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Forces prediction during material deformation in abrasive flow machining
Wear 260 (2006) 128–139
Forces prediction during material deformation in abrasive flow machining V.K. Gorana 1 , V.K. Jain ∗ , G.K. Lal Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, Uttar Pradesh, India Received 1 December 2004; received in revised form 11 December 2004; accepted 20 December 2004 Available online 17 February 2005
Abstract To study the finishing mechanism of abrasive flow machining (AFM), theoretical model of forces acting on a single grain has been developed. An experimental research has been carried out by measuring the axial force, radial force and active grain density during the AFM process. Results obtained from theoretical model for grain–workpiece interaction during material deformation have been compared with the experimental data of force and active grains obtained during AFM. Scratching experiments have also been carried out to study the mechanism of material removal during the AFM process. The conclusions arrived by the analysis about the presence of rubbing and ploughing is in agreement with the experimental AFM and scratching results. © 2005 Elsevier B.V. All rights reserved. Keywords: Abrasive flow machining; Axial force; Radial force; Active grain density; Rubbing; Ploughing
1. Introduction Abrasive flow machining (AFM) was developed by the Extrude Hone Corporation, USA in 1960s as a method to deburr and polish difficult-to-reach surfaces and edges by flowing abrasive laden polymer with special rheological properties. AFM can be applied to an impressive range of finishing operations, providing uniform repeatable and predictable results. In AFM, workpiece is placed in between the two opposite piston cylinder arrangement (Fig. 1). The surfaces and edges of the workpiece are finished by the flowing medium (abrasive laden polymer) across the workpiece. Rhoades [1–3] studied the basic principle of AFM and reported that the depth of cut primarily depends upon abrasive grain size, relative hardness and sharpness and extrusion pressure. Przylenk [4] described that with small bore diameter of workpiece, more grains come in contact with the wall and material removal increases. Perry [5] reported that ∗
Corresponding author. Tel.: +91 512 2597916; fax: +91 512 2597408. E-mail address: [email protected] (V.K. Jain). 1 On leave from Department of Mechanical Engineering, Engineering College, Kota 324010, Rajasthan, India. 0043-1648/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2004.12.038
abrasion is high where the medium velocity is high. An increase in pressure and medium viscosity increases material removal rate while surface finish value decreases. The type of machining operation used to prepare the specimens prior to AFM is found to significantly affect the improvement in the surface finish [6]. Williams and Rajurkar [7] reported that metal removal and surface finish in AFM are significantly affected by the medium viscosity. Jain [8] evaluated the ‘active grain density’ by counting the number of distinct grains per unit area by viewing over number of randomly selected areas on medium and developed a force model based on abrasion theory. Williams [9] used the acoustic emission technique to analyze the AFM process. The acoustic emission signals were compared with those found in grinding to analyze the mechanism of surface generation involved in abrasive flow machining. Singh and Shan [10] developed a new method of finishing by applying the magnetic field around a component being processed by AFM and an enhanced rate of material removal has been achieved. They considered as the basic mechanism of solid particle erosion for material removal which is proposed by Finne [11] in AFM with some modifications. They concluded that the momentum acquired by the abrasive particles is responsible for microploughing
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Nomenclature A b C d dg ds d Em F Fng Fng Fap Frp Fr FR Frm Fam Hw Me P P r R
contact area (mm2 ) diameter of projected area of grain in contact with workpiece (mm) flow constraint factor undeformed chip thickness from L’vov [15] (mm) diameter of abrasive grain (mm) undeformed grain depth of cut from Brecker model [20] (mm) depth of indentation by Hertz theory (mm) modulus of elasticity of workpiece material (kg/mm2 ) axial force during AFM (kg) radial force during AFM (kg) total normal load on a single abrasive grain (kg) axial force exerted by putty only (kg) radial force exerted by putty only (kg) resultant force during AFM (kg) friction force during AFM (kg) measured radial force exerted by the medium when abrasives are mixed (kg) measured axial force exerted by the medium when abrasives are mixed (kg) surface hardness of workpiece material, (BHN = kg/mm2 ) grain mesh number resultant force from Brecker model [20] (kg) ploughing force during AFM (kg) edge radius of the tool at the onset of chip formation (mm) radius of abrasive grain (mm)
Greek letters θ neutral point angle (◦ ) θ conical indenter cone angle (◦ ) σ uniaxial flow stress of material (kg/mm2 ) σ¯ mean stress on the contact area (kg/mm2 ) γ half cone angle (◦ ) δ ␥−90◦ (◦ ) µ assumed coefficient of friction between abrasive grain and workpiece material during AFM
and microchipping of the workpiece surface. But this mechanism is proposed for the case when magnetic field has been applied to AFM. The application of magnetic field changes the distribution of abrasive particles across the cross section of slug. Secondly, they have not reported the viscosity of the medium used which plays an important role in fixing the mode of finishing (by chip formation, plastic deformation or rubbing as discussed later) during AFM.
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It seems from the literature survey that only a little information is available about the basic mechanics of material deformation involved in the abrasive flow machining process under widely varied machining conditions. This paper reports the understanding of mechanics involved in grain–workpiece interaction during AFM. In comparison to the conventional machining operations such as turning, milling, drilling, etc., the study of the basic mechanics of the material deformation process in abrasive flow machining is complicated due to random nature of distribution of abrasive grains into putty, very low depth of indentation of abrasive grains and metal deformation at micro scale. AFM and grinding have some similarities namely, in both the processes, abrasive grains are distributed randomly and depth of penetration by an abrasive is low. The medium gently and uniformly abrades the surfaces and/or edges in AFM. However, in case of grinding, abrasives are held rigidly by hard (solid) bond material whereas in AFM abrasives are mixed and held with semisolid bond (or medium). Therefore, in AFM, medium acts as a “selfdeformable stone”. The medium used for the present experimentation is silly putty which is generally used for moulding clay toys; the detailed information about the same is available on www.sillyputty.com. The viscosity of this medium is expected to be different as compared to medium used for the industrial purposes. Finished surface characteristics have been studied by Williams and Rajurkar [12]. Three modes of metal deformation so far have been identified in any abrasive machining process which are as follows [13]: 1. elastic deformation associated with rubbing; 2. plastic deformation or ploughing where majority of the material is displaced without being removed; 3. micro-cutting where removal of material takes in the form of miniature chips. The occurrence of any particular mode of deformation strongly depends on the magnitude of cutting forces acting on an individual grain, and the resulting depth of indentation in the workpiece. In AFM, the mode of metal deformation may change as the grain passes through the workpiece surface. This change in the mode of deformation may take place due to variation in the workpiece material properties, and mainly due to the flexibility of medium holding the grains which are not held so rigidly by the medium as in the case of a grinding wheel. The combined effect may result a change in the depth of indentation during the process which may lead to change in material deformation mode from one to another, say, from plastic deformation to elastic deformation.
2. Theoretical analysis Many researchers [14–19] proposed the mode of grain–workpiece interaction and developed various theories. As referred in reference [14], L’vov [15] proposed a model to estimate the undeformed chip thickness at the onset of
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Fig. 1. Schematic diagram of experimental set-up.
chip formation. Marochkin [17] proposed three different regimes of grain–workpiece interactions (i.e., chip regime, plastic regime, elastic regime). Brecker et al. [20] proposed a model for the minimum depth of indentation and minimum load on a grain required for chip formation. These theories can be applied to AFM process considering that in AFM grain–workpiece interaction is taking place in any one or combination of the possible modes (i.e., chipping, rubbing, and ploughing). These estimations are carried out, as given in the following section, to identify theoretically about the nature of grain–workpiece interaction.
ing to cutting by considering the theory of metal rolling. He suggested that in order to admit the metal through the rolls, the force of rolls on metal should (in a critical case) be perpendicular to the direction of rolling. Using this concept, the relationship between the undeformed chip thickness d and the edge radius r of the tool at the onset of chip formation is given [15] as
2.1. Grain–workpiece interaction
Here, θ signifies the critical depth of cut at which transition starts from ploughing to cutting. This concept can be applied to AFM considering spherical abrasive grain as a tool. Thus, the undeformed chip thickness at the onset of chip formation can be estimated.
