities, respectively : magnitude of relative velocity : strain : constant and a function of relative density ρ only : flow stress of metal powder preform : coefficient of friction : relative density : apparent density of the apparent contact area : dimensionless, ρ ⁄ ρ∗ r : real density of the real contact area
σm σ τ τf τf
φ r y θ
: hydrostatic stress : yield stress of the non-work hardening matrix metal : shear stress : workpiece/punch friction stress : workpiece/container wall friction stress : specific cohesion of the contact surface : radial : axial : circumferential
k L n p rm
U Ur, Uθ, Uy dV
ε η λ µ ρ ρ∗ ρ
A K Gupta is with the Department of Mechanical Engineering, Inderprastha Engineering College, Ghaziabad 201 010 and A K Jha is with the Department of Mechanical Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221 005. This paper (modified) was received on January 20, 2004. Written discussion on the paper will be received until May 31, 2005.
INTRODUCTION The industrial processing of sintered powder preform is a rapidly developing technology used for mass production of engineering components at competitive rates. One technique, which has gained recent advancement, is sinter forging. It combines the advantages associated with two well-known techniques, namely, (i) powder metallurgy, and (ii) conventional forging technology. This technique involves production of a metal powder preform by conventional powder metallurgy technique of compaction and sintering. The sintered hot preform at working temperature is then forged into desired components within the closed dies, resulting in a part with density comparing fairly to that of wrought metals. Sinter forging is a net shape forging and generally performed by one blow within the confined dies to eliminate flash and scrap. Mechanical and metallurgical properties of metal powder components made by sinter forging compares favourably with those of wrought materials . The bulk processing of metal powder preforms, therefore, can be an alternative to many other manufacturing processes like casting, forging and machining. The current major effort in forging technology is towards the manufacture of as-forged near-net-shape parts. This entails the use of completely or nearly completely closed dies, normally on mechanical presses. In flashless forging, the effect of billet location and filling of die cavities to a pre-determined degree is of paramount importance, as it significantly affects the dimensional accuracy of the product, forging load and tool stress. The degree of non-uniformity of filling either top or bottom end of
work piece increases as off centre distance increases. At the final stage of forging a product, the unfilled corners require large working loads to completely fill them, and in some cases, this cannot be realized within the limits of tool strength. It is, therefore, important to understand the filling characteristics of forging in completely closed die cavities, particularly the later stage when corners of small curvature are formed in order to obtain forging of required dimensional accuracy. In the present study, various technological aspects of closed cavity die forging of sintered preform in later stage of deformation have been discussed. The relationship between frictional stress at interface and other process variables is discussed and an analysis has been made for the estimation of die load by upper bound method, which considers the corner filling characteristics in addition to effect of billet location on completely closed cavity die forging. The variation of various parameters is studied critically and shown in the form of graphs. A computer simulation model has also been formulated and developed in VB 6.0 and the results are presented in the form of graphs. PLASTIC DEFORMATION OF SINTERED PREFORM In conventional wrought metal forming analysis, the volumetric constancy is assumed for the deforming material . But during plastic deformation of porous metals, this assumption cannot be made where density does not remain constant and changes with deformation. The metal powder preforms consists of pores, which are eliminated during sinter forging and thus volume change occurs due to presence of porosity. Therefore, volume constancy is not valid.
Figure 1 Schematic representation of stages in forging%
h ⁄ 2 − y τ = µ ρ φ0 1 − m , for Container n L ⁄ 2 Workpiece Interface (4)
WORKPIECE DEFORMATION AND ANALYSIS TECHNIQUE FOR CLOSED DIE SINTER-FORGING PROCESS The deformation process consists of three stages. The first stage is free upsetting with bulging [as shown in Figure 1(a)]. Forging load estimates are obtained from a modified form of Avitzurs upper bound solution of solid disc forging with bulging . The bulge profile is approximated with straight lines [as shown by the dotted lines in Figure 1(a)]. The second stage is constrained deformation of the billet when corners are formed [Figure 1(b)], where load estimates are obtained using an upper bound solution based on the mode of deformation as shown in Figure 2. As symmetrical deformation about the billet mid height and axis is assumed, only one quarter of a workpiece section is considered. The third stage is elastic unloading of the punch. It is assumed that no deformation of the assumed rigid-plastic workpiece takes place in this stage.
