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# Dynamics of ECM and tool profile correction

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Electrochemical Machining (ECM)- Dynamics- MRR- Steady state- Tool profile modification.

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### Dynamics of ECM and tool profile correction

1. 1. Presentation on Dynamics of Electrochemical Machining and Tool profile correction by: PRADEEP KUMAR. T. P II sem. M.Tech in ME SOE, CUSAT.
2. 2. • Electrochemical Machining (ECM) is a non- traditional machining (NTM) process belonging to Electrochemical category. • ECM is opposite of electrochemical or galvanic coating or deposition process. • Thus ECM can be thought of a controlled anodic dissolution at atomic level of the work piece that is electrically conductive by a shaped tool due to flow of high current at relatively low potential difference through an electrolyte which is quite often water based neutral salt solution.
3. 3. Material removal rate(MRR) • In ECM, material removal takes place due to atomic dissolution of work material. Electrochemical dissolution is governed by Faraday’s laws of electrolysis. • The first law states that the amount of electrochemical dissolution or deposition is proportional to amount of charge passed through the electrochemical cell.
4. 4. • The first law may be expressed as: • m Q,∝ where m = mass of material dissolved or deposited Q = amount of charge passed The second law states that the amount of material deposited or dissolved further depends on Electrochemical Equivalence (ECE) of the material that is again the ratio of atomic weigh and valency.
5. 5. v QA m v A ECEm ∝ ∝∝ where F = Faraday’s constant = 96500 coulombs I = current (Amp) ρ= density of the material (kg/m3) t=time(s) A=Atomic weight v=valency η ρ η ρ η . . .0 vF IA t m MRR Fv Ita m = = =
6. 6. • η is the current efficiency, that is, the efficiency of the current in removing metal from the workpiece. • It is nearly 100% when NaCl is used as the electrolyte but for nitrates and sulphates, somewhat lower. • Assuming 100% efficiency,the specific MRRis )./(. 3 sampm vF A MRRSp ρ =
7. 7. • The engineering materials are quite often alloys rather than element consisting of different elements in a given proportion. • Let us assume there are ‘n’ elements in an alloy. The atomic weights are given as A1 , A2 , ………….., An with valency during electrochemical dissolution as ν1 , ν2, …………, νn . The weight percentages of different elements are α1 , α2 , ………….., αn (in decimal fraction)
8. 8. • For passing a current of I for a time t, the mass of material dissolved for any element ‘i’ is given by where Γa is the total volume of alloy dissolved(m3 ). Each element present in the alloy takes a certain amount of charge to dissolve. iaim ραΓ= i ii i i ii i A vFm Q Fv AQ m =⇒ =
9. 9. i iia i A vF Q ραΓ =⇒ The total charge passed, ∑ ∑ ∑ = Γ = Γ= == i ii a i ii a iT A v I Ft MRR A v F QItQ αρ α ρ . 1 , and,
10. 10. • ECM can be undertaken without any feed to the tool or with a feed to the tool so that a steady machining gap is maintained. • Let us first analyse the dynamics with NO FEED to the tool. • Fig. in the next slide schematically shows the machining (ECM) with no feed to the tool and an instantaneous gap between the tool and work piece of ‘h’.
11. 11. dh h job tool electrolyte Schematic representation of the ECM process with no feed to the tool
12. 12. • Now over a small time period ‘dt’ a current of ‘I’ is passed through the electrolyte and that leads to a electrochemical dissolution of the material of amount ‘dh’ over an area of ‘S’ rh Vs srh V R V I === )/(
13. 13. • Then, rh V v A F srh Vs v A Fdt dh x x x x .. 1 1 .. 1 ρ ρ =     =
14. 14. h c hrvF VA dt dh x x == 1 . ρ For a given potential difference and alloy, Where c is a constant.
15. 15. cdthdh h c dt dh A v rF V c rvF VA c i ii x x = =     = = ∑αρ ρ
16. 16. At t = 0, h= h0 and at t = t1, h = h1. cthh dtchdh h h t 2 2 01 0 2 1 0 =− =∫ ∫ That is, the tool – work piece gap under zero feed condition grows gradually following a parabolic curve as shown in the fig in the next slide.
17. 17. Variation of tool-work piece gap under zero feed condition h0 h t
