A STUDY ON THE INFLUENCE OF WORKPIECE PROPERTIES IN ULTRASONIC MACHINING

Transcription

1 Int. J. Mach. Tools Manufact. Vol. 33, No. 3, pp , / Printed in Great Britain 1993 Pergamon Press Ltd A STUDY ON TH INFLUNC OF WORKPIC PROPRTIS IN ULTRASONIC MACHINING M. KOMARAIAHt and P. NARASIMHA RDDY:~ (Received 19 November 1990; in final form 26 March 1992) Almtract--In ultrasonic machining (USM), brittle materials are machined by repeated impacts on the workpiece through a medium of abrasive slurry. Material removal rates are influenced by the various process parameters including the properties of the workpiece material. In this investigation, the influence of fracture toughness and hardness of workpiece materials are studied and reported. Fracture toughness is found to be an important parameter. xperiments are conducted with both conventional and rotary USM modes. Machining performance in the rotary mode is found to be much superior to the conventional mode. The results of static, sliding and rolling indentation tests reported by other investigators are used for explaining the importance of the fracture toughness. INTRODUCTION IN CONVNTIONAL ultrasonic machining (USM), a tool is mounted in the ultrasonic head, which is axially vibrated at a desired frequency. The amplitude of oscillations can be varied. The workpiece is mounted on a table and a desired static load is applied. An abrasive slurry is fed into the cutting zone as the tool is vibrated. The set-up is shown in Fig. l(a). In the present investigation, an attempt is made to study the material removal rate, when the workpiece is rotated (rotary USM mode). The details of this set-up are shown in Fig. l(b). The rotary mode offers an additional parameter for the control over the process. The work done by the authors on the rotary ultrasonic machining process is reported elsewhere [ 1 ]. A reference is also made by McGeough [2] in which an ultrasonically activated drill-bit was rotated against the workpiece in a similar fashion to that of conventional twist drilling. The mechanism of material removal in conventional ultrasonic machining has been studied by a number of investigators [3-5]. The hammering action of the abrasive particles into the workpiece material, causing removal as micro-chips, is widely accepted as a primary importance. Shaw [3] derived an equation for the material removal rate (MRR) due to the hammering action, which is given in Appendix (A.1). Miller [4] proposed another equation for material removal rate, which is given in Appendix (A.2). He had taken into consideration the amount of plastic deformation undergone by the workpiece per blow (PD) and other parameters. Cook [5] made an estimate for the penetration rate and proposed a relation given in Appendix (A.3). The important parameters considered are the static stress applied using a known static load and the workpiece hardness. Ultrasonic machining is suitable for drilling holes of any shape in hard and brittle materials. Markov [6] classified materials into three categories with regard to the suitability of USM for machining them. Type I materials, like glass, which are very brittle, are easily machinable by the USM process. The material is removed by the propagation of minute cracks that are inherently present in such materials. Type II materials, which exhibit some plastic deformation before fracture, like carburised, nitrided steels, can be machined although with some difficulty. Type III materials, like copper and soft steel, are ductile materials and are unsuitable for USM. The classification of the materials and field of application of USM are given in Table 1. tprofessor of Mechanical ngineering, College of ngineering, Osmania University, Hyderabad , India. ~tprofessor of Mechanical ngineering, C. B. Institute of Technology, Hyderabad , India. 495