A preform with high relative density yields with relatively high stress whereas a low relative density preform yields with relatively small stress. Yielding of porous materials is also sensitive to the hydrostatic stress imposed during processing . With the application of compressive hydrostatic stress, the pores close and the relative density increases whereas with application of tensile hydrostatic stress, the pores grow and the relative density decreases. The density distribution also does not seem to be uniform throughout. It is high in the central region and low at the edges.
The relationship between an external pressure p and a relative density ρ is given by the following equation
2 = − loge (1 − ρ) 3 λ Solving equation (1), one gets ρ = 1 − e− p ⁄ λ
Interfacial Friction Law The pattern of metal flow during forging of a sintered material is such that there exits two zone : an inner zone (where no relative movement between interface occurs, that is, the sticking zone) and an outer zone (where sliding occurs). Therefore, the appropriate friction laws for different interface are expressed as r − r τ = µ ρ φ0 1 − m , nb for Punch-Workpiece Interface
The analysis in the present study is based on the upper bound approach. This approach suggests two expressions for the load, the so called lower bound and upper bound. The former underestimates the load and, therefore, is of little practical interest, whereas the later provides realistic overestimates and is consequently acceptable to plant designers and production engineers, to work out rational production schedules and to produce high quality products. Analysis of Die Load An Upper Bound Approach The compressibility equation for axi-symmetric case is expressed as
εr + ∂ Ur
(1 − 2η) ε = 0 2 (1 + η) y
+ (1 − 2η) ∂Uy 2 (1 + η) ∂y = 0
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∂ Uy 1 ∂ Ur + = 0 2 ∂y ∂r
εry = εθy = 0 Power Dissipation and Estimation of Die Load
For plastic deformation of a sintered preform the external power J∗ supplied by the punch is given as J∗ = 2σ √3
2 εij εij ∫ √ d v + ∫ τf
|dv|ds + ∫ τf |dv|ds
The first term on the right hand side of equation (14) denotes the rate of internal energy dissipation Wi; the second term, the shear energy losses Wf along the punch-workpiece interface and the last term Wf denotes the shear energy losses along the container wall-workpiece interface.
The internal power of deformation Wi in each region is obtained from the following expression Wf =
τf |dv| ds
Figure 2 Mode of deformation for upper bound
The velocity fields in each region are given below. The origin of the cylindrical co-ordinate system is at the centre of the workpiece. Because of axial symmetry, it is assumed that no rotation of the workpiece occurs in the course of deformation, so that in all cases under consideration, the circumferential velocity Uθ is zero. Region 1 (Upper Bound) . 1 1 − η r a U Ur = 2 1 + η h Uθ = 0 y Uy = − a U h where 0 ≤ a ≤ 1. Region 2 (this region is assumed to be dead) Region 3 . 1 1 − η r a U Ur = 2 1 + η h Uθ = 0 y Uy = − a U h The strains rates can be expressed as εrr = εθθ εyy 54 ∂U 1 1 − 2η U a = 21+η h ∂r Ur 1 1 − 2η U a = εrr = = 21+η h r ∂ Uy U = = − a h ∂y
r − r τf = µ Pav + ρ φ 1 − m (16) nS The frictional power loss along the contact surfaces of container wall and workpiece is obtained from the following expression
1 0 0
τf |dv| dz
where (7) h ⁄ 2 − y τf = µ Pav + ρ φ 1 − m n L ⁄ 2
2 0 0
The external power J∗ supplied by the press through the punch can be expressed as J∗ = 2 (Wi + Wf + Wf ) = 2PU
The internal power of deformation Wi can be expressed as Wi = (8) Wt = 2σ
√ 3 2σ
1 εij ε ∫ √ d v ij 2
ε + 1 ε + √εry 2πrdrdy 2
Now putting the values from equation (9) and equation (11) into equation (20) and solving, one gets (9) (10) (11) Wi = where a = (1 − 2η) (1 + η) πσ aUR
√2 √ h 3
(L − H) (2R − 3S ) + 1 + H (22) 3(R − S)
The rate of energy dissipation Wf due to friction between punch-workpiece interface can be expressed as
Mathematical Modelling The first step in simulation of a manufacturing process is to formulate a deformation problem under consideration. This consists of defining areas to be collected and fed into model and specifying boundary conditions of problem. The second step consists of presenting governing equations of metal deformation in a form, which can simplify and fulfil simulation objectives. After carrying out simulation, the last step is the collection of output data and their interpretation in form of results. In closed die sinter forging process, plastic strain outweighs elastic strain and deforming material is assumed to be compressible, due to presence of pores. The deformation of preforms obeys Tabata and Masaki yield criterion and associated flow rule. The velocity and strain rate field is found by Upper Bound approach and forging load is estimated by Energy Method which considered three forms of energies, namely, internal energies of deformation, frictional shear energy between workpiece-punch interface and frictional shear energy between workpiece-container wall interface.
