Mathematical Model for Abrasive Jet machining Ajm for Brittle Material

Group Members : Deepak : Y8185 Ramanand :Y84024/3/2012

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CONTENTS1. 2. 3. 4. 5. 6. 7. 8. 9.4/3/2012

Literature survey and references Introduction Discussion on model 1 Mechanism of material removal Mathematical model for AJM Experimental results Conclusion Discussion on model 2 (similar steps as model 1) Comparison between model 1 and model 22

Literature survey1. The mechanism of material removal in the erosive

2.

3.

4. 5. 6.

cutting of Brittle material by: G.L. Sheldon and I.FINNIE Journal of Engineering for industry 1966, (393-399) : Model-2 Erosion by a stream of solid particle by Neilson and Gilchrist Wear II(1968) 111-114 A Model for the wear of brittle solid under Fixed abrasive conditions by: B.R.LAWN , Wear ,33(1975) 369-372; -Model-1 Advanced Machining Process by : Dr. V.K.Jain http://en.wikipedia.org/wiki/Contact_mechanics http://www.springer.com/materials/mechanics/book/97 8-3-642-10802-03

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Introduction of AJMHISTORY:

High pressure water without abrasives began to be used as a cutting tool for soft materials in about 1970 o The increase in cutting power by the addition of abrasives came in about 1980 for Hard materialo

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Working Principle and Model Abrasive particles are made to impinge on the work

material at a high velocity The jet of abrasive particles is carried by carrier gas (air) The high velocity stream of abrasive is generated by converting the pressure energy of the carrier gas to its kinetic energy and hence high velocity jet The nozzle directs the abrasive jet in a controlled manner such that Nozzle Tip Distance(NTD)and the impingement angle can be set desirably The high velocity abrasive particles remove the material by erosion as well as brittle fracture of the work material4/3/2012 5

Two type of erosion mechanism : 1)Deformation wear

Contd

mechanism 2)Cutting wear mechanism For Brittle material Deformation wear mechanism is dominant Deformation Wear Mechanism : The perpendicular component of velocity is responsible Abrasive particle hit the work piece surface and gets cracked there and subsequent intersection of cracks take place and material is removed

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Working Principle and Model

Courtesy:AMP by Dr.V.K. Jain4/3/2012 7

APPLICATION Manufacture of electronic devices, deburring of

plastics Making of nylon and Teflon parts Marking on electronic products and permanent marking on rubber stencils Deflashing small castings, cutting titanium foils Drilling glass wafers Frosting glass surface Cutting thin-sectioned fragile component4/3/2012 8

Model 1: Wear of Brittle solids under fixed abrasive condition Two body process-grit particles are ideally sharp

Courtesy :Wear of brittle material by: LAWN4/3/2012 9

Assumption and mathematical modeling

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ContddVi /dt= (Vi/t)=Ai l/t =(0/H) Pi , Pi indenter load and 0- velocity Summation over all events gives macroscopic wear rate (3) Equation 3 can be rearranged :

.(4) By equation 4 we can see that abrasive wear rate of brittle

ceramics can easily be determined by standard hardness test procedure4/3/2012 11

Conclusion Wear rate is independent of contact area between tool

and work piece, number and size of indenting particle Wear rate under ideal chipping condition is determined by material hardness The intensity of residual stress field about the deformation tract is sufficiently high

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Model:2The Mechanism of Material Removal in Erosive Cutting of Brittle Material Assumptions: 1. Impact of solid particle is normal to the surface of work piece. 2. Only for brittle materials 3. Volume of material removal is predicted to be W=krf1(m)Uf2(m) where, k= quantity involving material constants r=average radius of impacting particles U= velocity of impacting particles f1(m),f2(m) are prescribed functions of m4/3/2012 13

Out line of the analysisEnergy method: material removal kinetic energy of impacting particles Drawback: crushing studies on brittle material have shown that such an approach is not likely to be fruitful because essential energy requirement to produce fresh surface is found to be small and unpredictable fraction of total energy expended. This model is useful only when : 1. Energy requirement is known 2. Fragment size and surface area can be predicted in advance 3. Only for normal impact4/3/2012 14

We are considering interaction of eroding particle and surface Out line of our analysis: 1. Estimation of depth of penetration of impacting particle on work piece 2. Estimation of fracture radius when brittle materials are indented 3. Above two will be combined with some assumptions to predict volume removal

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Schematic DiagramWhere x= penetration depth r= radius of impacting particle involved in causing initial fracture r= average radius of impacting particle a= fracture radius on work piece a*= effective fracture radius when particle comes to halt in workpiece ie. When x=xm4/3/2012 16

Calculation of Depth of Penetration1. Newtons 2nd law of motion P= -M -------------------------------------------(1) 2. Hertz equation (Contact between a sphere and an elastic halfspace) P= X(3/2) -3r1/2 ------------------------------------(2) where P= force applied by impacting particle x= depth of penetration = acceleration of impacting particle r= radius of impacting particle involved in fracture

E= modulus of elasticity = Poisson's ratio4/3/2012 17

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1/2(0-U2)= -(3r1/2 xm (5/2) )/(10 r3 a 3) xm=(5/3)2/5 (a 3)2/5(r6/r)1/5U4/5 xmis depth of penetration by single impacting particle.

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Calculation of radius of fractureWhen a spherical indenter is pressed against a plane elastic surface then maximum tensile stress a occurs at contact radius a in radial direction. a=(1-2)P/2a2 ------------------------------------(7) Region under the indenter is in compression and radial surface stress are tensile In this approach it is assumed that initial fracture occurs when maximum tensile stress reaches a equal to tensile strength of material.

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Hertzian stress is given by SH=k2(rx2)-1/m -----------------------------(8)where From (7) and (8) we get (1-2)P/2a2 =k2(rx2)-1/m and replacing P from above equation by Hertz equation we get r=(k3/3k2)2m/m-1xm+4/m-2 -----------------------(9) Where K3=(1-2)/4

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2=2rx a

(approximation)

From triangle ABC, we have AC2=AB2+BC2 r2=(r-x)2+a2 r2=r2+x2-2rx+a2 a2=2rx-x2 If x