2 496 M. KOMARAIAH and P. N. RDDY (a) (b) 1. Transducer (magneto-stdctive) 1. Transducer 9. Scale 2. Horn 2. Horn 10. Pointer 3. Tool 3. Tool 11. Loading fixture 4. Workpiece 4. Rotary set-up 12. Compound slide 5. Slurry 5. Workpiece 13. Load 6. Cooling system 6. Centrifugal pump 14. Slurry tank 7. Cooling cylinder 7. Motor 15. Foot pedal 8. lectrical connections 8. Spindle assembly 16. Generator FIG. 1. (a) Conventional USM set-up. (b) Rotary USM set-up. TABL 1. CLASSIFICATION OF MATRIALS AND FILDS OF APPLICATION OF ULTRASONIC MACHINING [6] Group Criterion Predominant Type Field of and of type of of application of material brittleness deformation failure ultrasonic machining I glass over 2 elastic brittle 1. Making parts of mica semiconducting materials quartz 2. Cutting industrial diamonds ceramic 3. Cutting special ceramics diamond 4. Making parts of glass quartz, germanium and minerals in the optical silicon and jewellery industries ferrite 5. Machining ferrite, alsifier alsifier and other materials of high correctivity II alloys tempered to 1-2 elastic- brittle after work 1. Making and repairing hard high hardness plastic hardening by plastic alloy dies, press tools, and carburised and deformation purchases nitrided steels 2. Shaping and sharpening hard titanium alloys alloy tools III lead, copper, less than 1 plastic practically no failure Unsuitable for ultrasonic soft-steel (or ductile failure) machining Ultrasonic machining is particularly used for micro-drilling holes of up to 0.1 mm. To the other extreme, tools as large as 85 mm diameter were used for drilling holes with high capacity (2.5 kw) ultrasonic machines. ven threading is attempted by appropriately rotating and translating the workpiece/tool. Drilling of deep and accurate holes in graphite, germanium, quartz, etc. are reported with high productivity levels.

3 Workpiece Properties in Ultrasonic Machining INDNTATION STUDIS ON BRITTL MATRIALS In the literature there are reports where fracture of brittle materials has been studied. nomoto [7] and vans and Wilshaw [8] have studied the material removal in brittle materials under static and sliding identations. They found that the theoretical load required for the formation of Hertzian cracks was less in the case of sliding indentation when compared to the load required for static indentation. They further observed that in addition to the hardness of the workpiece the fracture toughness also plays an important part in the material removal. A schematic diagram showing the sequence of crack formation and growth during loading and unloading on a glass workpiece using a tungsten carbide ball is presented in Fig. 2. By the indentation, the radial, median and lateral cracks form and propagate. The material from the workpiece will be removed if the lateral cracks formed due to two adjacent indentations meet (Fig. 3). The lengths of the cracks Cr (radial crack length) and CL (laterial crack length) are given by [6]: Cr oc p1/2/(h1/4./(1/35 - -,.-,,,,.-,,, CL OC ( p/ Kc)3/, (1) (2) where P is the load applied (N), H, is the hardness of the workpiece (GPa), and Kc is the fracture toughness (MPa ml/2). The above equations indicate that fracture toughness of the material is of major C- Static load Tungsten carbide ~" ball Side view Top view "10 0 -I Radial cracks Radial cracks ~ l m ression P1 i~~ace ~ ~ p ~ taleral crack "rime - e,- Ps J ~ ~ c L h~ FIG. 2. Schematic diagram showing the sequence of crack formation and growth events during loading and unloading [4]. m ~z341