2.1.1. Critical depth of cut by L’vov model As reported in reference [14], L’vov [15] proposed the critical depth of cut which shows the transition from plough-
d = r(1 − cos θ) = 0.293r; taking neutral point angle, θ =
π 4
(1)
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2.1.2. Condition for different modes of deformation during grain–workpiece interaction Marochkin [17] has presented an axisymmetric analysis for plastic behavior while scratching with a truncated cone. The tendency for the cone to penetrate a plane surface will depend upon the geometry of the system and relative hardness of the two surfaces. Using several simplifying assumptions, required to Marochkin [17] found the total normal load Fng cause the cone to penetrate the flat surface by integrating the normal contact stress over the contact area (Fig. 2). This gives, Fng = CAσ
where A (= πb4 ) is the contact area, b is the diameter of projected area of grain in contact with workpiece (Fig. 2), σ is the uniaxial flow stress of the workpiece material (stress to cause plastic flow) in a simple compression test and C is flow constraint factor (= mean contact stress/uniaxial flow stress of the material). It has been shown [17] that abrasive grains, to a good approximation, can be assumed to be spherical in shape. Earlier researchers have applied Hertz theory to grinding process [19] to estimate the depth of indentation when abrasive grain is pressed against the flat workpiece. In AFM, we can also estimate the depth of indentation by abrasive grain using Hertz theory [19] because two processes (grinding and AFM) are similar in many respects as stated elsewhere. According to Hertz theory, the mean stress on the contact ¯ for elastic contact between a sphere of radius (R) and area (σ) a flat surface (Fig. 2) can be evaluated from 2
σ¯ = 0.410
3
E2 Fng m
4R2
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Fig. 3. Depth of indentation due to radial force.
of indentation (d ) for elastic loading [19] is given by, 2 Fng 3 d = 1.550 2 2REm
The maximum value of σ¯ will be at the onset of plastic deformation and will be equal to Hw , the surface hardness of flat surface. Substituting this value for σ¯ and eliminating , Eqs. (2) and (3) give Fng d Hw 2 = 9.22 2R Em
is normal load on the grain and E is Young’s where Fng m modulus of elasticity of the flat workpiece surface. The depth
(4)
Let the grain be assumed as spherical (Fig. 3) having a single cutting tip and radius of curvature equal to the radius of grain. Then three possible regimes of grain–workpiece interaction can be identified [19] using Eqs. (5)–(7) as given below: 1. chip forming regime: d > 0.029 2R
(2)
(3)
(5)
2. plastic regime:
Hw 9.22 Em
2 <
d < 0.029 2R
(6)
3. elastic regime: d Hw 2 < 9.22 2R Em
Fig. 2. Truncated cone subjected to normal load.
(7)
Normally all the three regimes can occur as the load increases and hence d increases. Chip will not form until a grain penetrates the surface to a depth equal to approximately 6% of its radius (R). When the indentation depth is more than 6% of grain radius, the workpiece surface will be cut and chip will be generated. When the depth of indentation (d ) is less than 0.058R then the displaced material will form ridges by undergoing plastic deformation and hence no metal is removed. 2 w If the depth of indentation (d ) is less than 18.44 H Em R then the material will simply undergo elastic deformation and only rubbing will take place.
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2.1.3. Critical depth of indentation by Shaw’s model Brecker et al. [20] suggested that there is a limiting undeformed depth of cut (ds ) caused by a grain below which there will be no upward flow of material and hence no chip formation will take place. The grain was assumed to be spherical. They reported that when a conical indenter is pressed into a surface, there will be no upward flow if the half cone angle is 80◦ or greater. If the grain shape is approximated by a sphere (Fig. 4) then it seems that no upward flow should be expected if θ > 80◦ . From Fig. 4, sin θ =
dg 2
− ds dg 2
2.2. Prediction of forces in AFM
Literature has reported the chip formation [8] as well as ploughing [10] during AFM under different machining conditions, specifically different rheological properties of the medium. In the present case, micrographs of machined surface taken after AFM have revealed mainly the presence of rubbing, and to small extent ploughing. Hence, it is safe to assume the value of θ near to the transition from ploughing to rubbing. Hence, θ = 80◦ has been assumed for the present conditions. For θ = 80◦ , a minimum value of ds can be obtained from the above equation, as ds = 0.0076dg = 0.0152R
Using the above discussed three models (Eq. (1), Eqs. (3) and (8)) proposed by different researchers, the critical depths of indentation have been calculated to check whether the condition of chip formation exists for the present medium and machining conditions during AFM. Another way to check whether the chip is formed or not during abrasion is that if the load per grain is less than that obtained from Eq. (9), then chip will not be formed but the surface will be merely burnished. Before making any conclusion about the mechanics of material removal during AFM under the present machining conditions, all the four tests have been implemented and discussed later.
(8)
where, ds is depth of indentation and R is radius of grain. It should be noted that the minimum depth of indentation proposed by Eq. (8) comes out to be lower than that proposed in Eq. (5). Its value depends mainly on the assumed value of half cone angle θ . Thus, if the actual depth of indentation is lower as compared to the value obtained by Eq. (8), the chips will not be formed by a spherical grain. This critical load on a grain (P ) can be estimated [20] (Fig. 4) as follows: 2 π ds P = Hw A = Hw (9) 4 sin 90−θ 2 where, Hw is hardness of the workpiece material.
Fig. 4. Circular grain having a rake so low that a chip is not produced.
In abrasive flow machining, grain depth of indentation can be evaluated using Eq. (3) when the forces on a single grain are known. Bowden et al. [21] have proposed a simple analysis of axial force composed of shearing and ploughing forces. They also analysed radial force on the single abrasive grain and the real area of contact between abrasive grain, and workpiece surface for the case of metal to metal sliding. They discussed that when one metal slides on the surface of another metal, penetration and distortion of metal occurs to some depth beneath the surface. The axial force and the nature of sliding are influenced by the bulk properties of the metal and the friction cannot be regarded as a purely surface effect. It has been suggested [21] that the frictional resistance between unlubricated metals/surfaces is primarily due to the shearing of metallic junctions formed by welding of surface asperities and rubbing or ploughing of the surface irregularities. Physical behavior of the sliding processes is, however, very complex in nature. It is found from the experimental observations of the machined surfaces that under the present machining conditions, evidences mainly of rubbing and to small extent of ploughing, during AFM exist. The above approach can, therefore, be modified for the case of AFM process by considering workpiece surface (metal) and abrasive grain surface (non-metal) as two body sliding. During AFM, the axial force consists of two components, one is ploughing force and another frictional force. Then an approximate value of radial force and axial force between metal surface and abrasive grain in terms of the known physical properties of the sliding material can be evaluated. Following are the assumptions made to simplify the model: 1. Abrasive grains are approximated as spheres in shape, having equal diameter. Although, in reality, abrasive grains are not spherical in shape but to make the problem mathematically tractable, this assumption is being made. 2. The abrasive grain resting on the plane surface of workpiece will penetrate in it until the area of contact between the two surfaces is sufficient to support the applied load (Fng ). Further, it is assumed that for the applied load, no rotation of the abrasive grains takes place. However, as shown in ref. [25], rotation of a grain would take place
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when the resistance offered by the workpiece to form the chip is more than the axial force acting on the grain. 3. The interaction between abrasive grain and workpiece is assumed to be rubbing and/or ploughing which is evidenced by the scanning electron micrographs (photographs) of scratch tests and abrasive flow machiningtest.
P is given by,
When extrusion pressure is applied on the medium by the piston, two type of forces are generated, i.e., radial force and axial force. Radial (normal) force is responsible for the indentation of abrasive grain in the workpiece surface. Axial force acting on the grain will displace the workpiece material with side pile-up during ploughing. However, it will burnish the workpiece surface if only rubbing takes place. Theoretical values of axial and radial forces can be estimated after certain modifications in the theory proposed by Bowden et al. [21] as follows.
FR = Fng × µ
2.2.1. Radial force on a single grain When the radial force (Fng ) is applied during AFM on a grain, it will indent to a depth d into the workpiece (Fig. 5) with a side flow of the material. The radial force on a single grain can be estimated as, Fng
2 b =σ×A=σ×π× 2
(10)
where b is diameter of projected area (Fig. 5) and σ is flow stress of workpiece material. From the experimental observations [24], it is found that under certain combination of workpiece material properties and machining conditions, ploughing also takes place in AFM. Secondly, the chip size formed during AFM is in the range of micro- or sub micron. Hence, the standard theories validated for the traditional machining (turning, milling, etc.) processes may not work well. 2.2.2. Axial force on a single grain The axial force F (Fig. 5b) required to move the abrasive grain forward in a direction parallel to the surface consists of two components. The first is force P required to displace (plough) the metal from the front of the abrading grain and will be equal to the cross-sectional area of the grooved track multiplied by the yield stress of the workpiece material [21].