18. 18. • As • Thus dissolution would gradually decrease with increase in gap as the potential drop across the electrolyte would increase • Now generally in ECM a feed (f) is given to the tool h c dt dh = f h c dt dh −=
19. 19. • If the feed rate is high as compared to rate of dissolution, then after some time the gap would diminish and may even lead to short circuiting. • Under steady state condition, the gap is uniform i.e. the approach of the tool is compensated by dissolution of the work material. • Thus, with respect to the tool, the work piece is not moving .
20. 20. • Thus , • Or, h* = steady state gap = c/f • Under practical ECM condition s, it is not possible to set exactly the value of h* as the initial gap. • So, it is required to be analyse whether the initial gap value has any effect on progress of the process. f h c dt dh == ;0
21. 21. f h c dt dh Thus dt dh fdt dh c f c f dt dh c tf h ft t c hf h h h −= == == == , . 1 . ' ' 2 2 * ' * '
22. 22. ' ' ' ' ' ' ' ' ' ' ' ' '*'' ' 1 1 1 . . dh h h dt h h dt dh h h f dt dh f f ch cf f hh c dt dh f − =       − =⇒       − =⇒ −=−=
23. 23. • Integrating between t’ = 0 to t’ = t’ when h’ changes from ho ’ to h1 ’       − − +−= −+ − −− = − = ∫∫ ∫∫ 1 1 log )1( 1 )1( 1 ' 1 ' 0' 1 ' 0 ' ' ' ' ' ' ' '' 0 ' ' 1 ' 0 ' 1 ' 0 ' 1 ' 0 h h hht hd h hd t dh h h dt e h h h h h h t
24. 24. Variation in steady state gap with time for different initial gap h1’ t1’ h0= 0.5 h0= 0 Simulation for ho'= 0, 0.5, 1, 2, 3, 4, 5 1
25. 25. s I vF A fie rh V vF A f hrvF VA h c f c fh h h h x x x x x x .; . 1 . 11 * ' ρ ρ ρ = = == =⇒== = MRR in m/sec. Thus, irrespective of the initial gap,
26. 26. From the above equation, it is seen that ECM is self regulating as MRR is equal to feed rate. If the feed rate, voltage and resistivity of the electrolyte are kept constant, a uniform gap will exist and absolute conformity to the tool shape will be obtained.
27. 27. • In actual practice, it is not possible to maintain constant resistivity of the electrolyte. • Temperature due to heat generated during chemical reaction tends to reduce resistivity. • The evolution of gas and any flow disturbances also affect resistivity. 2H
28. 28. • The process is further complicated by the presence of a polarized layer of ions at either or both of the electrodes. • Current density and field strength tend to be higher at sharp edges and corners. This results in non-uniform gaps because of higher MRR. • Therefore, it is difficult to machine sharp corners by this process.
29. 29. TOOL PROFILE CORRECTION • The shape of the ECM tool is not just the inverse or simple envelope of the shape to be machined. • The component shape finally obtained depends on: o Tool geometry o Tool feed direction o Flow path length o And other process parameters.
30. 30. • Involvement of several factors make the problem more complex. • Therefore empirical relations have been formulated for the tool shape correction. • Proper selection of working parameters can reduce the effects of process phenomena such as hydrogen formation. • That simplifies the problem of tool profile correction and analytical methods can be used to derive formulae for predicting it.
31. 31. Example of die sinking ECM tool Dark lines show the work profile and corrected tool profile. Dotted line shows uncorrected tool shape.
32. 32. • Tool correction, x = y-z • From triangles ABD and BCD, • Or, z = h sin α cosec γ • Taking the MRR as being inversely proportional to gap size, the incremental MRR at P qnd Q are related as αγ sinsin zh = h y z h = δ δ
33. 33. • The machining rate in the direction of tool feed at any point on the work surface would be the same under equilibrium machining conditions, and thus PS = QR, and • or, α δ γ δ sinsin zh = α γ δ δ sin sin = z h
34. 34. y =h sin γ cosec α The tool correction , x = h(sin γ cosec α –sin α cosec γ) In most die sinking operations, γ = 90 as the tool is fed orthogonally to some area of the work surface, therefore, x = h(cosec α - sin α α γ sin sin = h y
35. 35. CONCLUSION. • Though ECM is self regulating as MRR is equal to feed rate, variation in process parameters results in non-uniform gaps because of higher MRR. • Therefore, it is difficult to machine sharp corners by this process. • The shape of the ECM tool is not just the inverse or simple envelope of the shape to be machined, instead, correction in tool profile is required.