4 498 M. KOMARAIAH and P. N. RDDY significance in the formation of cracks and hence MRR. This factor is not considered in the experimental or theoretical study of the material removal rates in ultrasonic machining by any of the presently cited investigators. xperimental investigations on the influence of fracture toughness and hardness of the workpiece materials in the ultrasonic machining process are reported here. 3. XPRIMNTAL WORK xperiments were conducted in both conventional and rotary USM modes on different workpiece materials keeping the other parameters constant. The workpiece materials machined in this investigation were glass, ferrite, porcelain (hard), alumina (pure) and tungsten carbide (K2o). Their hardness values were 6, 7.25, 8.15, 13.2 and GPa respectively. The hardness of the materials was calculated by a formula taken from George and Peter's work [9]: P H = -- (3) (x a 2 where H is hardness (GPa), P is the load applied (N), ol is the indentor constant (2), and a is half the diagonal of the indentation (m). For these hardness tests a Vicker's micro-hardness tester was used. Tests were also conducted for the estimation of fracture toughness (Kc) of all the materials mentioned above, using a Vicker's micro-hardness tester. The load was increased in successive indentations only until a measurable crack length was observed. As an example, the indentation cracks formed in the tungsten carbide specimen are given in Fig. 4(a). A schematic diagram showing the cracks formed is given in Fig. 4(b). The fracture toughness was calculated by the formula taken from George and Peter's work [9]: K c - P ~.C3/2 where K~ is fracture toughness (MPa.ml/2), P is the load applied (N), 13 is the Vicker's indenter constant (7), and C is the semi-crack length (m). The values of the fracture toughness of the materials tested, i.e. glass, porcelain (hard), ferrite, alumina and tungsten carbide, were 1.02, 2.50, 2.80, 5.50 and MPa.m 1/2 respectively, comparable to those reported elsewhere [8,10,11]. The experiments were conducted on an Imeco-soni ultrasonic drilling machine of 250 W capacity and a frequency of khz. The amplitude of oscillation was set at 40 microns. The abrasive particles used in all the experiments were of silicon carbide with a mesh size of 220. In the experiments, an abrasive slurry of concentration 28.5% by volume was used. A static load of 500 g was used. xperiments were conducted in both conventional and rotary USM modes. In rotary mode, the workpiece was rotated at 220 rpm by using an external drive, as shown in Fig. l(b). (4) Critical distance ~~...~'~'~ for the lateral ~ = ~C cracks to meet FIG. 3. Critical distance between two adjacent indentations.

5 Workpiece Properties in Ultrasonic Machining 499 (b) -< Flo. 4. (a) Indentation crack in- tungsten carbide. (b) Schematic diagram showing a cracked micro-indentation impression. Holes of 3 mm diameter and 6 mm depth were made and the time taken for each of the workpiece materials was measured. The tests were replicated and the average machining time was arrived at. MRR was then calculated by dividing the volume removed by the machining time, and expressed in mm 3 min-1. The MRR is indicated as Vc in conventional USM and as VR in the case of rotary USM Influence of the workpiece hardness on material removal rate The materials machined in the investigation were glass, ferrite, porcelain, alumina and tungsten carbide as stated already. The MRR are plotted in Fig. 5 on log-log coordinates. One can observe that for the same workpiece material, the MRR in rotary USM (VR) is 3--4 times more than that in conventional USM (V ). The superior performance of rotary USM is because of the additional motion of the workpiece with respect to the tool. Due to the rotation of the workpiece there will be sliding and rolling contacts between the abrasive grains and workpiece, as well as impacts and indentations of the abrasive particles with the workpiece at ultrasonic frequency. A detailed explanation for the better performance of rotary USM is reported by the authors [1, 12]. The observation that the rotary USM has superior performance to conventional USM has a parallel in ultrasonic twist drilling [2]. It can be further observed that as the workpiece hardness is increased, there is a decrease in MRR in both conventional and rotary USM modes. The decrease of MRR as a function of hardness is almost linear. The slope of the mean-line is negative and the values are 0.62 and 0.64 for conventional and rotary modes, respectively.

6 500 M. KOMARAIAH and P. N. RDDY ~,R~aryUSM v o -J O~~ ~~ Conventional USM Porcelain x Glass 1 Ferrite Vc =< (/.4)0.62 o Alumina 1 o Tungsten carbide V R ~ (h~ 's I I Log hardness (G.Pa) FIG. 5. ffect of hardness on MRR Influence of fracture toughness of the workpiece on material removal rate ( MRR ) The material removal rates of the various materials were plotted as a function of their fracture toughness (Fig. 6). As the fracture toughness of the workpiece material increases, there is a linear decrease in MRR when plotted on log-log coordinates. The slope of the lines are negative and they are 1.2 and 0.66, respectively, for conventional and rotary USM modes. 4. DISCUSSION An attempt has been made to arrive at a theoretical relation for MRR as a function of hardness and fracture toughness for the materials machined. The analysis is made separately for conventional and rotary USM modes. vans and Wilshaw's investigations [8] extend ultrasonic machining. Here the experiments involve material removal by indentations (static or sliding). Where the indentor is fixed to the loading member, the situation differs slightly from that of ultrasonic machining (in which abrasive grains are free). A C 101 v > O r- o.-i I 10-1 V c =( KCl. 2 1 V R =< Kc0.Se z Porcelain x Glass A Ferrite a Alumina o Tungsten carbide I I USM ~C;nventional USM Log fracture toughness (MPa, m 1/2) I lo 2 FIG. 6. ffect of fracture toughness on MRR.