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1 b3 σ (11) 16 R The second one is friction force FR between the workpiece material and abrasive grains which are in contact during sliding. Thus, P =
(12)
where µ is friction coefficient between workpiece material and abrasive grain. Hence, F = P + FR
(13)
Substituting Eqs. (10)–(12) in Eq. (13), F can be approximated as, 2 1 b3 b F= σ+σ×π× ×µ (14) 16 R 2 The diameter of projected area (b) can be estimated geo√ metrically from Fig. 5 which is equal to b = 2 2Rd − d 2 . The average value of µ = 0.4, as reported by Lal et al. [23], has been used in the present case. They found that the sliding coefficient of friction (µ) does not vary to a large extent with the type of abrasive grain but changes with the sliding speed. The recommended [23] values of µ are 0.3 and 0.5 for higher and lower sliding speed, respectively. Hence, the average value of 0.4 has been taken in this case. By substituting the value of diameter of projected area (b) and coefficient of friction (µ) into Eq. (14), the axial force on a single grain in AFM can be evaluated by Eq. (15) as follows, 3/2 − d 2 ) (2Rd F = (15) + 1.2566(2Rd − d 2 ) × σ 2R By rearranging Eq. (15) and deleting square terms of d as d R, 1.414 × (R × d )1.5 (16) + 2.5132Rd × σ F= R The radial force from Eq. (10) and the axial force from Eq. (16) have been calculated for the present experimental conditions and the same have been compared with the experimentally obtained force data from the dynamometer as shown in Figs. 6 and 7.
Fig. 5. (a) Indentation of a grain into the workpiece with side pile-up and (b) hemisphere normal to the direction of motion.
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penetrate inside the workpiece and the workpiece will offer the resistance for its deformation. Hence, the forces will increase as compared to the earlier case. Let the measured axial force be Fam and the radial force be Frm when the abrasive particles are mixed in the medium. If the difference between these two forces is divided by the average number of active grains (Nag ), it will give the average force acting on individual grain (Fag and Frg ). This is an approximate method being followed because with the larger concentration of abrasive particles in the medium it is likely to change flow properties of the medium to some extent. The experimental values of forces on a single grain can be estimated as follows: Fag = Fig. 6. Variation of axial force on a single grain with extrusion pressure. Experimental conditions: 80-mesh grain size; 60% abrasive concentration.
3. Experimentation In abrasive flow machining, due to the lack of an experimental technique to measure the axial and radial force per grain, approximate values of these forces are obtained by measuring the average force exerted by medium (abrasive + silly putty), average force exerted by plain silly putty (without abrasive) and experimentally estimating the average active grain density. It is assumed that the losses in internal friction of the medium are negligible, and the force exerted on the silly putty remains the same in both the conditions (with abrasive and without abrasive). Using the dynamometer designed for the force measurement during AFM, the axial (Fap ) and radial (Frp ) forces acting on the fixture are measured when there are no abrasive particles in the medium. In this condition, in the absence of abrasives, there is no penetration of abrasive in the workpiece; hence, whatever forces are indicated by the dynamometer, they are the forces acting on the workpiece/fixture by the plane medium. When the abrasive particles are added in the medium, then the abrasives will
Fam − Fap Nag
(17)
where, Fag is average axial force on a single grain, Fam is average axial force on the medium, Fap is average axial force on the plain silly putty, and Nag is average number of active grains. Frg =
Frm − Frp Nag
(18)
where, Frg is average radial force on a single grain, Frm is average radial force on the medium, Frp is average radial force on the plain silly putty, and Nag is average number of active grains. Using above Eqs. (17) and (18), the experimental values of forces acting per grain are estimated and these are shown in Figs. 6 and 7. When the abrasive concentration in silly putty by volume is large then the substantial part of the workpiece, surface will be in contact with the abrasive grains rather than with the silly putty as assumed in Eqs. (17) and (18). To account its effect on Fag and Frg , following procedure is followed. To calculate the average and radial force acting on individual grain more accurately, let us assume that percent abrasive grain concentration by volume in the silly putty is C. Then Eqs. (17) and (18) are modified as follows: C Fam − Fap 1 − 100 Fag = (17’) Nag C Frm − Frp 1 − 100 Frg = (18’) Nag To evaluate the experimental values of average axial and radial forces and active grain density, following procedure is adopted. 3.1. Force measurement
Fig. 7. Variation of radial force on a single grain with extrusion pressure. Experimental conditions: 80-mesh grain size; 60% abrasive concentration.
The actual abrasive flow machining set-up used in the present work is shown in Fig. 1. A two-component dynamometer is designed and fabricated to measure both axial and radial forces [24].
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Fig. 8. Experimental set-up for scratch test.
3.2. Active grain density measurement The slug is taken out from the split workpiece by stopping the AFM operation instantaneously. Active grains are counted on the medium surface without disturbing the putty. The medium sample is placed under the stereomicroscope for topography examination. During examination, only those grains are counted which are visible and shining on the top surface of the medium. It is assumed that only these shining grains with metal deposit had been in contact with the workpiece and took part in the finishing process [24]. 3.3. Scratching experiments Scratching experiments are carried out to simulate and acquire the knowledge about the action of abrasive grains during the AFM process. For this a specific scratching apparatus is fabricated which is mounted on a conventional lathe machine whose details are given as follows. Such experiments have been carried out in the past [22] for the processes other than AFM. 3.3.1. Scratching apparatus and procedure The experiments are carried out on a lathe machine (Fig. 8). A piston cylinder arrangement is fabricated, with its one end having opening of 4 mm diameter covered with a teflon cap. The piston cylinder fitted on the steady rest of the
lathe machine is filled with medium. The teflon cap is kept in contact with the work piece. The sample is fixed on supporting clamp mounted on cross (or compound) slide as shown in Fig. 8. Pressure is applied to the piston through proven ring by tail stock of the lathe machine as shown in Fig. 8. Automatic feed is given to the cross slide of the lathe machine with a feed of 2.33 mm/s. After one pass, the machine is stopped and the workpiece is removed. The scratching marks are observed on the surface of the workpiece under the microscope. 3.3.2. Samples and test conditions Scratching experiments are carried out on samples of mild steel and aluminum work piece materials. The samples are prepared by subjecting them to the grinding and polishing operations. The samples are properly cleaned by acetone before placing it in the scratching apparatus. The test conditions and other details of the specimens are given in Table 1. 3.3.3. Scanning electron microscope examination The scratched specimens were examined under the scanning electron microscope as shown in Fig. 9a and b. These photographs can be compared with Fig. 10(a–d) which are taken after AFM. Comparison of the test conditions (Table 1) and SEM photographs (Fig. 9(a–b) and Fig. 10(a–d)) indicate that in both the processes, ploughing and rubbing are taking place. But it should be noted that this conclusion will hold true for the AFM conditions under
Table 1 Experimental condition for scratching and AFM experiments
Work piece material Abrasive concentration (wt%) Abrasive grain Abrasive grain mesh number Velocity of medium w.r.t. workpiece Pressure (kg/mm2 ) Average initial surface roughness value, Ra (m)
Scratching experiment (photograph (Fig. 9a,b))
Abrasive flow machining (photograph (Fig. 10a–d))
Mild steel and aluminum 60 Silicon carbide 80 Cross feed (workpiece) 2.33 mm/s 6.366 0.5–0.6
Mild steel 40, 55 and 60 Silicon carbide 80, 180 and 220 1.94, 0.790, 0.291 and 0.098 mm/s 0.4, 0.6, 0.7 and 0.8 0.7–0.9
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Fig. 9. Scanning electron microscope photograph of scratching experiment. Experimental conditions: 80-mesh grain size, 60% concentration, 6.366 kg/mm2 extrusion pressure: (a) on the aluminum workpiece and (b) on the mild steel workpiece.
which these experiments have been conducted. It is also to be noted that the medium used by Singh and Shan [10] was of very low viscosity. But on the other hand, the medium used by Jain and Jain [8] was of comparatively much higher viscosity compared to the silly putty; hence, they observed the presence of tiny chips in the used medium.
Table 2 Data for theoretical analysis
4. Results and discussion
diameter of the representative grain dg in mm in a given mesh size is estimated from the relation, dg = 28/Me1.1 , where Me is the mesh number [18]. Other data for theoretical analysis are listed in Table 2. The theoretical values of radial and axial forces acting on a single grain have been estimated from Eqs. (10) and (16), respectively. The curves have been plotted in
4.1. Force on a single grain The experimental values of axial and radial forces on a single grain are plotted in the form of points in Figs. 6 and 7. The
Workpiece material Flow pressure (yield stress) (kgf/mm2 ) Modulus of elasticity (kgf/mm2 ) Hardness (BHN) Assumed coefficient of friction
Mild steel 31 2.060 × 104 187 = 0.4 [23]
Fig. 10. Scanning electron microscope photograph of mild steel workpiece after abrasive flow machining. Experimental condition for figures: (a) 80-mesh grain size, 60% concentration, 0.7 kg/mm2 extrusion pressure; (b) 80-mesh grain size, 40% concentration, 0.4 kg/mm2 extrusion pressure; (c) 180-mesh grain size, 60% concentration, 0.8 kg/mm2 extrusion pressure; and (d) 220-mesh grain size, 55% concentration, 0.6 kg/mm2 extrusion pressure.