τf |dv| ds
r − r 1 − 2η arU 2πrdr (25) Wf = ∫ µ Pav + ρ φ 1 − m nS 1 + η h
1 0 0 0
The rate of energy dissipation Wf due to friction between punch-workpiece interface can be expressed as
τf2 |dv| ds
hm ⁄ 2 − y y 1 − a U 2πRdy (27) n L ⁄ 2 h
∫ µ Pav + ρ0 φ
The pressure distribution between punch and workpiece is required for the computation of the friction losses. If the pressure is assumed constant and equals to average pressure (Pav), then the frictional losses are reasonably accurate for practical purpose. Therefore, integrating and simplifying equation (25) and equation (27), one gets Wf =
External power ( J∗) supplied by the punch can be found from following relationship J∗ = 2[(Wi + Wf + Wf )] = 2PU
πµαaUR 3R rm Pav + σ φ0 1 + 4nS − nS 3h
3 0 2
The forging load (P ) can be found from the following relationship P = J∗ 2U J∗ 2πS U
πRµaUH 2H hm (29) Pav + ρ φ 1 + 3nL − nL 4h External powder supplied by the punch can be expressed as
Forging pressure ( p) can be found from the following equation p = (33)
P = (U)− (Wi + Wf + Wf2)
1 1 1 2
where Wi, Wf , and Wf are given by equation (22), equation (28) and equation (29), respectively. Simulation of Closed Die Sinter Forging Process In an environment, which is becoming increasingly complex due to shorter product life and small time to marker products, simulation is already been recognized as a tool to predict the behaviour of an actual process prior to production run in no time. This feature of simulation called Time Compression is used to obtain the operating characteristic estimates in much lesser time as compared from real process . The process simulation helps in conducting experiments without disrupting the real system and hence advantage from economical point also. The only constraint with the computer simulation is degree of accuracy to which model reflects the behaviour of real process .
The relationship between the forging pressure p and a relative density ρ is given by the following expression ρ = 1 − e− 1.5 p ⁄ λ (34) The relationship between punch movement ∆U and the final height H of billet after closed die sinter forging can be expressed as H = H ′ − ∆U (35) The relationship between punch movement ∆U and the final radius s of billet after closed die sinter forging can be expressed as S = S ′ + ∆DJ The percentage reduction in height of disc is expressed as H − H 50 − H (37) hred (%) = 100 = 100 H0 50 The percentage increment in radius of preform is expressed as
Closed die sinter forging is influenced by many factors like density of powder preform, flow stress of sintered preforms, deformation speed, contact time under load, etc which interact with each other in a complex manner. So, it is believed that realization of the above process and computer simulation of closed die sinter forging under axi-symmetric conditions provide definitely a better understanding during deformation. Vol 85, March 2005
S − S S − 20 S ′ (%) = 100 = (38) 100 S S In simulation model, dies are assumed to be moving towards each other with absolute velocity U. The value of U is
assumed to vary from 2 m/s to 8 m/s and initial parameters are assumed as follows : Die radius (R), mm : 25 Billet height (H), mm : 50 Billet/punch interface (S), mm : 20 Billet/container wall interface (L), mm : 30 Sticking zone radius, mm :3 Sticking zone height, mm :5 The equations (31)-(33) give the values of external power J∗ (in kJ), forging load (t) and forging pressure p (kg/mm ), respectively. The equation (34) suggests the value of relative density ρ for corresponding values of forging pressure (p) and flow stress (λ). The equation (35) and equation (36) suggest the instantaneous height and radius of the workpiece, respectively. The equation (37) and equation (38) give the value of percentage reduction in height and percentage increase in radius, respectively.
