Abstract
An analytical model is proposed to simulate and predict the surface roughness for different machining conditions in abrasive flow machining (AFM). The kinematic analysis is used to model the interaction between grain and workpiece. Fundamental AFM parameters, such as the grain size, grain concentration, active grain density, grain spacing, forces on the grain, initial topography, and initial surface finish (R a value) of the workpiece are used to describe the grain-workpiece interaction. The AFM process is studied under a systematic variation of grain size, grain concentration and extrusion pressure with initial surface finish of the workpiece. Simulation results show that the proposed model gives results that are consistent with experimental results.
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Abbreviations
- A :
-
Projected area of contact between the workpiece and abrasive grain, mm 2
- A 1 :
-
Area of the cylindrical workpiece in contact with the medium, mm 2
- A 2 :
-
Area of cuboidal element from any section of medium, mm 2
- A 3, A 4, A 5, A 6, A 7 :
-
Areas of peaks and valleys on an assumed surface, mm 2
- \(\overline{a} \) :
-
Effective grain spacing, mm
- b :
-
Diameter of projected area of a grain in contact with the workpiece, mm
- \(\overline{b} \) :
-
Mean diameter of projected area of grain (= mean width of cutting edge), mm
- C :
-
Percent abrasive concentration
- D :
-
Diameter of a cylindrical workpiece, mm
- d g :
-
Diameter of the abrasive grain, mm
- \(d^{\prime } \) :
-
Depth of indentation by a grain according to Hertz theory, mm
- \(d^{{\prime \prime }} \) :
-
Depth upto which material is displaced from a triangular peak after one pass, mm
- E m :
-
Modulus of elasticity of workpiece material, N/mm 2
- F ng :
-
Radial force on a single grain during AFM, N
- F am :
-
Measured axial force on the cylindrical workpiece during AFM, N
- G :
-
Volume ratio of the abrasive grain in medium
- G 1 :
-
Volume of groove produced by a single grain (Fig. 4), mm 3
- G 2 :
-
Volume of side flown material from the groove produced by a single grain (Fig. 4), mm 3
- h t :
-
Depth of indentation of a cutting tip inside the workpiece, mm
- h t 1, h t 2, h t 3, ...\(h_{{tn_{s} }} \) :
-
Depth of indentation of cutting tips inside the workpiece by grain 1, 2, 3, ....n s (Fig. 2).
- i :
-
Number of pass
- L :
-
Sampling length of an assumed surface, mm
- l :
-
Length of the cylindrical workpiece, mm
- l t :
-
Base length of the assumed equilateral triangular profile of the workpiece surface, mm
- \(l^{\prime } \) :
-
Assumed length on the medium surface, mm
- l m :
-
Length of the medium slug passed in one stroke through the workpiece, mm
- l s :
-
Length of stroke in medium cylinder, mm
- M e :
-
Grain mesh number
- m :
-
Total number of cutting edges on the \(l^{\prime } \) length of the strip on the medium surface
- N :
-
Total number of grains in cuboidal element from any section of the medium (Fig. 3)
- P e :
-
Applied extrusion pressure to medium, MPa
- n :
-
Number of grains per unit area
- n 1 :
-
Number of active grains per unit area on the medium
- n a :
-
Total number of active grains on the whole cylindrical workpiece surface area in contact with the medium
- n s :
-
Average number of grains in one line over the total length of the medium passed in one stroke (=l s )
- n mv :
-
Active grain density by multivariable model
- p i :
-
Indenting force acting on ith cutting grain (Fig. 2), N
- R :
-
Radius of grain, mm
- R t :
-
Tip radius of the grain (= radius of the grain), mm
- R a :
-
Center line average (CLA) value of surface roughness, μm
- R a(new) :
-
New CLA value of surface roughness after machining, μm
- r cy :
-
Radius of medium cylinder, mm
- r w :
-
Radius of cylindrical workpiece, mm
- V :
-
Volume of the cuboidal element, mm 3
- \(\overline{w} \) :
-
Mean spacing between the grains (or side of a square area assumed to have only one active grain), mm
- x, y :
-
Width of the sides of a cuboid (Fig. 3)
- σ :
-
Flow stress of workpiece material, N/mm 2
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Acknowledgement
Authors acknowledge the financial support provided by the Department of Science and Technology, Government of India, New Delhi for the project entitled “Abrasive flow machining process” (Project no. III/5(2) 96ET). Authors are thankful to Mr. Pulak Mohan Pandey, Mechanical Engineering Department, I.I.T. Delhi for his help and suggestions in this work.
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Gorana, V.K., Jain, V.K. & Lal, G.K. Prediction of surface roughness during abrasive flow machining. Int J Adv Manuf Technol 31, 258–267 (2006). https://doi.org/10.1007/s00170-005-0197-4
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DOI: https://doi.org/10.1007/s00170-005-0197-4