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Table 3 Undeformed chip thickness required at the onset of chip formation Extrusion pressure (bar)
Depth of indentation (d ) due to radial force (experimental) from Eq. (3) (mm)
Undeformed chip thickness (d) required at the onset of chip formation (theoretical) from Eq. (1) (mm)
Depth of indentation (ds ) (theoretical) from Eq. (8) (mm)
40 50 60 70 80
0.0000126 0.00000489 0.0000244 0.0000308 0.0000155
0.03307
0.001716
Experimental conditions: grain mesh number = 80; abrasive concentration = 60%.
Figs. 6 and 7. It can be seen that the theoretical values of forces are almost constant with variation in extrusion pressure. Further, there is discrepancy present in the trends of experimental and theoretical values of forces and it may be due to the following reasons. We have counted the active grains in an area of 4 mm2 which is very small as compared to the whole area of the cylindrical job (i.e., 4430 mm2 ). Therefore, there is a fair chance of some inaccuracy in the prediction of active grains in the whole area of cylindrical job, using the calculated active grain density. Theoretically, we have assumed that an abrasive grain is having only one single cutting tip while in real situation, an abrasive grain may have more than one cutting edge. In theoretical model of force, axial and radial forces are modeled in terms of physical properties of workpiece material but not as a function of extrusion pressure. Extrusion pressure affects the rheological behaviour (viscoelastic property) of the silly putty. This may be affecting the force on a single grain during experimentation. These may be the possible reasons for discrepancy between trends of experimental and theoretical values of forces. Further, use of Eqs. (17 ) and (18 ) in place of (17) and (18) would reduce the discrepancy exhibited in Figs. 6 and 7. 4.2. Minimum depth of indentation required for chip formation Based on Eq. (1), the minimum undeformed chip thickness d (i.e., depth of indentation) required for chip formation is estimated. This value is compared with the depth of indentation obtained by Hertz theory (Eq. (3)). The value of the radial force (Fng ) on a single grain is estimated by dividing the radial force (obtained from dynamometer)
by number of active grains. This comparison is given in Table 3. Here the value of diameter of grain has been calculated by using well known formula [18] for the known mesh number (Me ) as discussed earlier. It can be seen that the experimental value of depth of indentation (Table 3) is far lesser than the undeformed chip thickness obtained by L’vov [15] theory (Eq. (1)) in Table 3. Therefore, we can say that as per L’vov theory, no chip formation seems to occur in AFM under the present abrasive flow finishing conditions. Brecker et al. [20] (Eq. (8)) has proposed the condition for minimum depth of indentation for chip formation. To further confirm above conclusion, depth of indentation has been recalculated using Eq. (8) and it is compared in Table 3 with the experimental results. It reveals that the experimental results are again lower than the theoretical ones. It reaffirms that under the present finishing conditions, the probability of chip formation is very low. 4.3. Minimum resultant load required for chip formation Eq. (9) [20] shows the condition for minimum load required on a single grain for chip formation. To further confirm earlier conclusion (Section 4.2), load on a single grain has been calculated using Eq. (9). Experimental axial and radial forces on a single grain are calculated by using Eqs. (17) and (18), respectively. From these force values, resultant force has been calculated. Theoretical and experimental resultant loads have been compared in Table 4. It can be seen that the required theoretical load for chip formation on a single grain is much more than the experimental value of the load acting on a single grain. Therefore, it is concluded that no chip formation seems to occur.
Table 4 Load required for chip formation on a single grain Extrusion pressure (bar)
Axial force on a single grain (experimental) (kg)
Radial force on a single grain (experimental) (kg)
Resultant force on a single grain (experimental) (kg)
Load required (theoretical) from Eq. (9) (kg)
40 50 60 70 80
0.000864 0.000241 0.00234 0.000976 0.00117
0.000229 0.000055 0.000614 0.000870 0.000312
0.000893 0.000247 0.00241 0.001307 0.00121
0.0569
Experimental conditions: grain mesh number = 80; abrasive concentration = 60%.
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Table 5 Mechanism regime due to radial force on a single grain Extrusion pressure (bar)
Radial force on a single grain (kg) (experimental)
Possible mechanism for metal deformation (experimental)
Axial force on a single grain (theoretical) from Eq. (16) (kg)
Radial force on a single grain (theoretical) from Eq. (10) (kg)
Possible mechanism for metal deformation (theoretical)
40 50 60 70 80
0.000229 0.000055 0.000614 0.000870 0.000312
Elastic regime Elastic regime Elastic regime Elastic regime Elastic regime
0.0001664
0.000413
Elastic regime
Experimental conditions: grain mesh number = 80; abrasive concentration = 60%.
4.4. AFM and three different regimes Experimental values of radial force on a single grain are obtained by using Eq. (18). Eq. (3) is used to estimate the depth of indentation by a single grain. Using these values of depth of indentation the chip forming regime, plastic regime and elastic regime are estimated (Table 5) from Eqs. (5)–(7), respectively. Theoretical values of radial force on a single grain are calculated by using Eq. (10). These force values are used to find out the depth of indentation by a single grain using Eq. (3); then, theoretically chip forming regime, plastic regime and elastic regime are estimated (Table 5). It can be seen from Table 5 that AFM process under the present machining conditions satisfies the condition for elastic regime, i.e. rubbing only; however, from Fig. 10(a–d) some evidences of ploughing are also visible.
5. Conclusions The scratching experiment has provided a convenient means of studying the modes of material deformation under realistic conditions of grain–workpiece interaction. The AFM experimental results have shown that axial force, radial force, active grain density and grain depth of indentation, all have a significant influence on the scale of material deformation. Results suggest that considerable care should be exercised when evaluating and interpreting the force on a single grain followed by grain depth of indentation which is used in prediction of mode of material deformation. The two established grain–workpiece interaction parameters, viz., the minimum depth of indentation and minimum load required for chip formation, were found to correlate well with the mode of material deformation. The theoretical and experimental results shows that the rubbing mode of material deformation dominates in the present study; however, some evidences of ploughing during AFM are also present.
Acknowledgements Authors acknowledge the financial support provided by the Department of Science and Technology, Goverment of
India, New Delhi, for the project entitled “Abrasive flow machining process” (Project number III/5(2) 96ET). Authors are thankful to Mr. Joginder Singh of M/s Kalsi Micromeasurement, Kanpur, for his help in the fabrication of dynamometer.
References [1] L.J. Rhoades, Abrasive flow machining with not-so-silly putty, Met. Finish. (July, 1987) 27–29. [2] L.J. Rhoades, Abrasive flow machining, Manuf. Eng. (1988) 75–78. [3] L.J. Rhoades, Abrasive flow machining: a case study, J. Mater. Process. Technol. 28 (1991) 107–116. [4] K. Przylenk, AFM—A Process for Surface Finishing and Deburring of the Workpiece with a Complicated Shape by means of an Abrasive Laden Medium, ASME, New York, 1986, PED, Vol. 22, pp. 101–110. [5] W.B. Perry, Abrasive flow machining—principles and practices, in: Non-Traditional Conference Proceedings, 1989, pp. 121–127. [6] R.E. Wiiiams, K.P. Rajurkar, Metal removal and surface finish characteristics in abrasive flow machining, in: Mechanics of Deburring and Surface Finishing Process, ASME, New York, 1989, PED, Vol. 38, pp. 93–106. [7] R.E. Williams, K.P. Rajurkar, Stochastic modeling and analysis of abrasive flow machining, Trans. ASME, J. Eng. Ind. 114 (1992) 74–81. [8] R.K. Jain, Modeling and simulation of abrasive flow machining process, Ph.D. Thesis, I.I.T., Kanpur, India, 1999. [9] R.E. Williams, Acoustic emission characteristics of abrasive flow machining, Trans. ASME, J. Manuf. Sci. Eng. 120 (1998) 264–271. [10] S. Singh, H.S. Shan, Development of magneto abrasive flow machining process, Int. J. Mach. Tools Manuf. 42 (2002) 953– 959. [11] I. Finne, Some observations on the erosion of ductile metals, Wear 19 (1972) 81–90. [12] R.E. Williams, K.P. Rajurkar, Metal removal and surface finish characteristics in AFM, in: Mechanics of Deburring and Surface Finishing Process, ASME, New York, 1989, PED, Vol. 38, pp. 93– 106. [13] D. Graham, R.M. Baual, An investigation into the mode of metal removal in the grinding process, Wear 19 (1972) 301–314. [14] P.K. Basuray, B.K. Misra, G.K. Lal, Transition from ploughing to cutting during machining with blunt tools, Wear 43 (1977) 341–349. [15] N.P. L’vov, Determining the minimum possible chip thickness, Mach. Tool. (USSR) 40 (1969) 45. [16] M.M. Khruschov, M.A. Babichev, Investigation of the effect of abrasive hardness on wear of metals, Friction Wear Mach., 11, ASME, 1958. [17] V.N. Marochkin, The limiting plastic state in indenting and compressing a truncated cone, Friction Wear Mach., 13, ASME, 1959.