This software has been generated in three parts, namely, the main form (named Frmmain), the module and the authorinformation form (named Dialog). The main form is used for displaying the simulation process. When the simulation process has to be shown, the controls for taking user input, displaying the initial, instantaneous and final values of parameters are used. The module comprises of various sub-routines and function used for calculation, displaying the various stages of die movement and compression of billet preform. The inter- relation of these sub-routines and the program flow are shown in Figure 3. CONSULATION SESSION The files of software are stored in a folder named forging. This contains all the files generated by VB 6.0,especially the file named project1.vbb that has formed and related code and file Module1.bas that stores the sub-routines of module. The folder also has an executable version of the software named CLOSED DIE SINTER FORGING SIMULATOR that can be executed directly from the command line. When the software is executed either using executable version or from the VB-IDE (using F5 or the play button), the main form is displayed. At this time, it shows the initial position of the billet. The initial frame displays the initial assumed parameters. The user has to enter the values of ram velocity U, relative density ρ, and flow stress λ in respective input boxes. The range of U and λ are specified values and any value out of range is not accepted. After entering these values, the user has to click START THE PROCESS button to start the process. Once the process starts, the ram moves velocity U towards each other and compression begins. The subsequent stages of compression and the corresponding intermediate values of parameters (height, radius, density, power etc) are displayed on the INSTANTANEOUS VALUES frame. RESULTS AND DISCUSSION The simulation results of computer model of closed die sinter forging are also presented in form of graphs. The curves of the graph relate to deformation only after contact is made with the die wall. However, the precise load at which contact is made has not been identified. Figure 4 shows the relationship between the percentage reduction in height of billet and the percentage increase in radius of billet. This variation is found to be more or less linear.
CLOSED DIE SINTER FORGING SIMULATOR A software has been developed for the analysis of different characteristics of closed die sinter forging in VB 6.0. The input parameters to this simulation software are U, ρinitial, and λ and the output parameters generated are ρ, hred (%), rinc (%), forging pressure p, forging load P and external power supplied J. This simulation software also provides instantaneous values of ρ, hred (%), rinc (%), forging pressure p, forging load P and external power supplied J.
Figure 3 Flow chart for closed die sinter forging simulator
Figure 4 Increase in radius against height reduction
Figure 5 Forging pressure against height reduction
Figure 8 Power against height reduction
Figure 6 Forging pressure against increase in radius Figure 9 Forging load against height reduction
Figure 7 Relative density against forging pressure
This shows that percentage decrease in height is accompanied with more or less same in percentage increase in radius of the billet. Figure 5 shows the variation of percentage reduction in height of preform with the forging pressure. The percentage reduction in the height of preform is found to increase with increase in forging pressure. Initially, the forging pressure is less but at later stage it is increasing, which states that at later stage forging process requires more load to fill the corners. The reduction in height of billet is found to be nearly 8.16 %. Figure 6 shows the variation of percentage increase in radius of billet with forging pressure. The percentage increase in the radius of billet is found to increase with the die load and the increment in radius of billet is found to be nearly 25%. Figure 7 shows the variation of relative density ρ of preform with the external pressure applied on the preform. It is found that the relative density increases with increase in external pressure initially, the increase in relative density is rapid but as the deformation Vol 85, March 2005
Figure 10 Relative density against height reduction
progresses, the pores resist their closing and, hence, the rate of increase in relative density decreases. Figure 8 shows the variation of the external power supplied with the percentage reduction in height. It conforms that the external power supplied increases with percentage reduction in height. Figure 9 shows the forging load against the percentage reduction in height under symmetry conditions. The curves express results for a particular value of the coefficient of friction µ, initially relative density ρ and the ram velocity U. The forging load is found to increase with percentage reduction in height. Figure 10 shows the variation of relative density ρ with percentage reduction in height of billet. During closed die sinter forging process, the compressive forces close the pores gradually and thus relative density of sintered materials increase with an increase in percentage reduction in height of billet. Figure 11 shows the variation of the external power supplied with respect 57