7 Workpiece Properties in Ultrasonic Machining xtension of vans and Wilshaw's analysis to conventional USM In ultrasonic machining as stated already, there are a number of free grains which are indented into the workpiece due to ultrasonic oscillations of the tool. The patterns of the indentations and the resulting lateral cracks are shown in Fig. 7(a). ach indentation will lead to the formation of a circular lateral crack lying at a depth of hi. When the lateral cracks formed by the adjacent cracks meet, a layer of work material with a thickness of hi will be removed. Based on this approach, the relationship for the material removal rate is proposed. The volume of material that might be removed due to each indentation of an abrasive particle or grain will be: (a) O::Ysf::w,:dentations 7 -- (b) ~ Indentations ~,~'~ \ ~... /X Lateral crank circles V.,uu,~wur~p,~,~u/ in the sub-surface at a depth (hi) ~ ~ nveloping path of The distance betwean_l. ~-~ ~,~.---,~-x",x../ lateral crack circles the identer path must /~-7-'-1 "~:~F-.~.~ ~.~)~x~,,~ be less than critical / /." _ ~- ---"-~-'.,cx x\'.'~ X \ ~ Identar paths in distance tar lateral ~ / / /, ~,-~.--'~,.I~ rotary USM created cracksto moot / /,' / L~'7- "~.~" \ \ \ by embedded a~rasives ~n the tool N (C) nveloping paths of the lateral crack circles Successive lateral..--" crack.'ircles,..." _ k\ Ii.,'/ J/../ f Oir r~;'ection of rotation of ',J / J" workplace Successive indentations FIG. 7. (a) Indentations and lateral cracks formed in conventional USM. (b) Indentations and enveloping lateral crack paths in rotary USM. (c) Magnified view of indentations and lateral cracks in rotary USM.

8 502 M. KOMARAIAH and P. N. RDDV Vc (per grain) oc C 2. hi. (5) Substituting for CL from equation (5) and assuming the depth of indentation hi to be proportional to the factor (P~/H) lj2, the material removed per grain per indentation becomes: [ Ieg ]3/412 Vc~[I_KcJ J (~_)1,2 where Pg is the static load applied per grain. Hence: or Vc ~ Ky 2 H1/2 (P/Ni) 2 Vc ~ Ka/-3~H1/2 ~vi where P is the static load applied, which is equal to Pg'Ni and Ni is the effective number of grains in the gap between the tool and workpiece. The material removed per second can be expressed as: p2 f Vc oc g 3/2 H1/2. Nil (7) where f is the frequency of ultrasonic oscillations, generally constant at ~ 20 khz. From equation (7), one can observe that the material removal rate is inversely proportional to K 3/2 and H 1/2. Thus, the theoretical exponents of Kc and H are 1.5 and 0.5, respectively, which compare well with the experimental values of 1.2 and These values are slightly different in view of the fact that the abrasive grains in USM are free in contrast to the fixed indentor in the experiments of vans and Wilshaw xtension of vans and Wilshaw's analysis to rotary USM When the workpiece is rotated, while the tool is oscillated as usual, the situation will be different from conventional USM. The indentation pattern and the resulting cracks in the workpiece will be as follows. By the time the tool comes back for indenting the abrasive grains into the workpiece in the successive cycles, the workpiece rotates to a new position. The abrasive grains will also roll during this minute rotation of workpiece. When the tool hits the abrasive grain in the succeeding cycle, a fresh indentation results that has considerable overlapping with the preceding indentation. The lateral crack circles, which form due to the indentations, can be enveloped by two arcs of circles as shown in Fig. 7(c). The overall situation is presented in Fig. 7(b). In effect, there will be a number of scratches that can be said to be formed by the large number of abrasive grains present in the cutting zone leading to material removal. In addition, some abrasive grains will be embedded in the tool causing scratches similar to those formed in sliding indentation experiments. The material removed by each indentation path in one revolution of the workpiece is: VR = CL 2~rR hi where R is the radius at which the abrasive grain is located from the centre of the workpiece. The material removed per second (VR) can be written as:

9 VR = CL 2"trR h i N i n Workpiece Properties in Ultrasonic Machining 503 (8) where Ni is the number of effective grains in the cutting zone, and n is the revolution of the workpiece per second. The above equation can be re-written as: VR = Ni CL " 2~rR.... " h i n. (9) R is replaced by R... as the indentation paths are at distances from zero to Rma x and R.... may be taken as Rmax/2. Now substituting the values of CL from equation (2) and making hi proportional to (Pg/H) 1/2, it follows: N. P )13/4 (pg)l/2 Rmax VR ~ 1\ g~. 2~ n. (10) K3/4 H1/2 Substituting Pg = P/Ni, equation (10) becomes: (p)5/4 Rmax VR ~ K3/4H1/2 N1/4 " n. (11) The exponents of Kc and H from equation (11) are 0.75 and 0.5, respectively. From the experimental results, the values obtained are 0.66 and 0.64, respectively, which are comparable to the theoretical values. The differences are quite small in the light of the explanation given in the previous section Influence of static load on material removal rates xperiments were also conducted to study the influence of static load on MRR in both the conventional and rotary USM modes keeping all other parameters constant. The static load was varied from 150 to 600 g, while tools of the same diameter of 3 mm were used in these experiments. The variation of MRR as the load is increased is shown in Fig. 8 on log-log coordinates. The increase in MRR is almost linear for both the modes and the MRR can be expressed as follows: Vc ~ p1.63 and VR ~ pl.o7. These exponents of the static load (P) compare well with the theoretical exponents of 2 and 1.25, respectively derived and shown in equations (7) and (11). These results confirm the validity of the theoretical models for material removal. The material removal rates in rotary USM are observed to be of the order of 3-4 times greater when compared to conventional USM. The superior performance of rotary USM may be explained by the combined effects of the material removal due to the sliding type of indentations, scratching by the embedded grains and the effect of rolling contact of free abrasive grains on the workpiece. The effects resulting from the rotation of the workpiece leads to more material removal. The superiority of the sliding indentation over static indentation is demonstrated by nomoto [7]. It is also reported that the rolling contact of the abrasive grain on a brittle surface causes a tensile stress field in the workpiece surface at the trailing side of the grain leading to easier fracture of the workpiece into microchips. However, rotary USM can be used only for drilling axi-symmetric holes. In general, as the static load is increased, the MRR increases, reaches a maximum and then reduces. The reduction is due to the crushing of the abrasive grains and other effects. The results presented in Fig. 8 correspond to the static loads less than those of the optimum load. The optimum static load in the present investigations was 650 g beyond which the MRR was found to fall. The objectives set in the present range of