V.K. Gorana et al. / Wear 260 (2006) 128–139 [18] S. Malkin, Grinding Technology: Theory and Applications of Machining with Abrasives, John Wiley & Sons, 1989, pp. 20–21. [19] G.K. Lal, J.N. Brecker, W.J. Sauer, M.C. Shaw, Fifth Annual Report on Abrasive Grain Association Investigation of Abrasive Grain Characteristics, Carnegie Institute of Technology, 1970. [20] J.N. Brecker, R. Brown, T. Matsuo, K. Saito, J.A. Sweeney, J.B. Van Saun, M.C. Shaw, Fourth Annual Report on Abrasive Grain Association Investigation of Abrasive Grain Characteristics, Carnegie Institute of Technology, 1969. [21] F.P. Bowden, A.J.W. Moore, D. Tabor, Ploughing and adhesion of sliding of metals, J. Appl. Phys. 14 (1943) 80–91.
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[22] A. Groenou van Broese, N. Maan, J.D.B. Veldkamp, Scratching experiments on various ceramic materials, Phillips Res. Rep. 30 (1975) 320–359. [23] G.K. Lal, T. Matsuo, M.C. Shaw, An investigation of the wear of abrasive grains by rubbing on ferrous and non-ferrous surfaces, Wear 24 (1973) 279–293. [24] V.K. Gorana, V.K. Jain, G.K. Lal, On the effect of cutting forces and active grain density on surface roughness in abrasive flow machining, Int. J. Mach. Tool Manuf. 44 (2004) 201–211. [25] S.C. Jayswal, V.K. Jain, P.M. Dixit, Modeling and simulation of magnetic abrasive finishing process, Adv. Manuf. Technol., 2005.
Forces prediction during material deformation in abrasive flow machining V.K. Gorana 1 , V.K. Jain ∗ , G.K. Lal Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, Uttar Pradesh, India Received 1 December 2004; received in revised form 11 December 2004; accepted 20 December 2004 Available online 17 February 2005
Abstract To study the finishing mechanism of abrasive flow machining (AFM), theoretical model of forces acting on a single grain has been developed. An experimental research has been carried out by measuring the axial force, radial force and active grain density during the AFM process. Results obtained from theoretical model for grain–workpiece interaction during material deformation have been compared with the experimental data of force and active grains obtained during AFM. Scratching experiments have also been carried out to study the mechanism of material removal during the AFM process. The conclusions arrived by the analysis about the presence of rubbing and ploughing is in agreement with the experimental AFM and scratching results. © 2005 Elsevier B.V. All rights reserved. Keywords: Abrasive flow machining; Axial force; Radial force; Active grain density; Rubbing; Ploughing
1. Introduction Abrasive flow machining (AFM) was developed by the Extrude Hone Corporation, USA in 1960s as a method to deburr and polish difficult-to-reach surfaces and edges by flowing abrasive laden polymer with special rheological properties. AFM can be applied to an impressive range of finishing operations, providing uniform repeatable and predictable results. In AFM, workpiece is placed in between the two opposite piston cylinder arrangement (Fig. 1). The surfaces and edges of the workpiece are finished by the flowing medium (abrasive laden polymer) across the workpiece. Rhoades [1–3] studied the basic principle of AFM and reported that the depth of cut primarily depends upon abrasive grain size, relative hardness and sharpness and extrusion pressure. Przylenk [4] described that with small bore diameter of workpiece, more grains come in contact with the wall and material removal increases. Perry [5] reported that ∗
Corresponding author. Tel.: +91 512 2597916; fax: +91 512 2597408. E-mail address: [email protected] (V.K. Jain). 1 On leave from Department of Mechanical Engineering, Engineering College, Kota 324010, Rajasthan, India. 0043-1648/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2004.12.038
abrasion is high where the medium velocity is high. An increase in pressure and medium viscosity increases material removal rate while surface finish value decreases. The type of machining operation used to prepare the specimens prior to AFM is found to significantly affect the improvement in the surface finish [6]. Williams and Rajurkar [7] reported that metal removal and surface finish in AFM are significantly affected by the medium viscosity. Jain [8] evaluated the ‘active grain density’ by counting the number of distinct grains per unit area by viewing over number of randomly selected areas on medium and developed a force model based on abrasion theory. Williams [9] used the acoustic emission technique to analyze the AFM process. The acoustic emission signals were compared with those found in grinding to analyze the mechanism of surface generation involved in abrasive flow machining. Singh and Shan [10] developed a new method of finishing by applying the magnetic field around a component being processed by AFM and an enhanced rate of material removal has been achieved. They considered as the basic mechanism of solid particle erosion for material removal which is proposed by Finne [11] in AFM with some modifications. They concluded that the momentum acquired by the abrasive particles is responsible for microploughing
V.K. Gorana et al. / Wear 260 (2006) 128–139
Nomenclature A b C d dg ds d Em F Fng Fng Fap Frp Fr FR Frm Fam Hw Me P P r R
contact area (mm2 ) diameter of projected area of grain in contact with workpiece (mm) flow constraint factor undeformed chip thickness from L’vov [15] (mm) diameter of abrasive grain (mm) undeformed grain depth of cut from Brecker model [20] (mm) depth of indentation by Hertz theory (mm) modulus of elasticity of workpiece material (kg/mm2 ) axial force during AFM (kg) radial force during AFM (kg) total normal load on a single abrasive grain (kg) axial force exerted by putty only (kg) radial force exerted by putty only (kg) resultant force during AFM (kg) friction force during AFM (kg) measured radial force exerted by the medium when abrasives are mixed (kg) measured axial force exerted by the medium when abrasives are mixed (kg) surface hardness of workpiece material, (BHN = kg/mm2 ) grain mesh number resultant force from Brecker model [20] (kg) ploughing force during AFM (kg) edge radius of the tool at the onset of chip formation (mm) radius of abrasive grain (mm)
Greek letters θ neutral point angle (◦ ) θ conical indenter cone angle (◦ ) σ uniaxial flow stress of material (kg/mm2 ) σ¯ mean stress on the contact area (kg/mm2 ) γ half cone angle (◦ ) δ ␥−90◦ (◦ ) µ assumed coefficient of friction between abrasive grain and workpiece material during AFM
and microchipping of the workpiece surface. But this mechanism is proposed for the case when magnetic field has been applied to AFM. The application of magnetic field changes the distribution of abrasive particles across the cross section of slug. Secondly, they have not reported the viscosity of the medium used which plays an important role in fixing the mode of finishing (by chip formation, plastic deformation or rubbing as discussed later) during AFM.
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It seems from the literature survey that only a little information is available about the basic mechanics of material deformation involved in the abrasive flow machining process under widely varied machining conditions. This paper reports the understanding of mechanics involved in grain–workpiece interaction during AFM. In comparison to the conventional machining operations such as turning, milling, drilling, etc., the study of the basic mechanics of the material deformation process in abrasive flow machining is complicated due to random nature of distribution of abrasive grains into putty, very low depth of indentation of abrasive grains and metal deformation at micro scale. AFM and grinding have some similarities namely, in both the processes, abrasive grains are distributed randomly and depth of penetration by an abrasive is low. The medium gently and uniformly abrades the surfaces and/or edges in AFM. However, in case of grinding, abrasives are held rigidly by hard (solid) bond material whereas in AFM abrasives are mixed and held with semisolid bond (or medium). Therefore, in AFM, medium acts as a “selfdeformable stone”. The medium used for the present experimentation is silly putty which is generally used for moulding clay toys; the detailed information about the same is available on www.sillyputty.com. The viscosity of this medium is expected to be different as compared to medium used for the industrial purposes. Finished surface characteristics have been studied by Williams and Rajurkar [12]. Three modes of metal deformation so far have been identified in any abrasive machining process which are as follows [13]: 1. elastic deformation associated with rubbing; 2. plastic deformation or ploughing where majority of the material is displaced without being removed; 3. micro-cutting where removal of material takes in the form of miniature chips. The occurrence of any particular mode of deformation strongly depends on the magnitude of cutting forces acting on an individual grain, and the resulting depth of indentation in the workpiece. In AFM, the mode of metal deformation may change as the grain passes through the workpiece surface. This change in the mode of deformation may take place due to variation in the workpiece material properties, and mainly due to the flexibility of medium holding the grains which are not held so rigidly by the medium as in the case of a grinding wheel. The combined effect may result a change in the depth of indentation during the process which may lead to change in material deformation mode from one to another, say, from plastic deformation to elastic deformation.