CONCLUSION The deformation pattern during closed die sinter forging process is influenced by several factors, which interact with each other in a complex manner. The main controlling factors are preform density, friction condition at punch-workpiece and workpiece-container wall interface, flow stress of sintered preform and factors related to forging equipments (such as, punch velocity). It has been shown that billet geometry and surface condition also affects load requirements and workpiece corner dimensions during die cavity filling. The theory model developed provides realistic load estimates over a fairly wide range of die cavity filling . This model is useful particularly for predicting full filling load. The corner filling during closed die sintered forging process has been analyzed and discussed critically. It is seen that progressively large forming loads are required to achieve full filling. Depending on the forging conditions, these filling loads are much greater than the load at which contact with the die wall is made. The study is found to be effective for assessment of the forging pressure, variation of relative density, estimation of external power supplied, percentage reduction in height and percentage increment in radius, during closed die sinter forging of powder preforms. It is expected that the present closed die sinter forging analysis using upper bound method and its computer simulation using a mathematical model can be used in expanding the research and development work in industrial processing of sintered preform area. REFERENCES
1. G W Cull. Mechanical and Metallurgical Properties of Powder-forged Products. Powder Metallurgy, vol 13, no 26, 1970,p 156. 2. R T Cundill. Mechanical Properties of Sintered Forged Low- alloy Steels. Powder Metallurgy, vol 13, no 26, 1970, p 130. 3. A K Jha, S Kumar, S Singh and R K Singh. Sintered Preform Adds Better Value to Aerospace Components. Journal of The Institution of Engineers (India), vol 82, pt AS 2, May 2001, p 1. 4. T Tabata, S Masaki and K Hosokawa. A Compression Test to Determine the Coefficient of Friction in Forging Powder Metallurgy Preforms. International Journal of Powder Metallurgy and Powder Technology, vol 16, no 2, 1980, p 149. 5. A K Jha and S Kumar. Deformation Characteristics and Fracture Mechanisms during the Cold Forging of Metal Powder Preforms. International Journal of Machanical Tools Design and Research, vol 26, no 4, 1986, p 229. 6. S Shima and J M Alexander. The Inter-relation of Density and Hardness in Isostatic Compaction of Powders. Proceedings of the Thirteenth International MTDR Conference, 1973, p 471. 7. B Avitzur. Metal Forming: Process and Analysis. McGraw- Hill Book Co, New York, 1965, p 63. 8. L J Krajewski and L P Ritzman. Operation Management: Strategy and Analysis. Addison-Wesley Publishing Co, (4th edition), 1996, p 323. 9. C Chrystall and M M Kaye. Selection of a Manufacturing Simulation Tool. Journal of Production Engineering, vol 66, no 11, 1987, p 24. 10. T Tabata and S Masaki. A Yield Criterion for Porous Metals and Analysis of Axial Compression of Porous Disks. Journal of Japanese Society of Technology and Plasticity, vol 18, 1977, p 373. 11. S Kumar. Principals of Metal Working. Oxford IBH, New Delhi, 1976.
Figure 11 Curves for power against time
Figure 12 Curves depicting height reduction against time
Figure 13 Forging load against height reduction curves
to time for different values of ram velocity U. It conforms that the external power supplied increases with an increase in ram velocity and the graph shifts for higher values of power supplied. These data can be found to be very useful from the design point of view, as these can be used for the design of the dies and presses for a particular application. Figure 12 shows the variation of percentage reduction in height with respect to time for different values of ram velocity. From the figure, it is very clear that as the ram velocity increases the graph shifts to the higher values of percentage reduction in height. Figure 13 shows the variation of forging load with percentage reduction in height for different densities. From figure it is clear that as the density of the preform increases, the graph shifts to the higher values of the forging load. It states that at the final stages of forging a product, the unfilled corners require large working loads to completely fill them. 58
12. A O A Ibhadode and T A Dean. Simulation and Experimental Verification of Completely Closed Cavity Die Forging on a Mechanical Press. Proceedings of Institutions of Mechanical Engineers, vol 203, 1989, p 17. 13. H H Hausner. Forging of Powder Metallurgy Preforms. New Prospective in Powder Metallurgy, vol 6, 1973. 14. A K Jha and S Kumar. Dynamics Effects during High-Speed Sinter-Forging Process. International Journal of Machanical Tools Manufacture, vol 36, 1996, p 109.