10 504 M, KOMARAIAH and P. N, RDD A - VC~< p1.63 VR = p 1.07 /~ v D / Rotary USM :> O P t- (D I USM O 100 i I i I i I I I II Log load (g) FIG. 8. ffect of static load on MRR. experiments were to verify the validity of the theoretical models involving the fracture toughness and hardness. All other process parameters, i.e. the diameter of the tool, the abrasive type, abrasive size and abrasive concentration of the slurry, the material, etc. were kept constant in all the experiments. Thus, the parameters Rmax and Ni in equations (7) and (11) are not changed and remain constant. 5. CONCLUSIONS 1. The fracture toughness and hardness of the work material play an important role with respect to MRR in ultrasonic machining. 2. As the fracture toughness and hardness increase, there is reduction in the MRR. 3. xperiments conducted confirm, to a reasonable extent, the validity of theoretical models developed. Hence, it is necessary that fracture toughness should be incorporated in the theoretical models of MRR. 4. Indentation tests can be used to evaluate the fracture toughness and hardness of the brittle materials. 5. The MRR in rotary USM are very much higher than in conventional USM. Acknowledgements--The authors wish to acknowledge with thanks the facilities provided by the authorities of the Department of Mechanical ngineering, Osmania University for conducting the experiments presented in this paper. RFRNCS [1] M. KOMARAIAH and P. N. RDDY, Rotary ultrasonic machining--a new cutting process and its performance, Int. J. Prod. Res. 29, (1991). [2] MCGOUGH, Advanced Methods of Machining, p Chapman and Hall Ltd., London, U.K. (1988). [3] M. C. SHAW, Ultrasonic grinding, Micro-Technique 10, 6 (1956). [4] G.. MILLR, Speed theory of ultrasonic machining, J. Appl.Phys. 28, (1957). [5] N. H. COOK, Manufacturing Analysis, pp Addison Wesley, New York (1966). [6] I. A. MARKOV, Machining of Intractable Materials with Ultrasonic and Sonic Vibrations. Illife Books (1966). [7] Y. NOMOTO, Sliding fracture of soda-lime glass in liquid cnvironmentais, J. Mater. Sci. 16, (1981). [8] A. G. VANS and S. WIt.SHAW, Quasi static particle damage in brittle solids, Acta Metall. 24, (1976). [9] J. GORG and G. PTR, Micro-indentation analysis of di-ammonium hydrogen citrate single crystals, ]. Mater. Sci. 20, (1985). [10] G. R. AN~SH, CHANTIKULP, B. R. LAWN and D. D. MARSHALL, A critical evaluation of indentation

11 Workpiece Properties in Ultrasonic Machining 505 technique for measuring fracture toughness--i. Direct crack measurements, J. Am. Ceramic Soc. 64, (1981). [11] A. G. vans and. A. CHARLS, Fracture toughness determination by indentation, J. Am. Ceram. Soc. Sg, (1976). [12] M. KOrO, lo, IAH and P. N. RrmY, Role of tool materials in USM, Proc. 14th AIMTDR Conf., I.I.T., Bombay, India (1990). APPNDIX A. 1. quation for MRR as proposed by Shaw [3] where: Kl r~ a d' K3 f d I" 4a d' ] 3/+ MRR = K1 " K 1/4 /..... ~112 [~(1 ;k, ij ' f" -- a constant; -- the fraction of work area covered by abrasive particles; -- amplitude of ultrasonic oscillations in microns; -- the diameter corresponding to actual particle curvature at the point of contact; -- mean surface stress of the workpiece material at rupture; -- Brinnel hardness ratio of workpieee and tool material; -- frequency of oscillation; and -- equivalent diameter of the abrasive particles. A.2. quation for MRR as proposed by Miller [4] MRR = C. ( P.D. ) ( TN) (WHR) (VC) (CR) K2 where: C PD TN WHR VC CR K2 -- a constant; -- plastic deformation undergone by the workpiece per blow of the tool; -- number of blows per second; -- work hardening energy per unit plastic deformation; -- volume of material removed per blow; -- rate of chipping blows; and -- fraction of tool area covered by abrasive particles. A.3. quation for penetration rate proposed by Cook [5] V = 5.9f" (tr/hw) (a) 1,2 (R) v2 where: f t/. a R -- frequency of oscillation; -- static stress applied in the cutting zone in Kgf mm-2; -- brittle fracture hardness of the workpiece material in Kgf ram-2; -- amplitude of vibration in ram; and -- mean radius of abrasive grain.

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