2. Theoretical analysis Many researchers [14–19] proposed the mode of grain–workpiece interaction and developed various theories. As referred in reference [14], L’vov [15] proposed a model to estimate the undeformed chip thickness at the onset of
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Fig. 1. Schematic diagram of experimental set-up.
chip formation. Marochkin [17] proposed three different regimes of grain–workpiece interactions (i.e., chip regime, plastic regime, elastic regime). Brecker et al. [20] proposed a model for the minimum depth of indentation and minimum load on a grain required for chip formation. These theories can be applied to AFM process considering that in AFM grain–workpiece interaction is taking place in any one or combination of the possible modes (i.e., chipping, rubbing, and ploughing). These estimations are carried out, as given in the following section, to identify theoretically about the nature of grain–workpiece interaction.
ing to cutting by considering the theory of metal rolling. He suggested that in order to admit the metal through the rolls, the force of rolls on metal should (in a critical case) be perpendicular to the direction of rolling. Using this concept, the relationship between the undeformed chip thickness d and the edge radius r of the tool at the onset of chip formation is given [15] as
2.1. Grain–workpiece interaction
Here, θ signifies the critical depth of cut at which transition starts from ploughing to cutting. This concept can be applied to AFM considering spherical abrasive grain as a tool. Thus, the undeformed chip thickness at the onset of chip formation can be estimated.
2.1.1. Critical depth of cut by L’vov model As reported in reference [14], L’vov [15] proposed the critical depth of cut which shows the transition from plough-
d = r(1 − cos θ) = 0.293r; taking neutral point angle, θ =
π 4
(1)
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2.1.2. Condition for different modes of deformation during grain–workpiece interaction Marochkin [17] has presented an axisymmetric analysis for plastic behavior while scratching with a truncated cone. The tendency for the cone to penetrate a plane surface will depend upon the geometry of the system and relative hardness of the two surfaces. Using several simplifying assumptions, required to Marochkin [17] found the total normal load Fng cause the cone to penetrate the flat surface by integrating the normal contact stress over the contact area (Fig. 2). This gives, Fng = CAσ
where A (= πb4 ) is the contact area, b is the diameter of projected area of grain in contact with workpiece (Fig. 2), σ is the uniaxial flow stress of the workpiece material (stress to cause plastic flow) in a simple compression test and C is flow constraint factor (= mean contact stress/uniaxial flow stress of the material). It has been shown [17] that abrasive grains, to a good approximation, can be assumed to be spherical in shape. Earlier researchers have applied Hertz theory to grinding process [19] to estimate the depth of indentation when abrasive grain is pressed against the flat workpiece. In AFM, we can also estimate the depth of indentation by abrasive grain using Hertz theory [19] because two processes (grinding and AFM) are similar in many respects as stated elsewhere. According to Hertz theory, the mean stress on the contact ¯ for elastic contact between a sphere of radius (R) and area (σ) a flat surface (Fig. 2) can be evaluated from 2
σ¯ = 0.410
3
E2 Fng m
4R2
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Fig. 3. Depth of indentation due to radial force.
of indentation (d ) for elastic loading [19] is given by, 2 Fng 3 d = 1.550 2 2REm
The maximum value of σ¯ will be at the onset of plastic deformation and will be equal to Hw , the surface hardness of flat surface. Substituting this value for σ¯ and eliminating , Eqs. (2) and (3) give Fng d Hw 2 = 9.22 2R Em
is normal load on the grain and E is Young’s where Fng m modulus of elasticity of the flat workpiece surface. The depth
(4)
Let the grain be assumed as spherical (Fig. 3) having a single cutting tip and radius of curvature equal to the radius of grain. Then three possible regimes of grain–workpiece interaction can be identified [19] using Eqs. (5)–(7) as given below: 1. chip forming regime: d > 0.029 2R
(2)
(3)
(5)
2. plastic regime:
Hw 9.22 Em
2 <
d < 0.029 2R
(6)
3. elastic regime: d Hw 2 < 9.22 2R Em
Fig. 2. Truncated cone subjected to normal load.
(7)
Normally all the three regimes can occur as the load increases and hence d increases. Chip will not form until a grain penetrates the surface to a depth equal to approximately 6% of its radius (R). When the indentation depth is more than 6% of grain radius, the workpiece surface will be cut and chip will be generated. When the depth of indentation (d ) is less than 0.058R then the displaced material will form ridges by undergoing plastic deformation and hence no metal is removed. 2 w If the depth of indentation (d ) is less than 18.44 H Em R then the material will simply undergo elastic deformation and only rubbing will take place.
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2.1.3. Critical depth of indentation by Shaw’s model Brecker et al. [20] suggested that there is a limiting undeformed depth of cut (ds ) caused by a grain below which there will be no upward flow of material and hence no chip formation will take place. The grain was assumed to be spherical. They reported that when a conical indenter is pressed into a surface, there will be no upward flow if the half cone angle is 80◦ or greater. If the grain shape is approximated by a sphere (Fig. 4) then it seems that no upward flow should be expected if θ > 80◦ . From Fig. 4, sin θ =
dg 2
− ds dg 2
2.2. Prediction of forces in AFM
Literature has reported the chip formation [8] as well as ploughing [10] during AFM under different machining conditions, specifically different rheological properties of the medium. In the present case, micrographs of machined surface taken after AFM have revealed mainly the presence of rubbing, and to small extent ploughing. Hence, it is safe to assume the value of θ near to the transition from ploughing to rubbing. Hence, θ = 80◦ has been assumed for the present conditions. For θ = 80◦ , a minimum value of ds can be obtained from the above equation, as ds = 0.0076dg = 0.0152R
Using the above discussed three models (Eq. (1), Eqs. (3) and (8)) proposed by different researchers, the critical depths of indentation have been calculated to check whether the condition of chip formation exists for the present medium and machining conditions during AFM. Another way to check whether the chip is formed or not during abrasion is that if the load per grain is less than that obtained from Eq. (9), then chip will not be formed but the surface will be merely burnished. Before making any conclusion about the mechanics of material removal during AFM under the present machining conditions, all the four tests have been implemented and discussed later.
(8)
where, ds is depth of indentation and R is radius of grain. It should be noted that the minimum depth of indentation proposed by Eq. (8) comes out to be lower than that proposed in Eq. (5). Its value depends mainly on the assumed value of half cone angle θ . Thus, if the actual depth of indentation is lower as compared to the value obtained by Eq. (8), the chips will not be formed by a spherical grain. This critical load on a grain (P ) can be estimated [20] (Fig. 4) as follows: 2 π ds P = Hw A = Hw (9) 4 sin 90−θ 2 where, Hw is hardness of the workpiece material.
Fig. 4. Circular grain having a rake so low that a chip is not produced.
In abrasive flow machining, grain depth of indentation can be evaluated using Eq. (3) when the forces on a single grain are known. Bowden et al. [21] have proposed a simple analysis of axial force composed of shearing and ploughing forces. They also analysed radial force on the single abrasive grain and the real area of contact between abrasive grain, and workpiece surface for the case of metal to metal sliding. They discussed that when one metal slides on the surface of another metal, penetration and distortion of metal occurs to some depth beneath the surface. The axial force and the nature of sliding are influenced by the bulk properties of the metal and the friction cannot be regarded as a purely surface effect. It has been suggested [21] that the frictional resistance between unlubricated metals/surfaces is primarily due to the shearing of metallic junctions formed by welding of surface asperities and rubbing or ploughing of the surface irregularities. Physical behavior of the sliding processes is, however, very complex in nature. It is found from the experimental observations of the machined surfaces that under the present machining conditions, evidences mainly of rubbing and to small extent of ploughing, during AFM exist. The above approach can, therefore, be modified for the case of AFM process by considering workpiece surface (metal) and abrasive grain surface (non-metal) as two body sliding. During AFM, the axial force consists of two components, one is ploughing force and another frictional force. Then an approximate value of radial force and axial force between metal surface and abrasive grain in terms of the known physical properties of the sliding material can be evaluated. Following are the assumptions made to simplify the model: 1. Abrasive grains are approximated as spheres in shape, having equal diameter. Although, in reality, abrasive grains are not spherical in shape but to make the problem mathematically tractable, this assumption is being made. 2. The abrasive grain resting on the plane surface of workpiece will penetrate in it until the area of contact between the two surfaces is sufficient to support the applied load (Fng ). Further, it is assumed that for the applied load, no rotation of the abrasive grains takes place. However, as shown in ref. [25], rotation of a grain would take place
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when the resistance offered by the workpiece to form the chip is more than the axial force acting on the grain. 3. The interaction between abrasive grain and workpiece is assumed to be rubbing and/or ploughing which is evidenced by the scanning electron micrographs (photographs) of scratch tests and abrasive flow machiningtest.