15. S Singh and A K Jha. Analysis of Dynamic Effects during High-speed Forging of Sintered Preforms. Journal of Materials Processing Technology, vol 112, 2001, p 53. 16. A K Jha and S Kumar. Compatibility of Sintered Materials during Cold Forging. International Journal of Materials and Product Technology, vol 9, nos 4/5/6, 1994, p 281. 17. P K Jones. Technical and Economic Advantage of Powder Forged Products. Powder Metallurgy, vol 13, no26, 1970,p 114.
The Institution of Engineers (India) acknowledges the valuable guidance provided by the following experts which immensely helped in maintaining the technical standard of the Journal. Ahuja, Dr B B. Assistant Professor of Production Engineering, Government College of Engineering, Pune 411 005. Basu, Dr Jhankar. Scientist, Central Mechanical Engineering Research Institute (CMERI), Durgapur 713 209. Bhadury, Dr Bikash. 241, Jodhpur Park (2nd Floor), Kolkata 700 078. Chattopadhyay, Dr A B. Professor, Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721 302. Datta, Dr G L. Professor, Mechanical Engineering Department, Indian Institute of Technology, Kharagpur 721 302. Dube, Dr R K. Metallurgical Engineering Department, Indian Institute of Technology, Kanpur 208 016. Jain, Dr V K. Mechanical Engineering Department, Indian Institute of Technology, Kanpur 208 016. Kumar, Dr B. Head, Production Engineering Section, Department of Mechanical Engineering, Regional Institute of Technology, Jamshedpur 831 014. Lahiri, Dr B N. Professor, Production Engineering Division, Jadavpur University, Kolkata 700 032. Mukherjee, Dr N P. Deputy Director, Central Mechanical Engineering Research Institute (CMERI), Durgapur 713 209. Mukherjee, Dr Sanat. Vice Chancellor, Birla Institute of Technology, Mesra, Ranchi 835 215. Murthy, Shri T S R. CMTI, Turnkur Road, Bangalore 560 022 Navale, Prof L G. Production Engineering Department, Government College of Engineering, Shivajinagar, Pune 411 005. Pal, Dr D K. Department of Mechanical Engineering, Regional Engineering College, Durgapur 713 209. Pathak, Dr S C. Professor, Mechanical Engineering Department, Malaviya Regional Engineering College, Jaipur 302 017, Rajasthan. Prasad, Dr S. 39 Neeraj Nagar, near Asopa Hospital, Agra 282 007. Radhakrishnan, Prof V. Manufacturing Engineering Section, Department of Mechanical Engineering, Indian Institute of Technology, Chennai 600 036. Rajan, Dr T V. Metallurgical Engineering Department, M R Engineering College, Jaipur 302 017. Ramaswamy, Prof N. S-7, Madhuram Apartments, 6, Orur Olcot Road, Chennai 600 090. Roy, Dr P K. Scientist G Associate Director, Government of India, Ministry of Defence, Defence Research & Development Organisation, Institute of Armament Technology, Girinagar, Pune 411 025. Saha, Dr J. Department of Production Engineering, Jadavpur University, Kolkata 700 032. Sarkar, Dr Bijan. Assistant Professor of Production Engineering Department, Jadavpur University, Kolkata 700 032. Sen, Dr Ranjan. Scuebtust Em CMERI, Mahatma Gandhi Avenue, Durgapur 713 209. Siva Prasad, Dr N. Professor, Machine Design Section, Department of Mechanical Engineering, Indian Institute of Technology, Chennai 600 036. Waghodekar, Dr P H. Principal, AISSMS College of Engineering, Kennedy Road, near RTO, Pune 411 001.
Vol 85, March 2005