P is given by,
When extrusion pressure is applied on the medium by the piston, two type of forces are generated, i.e., radial force and axial force. Radial (normal) force is responsible for the indentation of abrasive grain in the workpiece surface. Axial force acting on the grain will displace the workpiece material with side pile-up during ploughing. However, it will burnish the workpiece surface if only rubbing takes place. Theoretical values of axial and radial forces can be estimated after certain modifications in the theory proposed by Bowden et al. [21] as follows.
FR = Fng × µ
2.2.1. Radial force on a single grain When the radial force (Fng ) is applied during AFM on a grain, it will indent to a depth d into the workpiece (Fig. 5) with a side flow of the material. The radial force on a single grain can be estimated as, Fng
2 b =σ×A=σ×π× 2
(10)
where b is diameter of projected area (Fig. 5) and σ is flow stress of workpiece material. From the experimental observations [24], it is found that under certain combination of workpiece material properties and machining conditions, ploughing also takes place in AFM. Secondly, the chip size formed during AFM is in the range of micro- or sub micron. Hence, the standard theories validated for the traditional machining (turning, milling, etc.) processes may not work well. 2.2.2. Axial force on a single grain The axial force F (Fig. 5b) required to move the abrasive grain forward in a direction parallel to the surface consists of two components. The first is force P required to displace (plough) the metal from the front of the abrading grain and will be equal to the cross-sectional area of the grooved track multiplied by the yield stress of the workpiece material [21].
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1 b3 σ (11) 16 R The second one is friction force FR between the workpiece material and abrasive grains which are in contact during sliding. Thus, P =
(12)
where µ is friction coefficient between workpiece material and abrasive grain. Hence, F = P + FR
(13)
Substituting Eqs. (10)–(12) in Eq. (13), F can be approximated as, 2 1 b3 b F= σ+σ×π× ×µ (14) 16 R 2 The diameter of projected area (b) can be estimated geo√ metrically from Fig. 5 which is equal to b = 2 2Rd − d 2 . The average value of µ = 0.4, as reported by Lal et al. [23], has been used in the present case. They found that the sliding coefficient of friction (µ) does not vary to a large extent with the type of abrasive grain but changes with the sliding speed. The recommended [23] values of µ are 0.3 and 0.5 for higher and lower sliding speed, respectively. Hence, the average value of 0.4 has been taken in this case. By substituting the value of diameter of projected area (b) and coefficient of friction (µ) into Eq. (14), the axial force on a single grain in AFM can be evaluated by Eq. (15) as follows, 3/2 − d 2 ) (2Rd F = (15) + 1.2566(2Rd − d 2 ) × σ 2R By rearranging Eq. (15) and deleting square terms of d as d R, 1.414 × (R × d )1.5 (16) + 2.5132Rd × σ F= R The radial force from Eq. (10) and the axial force from Eq. (16) have been calculated for the present experimental conditions and the same have been compared with the experimentally obtained force data from the dynamometer as shown in Figs. 6 and 7.
Fig. 5. (a) Indentation of a grain into the workpiece with side pile-up and (b) hemisphere normal to the direction of motion.
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penetrate inside the workpiece and the workpiece will offer the resistance for its deformation. Hence, the forces will increase as compared to the earlier case. Let the measured axial force be Fam and the radial force be Frm when the abrasive particles are mixed in the medium. If the difference between these two forces is divided by the average number of active grains (Nag ), it will give the average force acting on individual grain (Fag and Frg ). This is an approximate method being followed because with the larger concentration of abrasive particles in the medium it is likely to change flow properties of the medium to some extent. The experimental values of forces on a single grain can be estimated as follows: Fag = Fig. 6. Variation of axial force on a single grain with extrusion pressure. Experimental conditions: 80-mesh grain size; 60% abrasive concentration.
3. Experimentation In abrasive flow machining, due to the lack of an experimental technique to measure the axial and radial force per grain, approximate values of these forces are obtained by measuring the average force exerted by medium (abrasive + silly putty), average force exerted by plain silly putty (without abrasive) and experimentally estimating the average active grain density. It is assumed that the losses in internal friction of the medium are negligible, and the force exerted on the silly putty remains the same in both the conditions (with abrasive and without abrasive). Using the dynamometer designed for the force measurement during AFM, the axial (Fap ) and radial (Frp ) forces acting on the fixture are measured when there are no abrasive particles in the medium. In this condition, in the absence of abrasives, there is no penetration of abrasive in the workpiece; hence, whatever forces are indicated by the dynamometer, they are the forces acting on the workpiece/fixture by the plane medium. When the abrasive particles are added in the medium, then the abrasives will
Fam − Fap Nag
(17)
where, Fag is average axial force on a single grain, Fam is average axial force on the medium, Fap is average axial force on the plain silly putty, and Nag is average number of active grains. Frg =
Frm − Frp Nag
(18)
where, Frg is average radial force on a single grain, Frm is average radial force on the medium, Frp is average radial force on the plain silly putty, and Nag is average number of active grains. Using above Eqs. (17) and (18), the experimental values of forces acting per grain are estimated and these are shown in Figs. 6 and 7. When the abrasive concentration in silly putty by volume is large then the substantial part of the workpiece, surface will be in contact with the abrasive grains rather than with the silly putty as assumed in Eqs. (17) and (18). To account its effect on Fag and Frg , following procedure is followed. To calculate the average and radial force acting on individual grain more accurately, let us assume that percent abrasive grain concentration by volume in the silly putty is C. Then Eqs. (17) and (18) are modified as follows: C Fam − Fap 1 − 100 Fag = (17’) Nag C Frm − Frp 1 − 100 Frg = (18’) Nag To evaluate the experimental values of average axial and radial forces and active grain density, following procedure is adopted. 3.1. Force measurement
Fig. 7. Variation of radial force on a single grain with extrusion pressure. Experimental conditions: 80-mesh grain size; 60% abrasive concentration.
The actual abrasive flow machining set-up used in the present work is shown in Fig. 1. A two-component dynamometer is designed and fabricated to measure both axial and radial forces [24].
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Fig. 8. Experimental set-up for scratch test.
3.2. Active grain density measurement The slug is taken out from the split workpiece by stopping the AFM operation instantaneously. Active grains are counted on the medium surface without disturbing the putty. The medium sample is placed under the stereomicroscope for topography examination. During examination, only those grains are counted which are visible and shining on the top surface of the medium. It is assumed that only these shining grains with metal deposit had been in contact with the workpiece and took part in the finishing process [24]. 3.3. Scratching experiments Scratching experiments are carried out to simulate and acquire the knowledge about the action of abrasive grains during the AFM process. For this a specific scratching apparatus is fabricated which is mounted on a conventional lathe machine whose details are given as follows. Such experiments have been carried out in the past [22] for the processes other than AFM. 3.3.1. Scratching apparatus and procedure The experiments are carried out on a lathe machine (Fig. 8). A piston cylinder arrangement is fabricated, with its one end having opening of 4 mm diameter covered with a teflon cap. The piston cylinder fitted on the steady rest of the
lathe machine is filled with medium. The teflon cap is kept in contact with the work piece. The sample is fixed on supporting clamp mounted on cross (or compound) slide as shown in Fig. 8. Pressure is applied to the piston through proven ring by tail stock of the lathe machine as shown in Fig. 8. Automatic feed is given to the cross slide of the lathe machine with a feed of 2.33 mm/s. After one pass, the machine is stopped and the workpiece is removed. The scratching marks are observed on the surface of the workpiece under the microscope. 3.3.2. Samples and test conditions Scratching experiments are carried out on samples of mild steel and aluminum work piece materials. The samples are prepared by subjecting them to the grinding and polishing operations. The samples are properly cleaned by acetone before placing it in the scratching apparatus. The test conditions and other details of the specimens are given in Table 1. 3.3.3. Scanning electron microscope examination The scratched specimens were examined under the scanning electron microscope as shown in Fig. 9a and b. These photographs can be compared with Fig. 10(a–d) which are taken after AFM. Comparison of the test conditions (Table 1) and SEM photographs (Fig. 9(a–b) and Fig. 10(a–d)) indicate that in both the processes, ploughing and rubbing are taking place. But it should be noted that this conclusion will hold true for the AFM conditions under
Table 1 Experimental condition for scratching and AFM experiments
Work piece material Abrasive concentration (wt%) Abrasive grain Abrasive grain mesh number Velocity of medium w.r.t. workpiece Pressure (kg/mm2 ) Average initial surface roughness value, Ra (m)
Scratching experiment (photograph (Fig. 9a,b))
Abrasive flow machining (photograph (Fig. 10a–d))
Mild steel and aluminum 60 Silicon carbide 80 Cross feed (workpiece) 2.33 mm/s 6.366 0.5–0.6
Mild steel 40, 55 and 60 Silicon carbide 80, 180 and 220 1.94, 0.790, 0.291 and 0.098 mm/s 0.4, 0.6, 0.7 and 0.8 0.7–0.9
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Fig. 9. Scanning electron microscope photograph of scratching experiment. Experimental conditions: 80-mesh grain size, 60% concentration, 6.366 kg/mm2 extrusion pressure: (a) on the aluminum workpiece and (b) on the mild steel workpiece.
which these experiments have been conducted. It is also to be noted that the medium used by Singh and Shan [10] was of very low viscosity. But on the other hand, the medium used by Jain and Jain [8] was of comparatively much higher viscosity compared to the silly putty; hence, they observed the presence of tiny chips in the used medium.
Table 2 Data for theoretical analysis
4. Results and discussion
diameter of the representative grain dg in mm in a given mesh size is estimated from the relation, dg = 28/Me1.1 , where Me is the mesh number [18]. Other data for theoretical analysis are listed in Table 2. The theoretical values of radial and axial forces acting on a single grain have been estimated from Eqs. (10) and (16), respectively. The curves have been plotted in
4.1. Force on a single grain The experimental values of axial and radial forces on a single grain are plotted in the form of points in Figs. 6 and 7. The
Workpiece material Flow pressure (yield stress) (kgf/mm2 ) Modulus of elasticity (kgf/mm2 ) Hardness (BHN) Assumed coefficient of friction
Mild steel 31 2.060 × 104 187 = 0.4 [23]
Fig. 10. Scanning electron microscope photograph of mild steel workpiece after abrasive flow machining. Experimental condition for figures: (a) 80-mesh grain size, 60% concentration, 0.7 kg/mm2 extrusion pressure; (b) 80-mesh grain size, 40% concentration, 0.4 kg/mm2 extrusion pressure; (c) 180-mesh grain size, 60% concentration, 0.8 kg/mm2 extrusion pressure; and (d) 220-mesh grain size, 55% concentration, 0.6 kg/mm2 extrusion pressure.
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Table 3 Undeformed chip thickness required at the onset of chip formation Extrusion pressure (bar)
Depth of indentation (d ) due to radial force (experimental) from Eq. (3) (mm)
Undeformed chip thickness (d) required at the onset of chip formation (theoretical) from Eq. (1) (mm)
Depth of indentation (ds ) (theoretical) from Eq. (8) (mm)
40 50 60 70 80
0.0000126 0.00000489 0.0000244 0.0000308 0.0000155
0.03307
0.001716
Experimental conditions: grain mesh number = 80; abrasive concentration = 60%.
Figs. 6 and 7. It can be seen that the theoretical values of forces are almost constant with variation in extrusion pressure. Further, there is discrepancy present in the trends of experimental and theoretical values of forces and it may be due to the following reasons. We have counted the active grains in an area of 4 mm2 which is very small as compared to the whole area of the cylindrical job (i.e., 4430 mm2 ). Therefore, there is a fair chance of some inaccuracy in the prediction of active grains in the whole area of cylindrical job, using the calculated active grain density. Theoretically, we have assumed that an abrasive grain is having only one single cutting tip while in real situation, an abrasive grain may have more than one cutting edge. In theoretical model of force, axial and radial forces are modeled in terms of physical properties of workpiece material but not as a function of extrusion pressure. Extrusion pressure affects the rheological behaviour (viscoelastic property) of the silly putty. This may be affecting the force on a single grain during experimentation. These may be the possible reasons for discrepancy between trends of experimental and theoretical values of forces. Further, use of Eqs. (17 ) and (18 ) in place of (17) and (18) would reduce the discrepancy exhibited in Figs. 6 and 7. 4.2. Minimum depth of indentation required for chip formation Based on Eq. (1), the minimum undeformed chip thickness d (i.e., depth of indentation) required for chip formation is estimated. This value is compared with the depth of indentation obtained by Hertz theory (Eq. (3)). The value of the radial force (Fng ) on a single grain is estimated by dividing the radial force (obtained from dynamometer)
by number of active grains. This comparison is given in Table 3. Here the value of diameter of grain has been calculated by using well known formula [18] for the known mesh number (Me ) as discussed earlier. It can be seen that the experimental value of depth of indentation (Table 3) is far lesser than the undeformed chip thickness obtained by L’vov [15] theory (Eq. (1)) in Table 3. Therefore, we can say that as per L’vov theory, no chip formation seems to occur in AFM under the present abrasive flow finishing conditions. Brecker et al. [20] (Eq. (8)) has proposed the condition for minimum depth of indentation for chip formation. To further confirm above conclusion, depth of indentation has been recalculated using Eq. (8) and it is compared in Table 3 with the experimental results. It reveals that the experimental results are again lower than the theoretical ones. It reaffirms that under the present finishing conditions, the probability of chip formation is very low. 4.3. Minimum resultant load required for chip formation Eq. (9) [20] shows the condition for minimum load required on a single grain for chip formation. To further confirm earlier conclusion (Section 4.2), load on a single grain has been calculated using Eq. (9). Experimental axial and radial forces on a single grain are calculated by using Eqs. (17) and (18), respectively. From these force values, resultant force has been calculated. Theoretical and experimental resultant loads have been compared in Table 4. It can be seen that the required theoretical load for chip formation on a single grain is much more than the experimental value of the load acting on a single grain. Therefore, it is concluded that no chip formation seems to occur.
Table 4 Load required for chip formation on a single grain Extrusion pressure (bar)
Axial force on a single grain (experimental) (kg)
Radial force on a single grain (experimental) (kg)
Resultant force on a single grain (experimental) (kg)
Load required (theoretical) from Eq. (9) (kg)
40 50 60 70 80
0.000864 0.000241 0.00234 0.000976 0.00117
0.000229 0.000055 0.000614 0.000870 0.000312
0.000893 0.000247 0.00241 0.001307 0.00121
0.0569
Experimental conditions: grain mesh number = 80; abrasive concentration = 60%.
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Table 5 Mechanism regime due to radial force on a single grain Extrusion pressure (bar)
Radial force on a single grain (kg) (experimental)
Possible mechanism for metal deformation (experimental)
Axial force on a single grain (theoretical) from Eq. (16) (kg)
Radial force on a single grain (theoretical) from Eq. (10) (kg)
Possible mechanism for metal deformation (theoretical)
40 50 60 70 80
0.000229 0.000055 0.000614 0.000870 0.000312
Elastic regime Elastic regime Elastic regime Elastic regime Elastic regime
0.0001664
0.000413
Elastic regime
Experimental conditions: grain mesh number = 80; abrasive concentration = 60%.
4.4. AFM and three different regimes Experimental values of radial force on a single grain are obtained by using Eq. (18). Eq. (3) is used to estimate the depth of indentation by a single grain. Using these values of depth of indentation the chip forming regime, plastic regime and elastic regime are estimated (Table 5) from Eqs. (5)–(7), respectively. Theoretical values of radial force on a single grain are calculated by using Eq. (10). These force values are used to find out the depth of indentation by a single grain using Eq. (3); then, theoretically chip forming regime, plastic regime and elastic regime are estimated (Table 5). It can be seen from Table 5 that AFM process under the present machining conditions satisfies the condition for elastic regime, i.e. rubbing only; however, from Fig. 10(a–d) some evidences of ploughing are also visible.
5. Conclusions The scratching experiment has provided a convenient means of studying the modes of material deformation under realistic conditions of grain–workpiece interaction. The AFM experimental results have shown that axial force, radial force, active grain density and grain depth of indentation, all have a significant influence on the scale of material deformation. Results suggest that considerable care should be exercised when evaluating and interpreting the force on a single grain followed by grain depth of indentation which is used in prediction of mode of material deformation. The two established grain–workpiece interaction parameters, viz., the minimum depth of indentation and minimum load required for chip formation, were found to correlate well with the mode of material deformation. The theoretical and experimental results shows that the rubbing mode of material deformation dominates in the present study; however, some evidences of ploughing during AFM are also present.
Acknowledgements Authors acknowledge the financial support provided by the Department of Science and Technology, Goverment of
India, New Delhi, for the project entitled “Abrasive flow machining process” (Project number III/5(2) 96ET). Authors are thankful to Mr. Joginder Singh of M/s Kalsi Micromeasurement, Kanpur, for his help in the fabrication of dynamometer.
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