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# Grinding and economics of machining operation

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### Grinding and economics of machining operation

1. 1. Grinding
2. 2. Common Grinding Processes
3. 3. Details of Surface grinding
4. 4. Mechanics of GrindingUncut Chip thickness per grit f t1 = mm ZN Where Z = Number of active grains N = rpm of the wheel
5. 5. Z = π DCb Where D = Diameter of the wheel C = Surface density of active grains (mm-2) b’ = Average grain width of cut (mm) rg = b / t1 f t1 = π DNCrgPower AfU c W= Where A cross sectional area of the job 60 Uc = Specific energyForce per single grit 60, 000W 1000 fU c Fc= N= N π DACN π DCN
6. 6. Chip Formation during surface grinding Dl≈ β 2 D D 2dCos β = ( − d ) / = 1 − 2 2 D β2Cos β ≈ 1 − 2l ≈ Dd 1 (π NDBC ) × bmax t1max l = fdB 6
7. 7. 6f d t1max = π NDrg C D BfdU c W= W 60 60, 000W 1000 BfdU c Fc = = π ND π ND Components of Grinding ForceAverage force per grit 60, 000W F = c N π NDCB Dd 369U o f 0.8 d 0.4 rg0.2 N Fc = N 0.8 D1.2C 0.8
8. 8. Thermal aspectsEnergy spent per unit surface area ground Fcπ NDθ sα BfSince −0.4 1θ sα dU c and U c = U o (t1av ) and t1av = t1max 2 d 0.9 D 0.3C 0.2 N 0.2θ sα f 0.2 Grain chip interface temperature vt1max θ g = ΘU c k ρC
9. 9. Residual stress in workpiece after surface grinding
10. 10. Growth of power requirement of different wheel grades
11. 11. Grinding Wheel Specification
12. 12. Grinding Wheel Wear
13. 13. Types of grinding operations
14. 14. Honing Operation
15. 15. Lapping
16. 16. Abrasive Flow Machining (AFM)
17. 17. Magnetic Abrasive Finishing (MAF) Sintered ferromagnetic abrasive particle Ferromagnetic abrasive particle in actionMagnetic Abrasive Finishing
18. 18. MAFExternal Finishing by MAF Internal Finishing by MAF
19. 19. Ideal roughness in turningMaximum height of unevenness where f H max = ψ side cutting edge angle tanψ + cot γ γ end cutting edge angleMaximum height of unevenness, when nose radius (r) is used f2 H max = 8r
20. 20. Generation of Ideal roughness in slab milling
21. 21. Verification of surface roughness with cutting Speedduring turning mild steel bar
22. 22. Economics of Machining Operation
23. 23. Optimizing cutting parameters for Minimum costR = R1 + R2 + R3 + R4 + R5 R = Total Cost/ piece R1 = Material Cost/ piece R2 = Set up and idle time Cost/ piece R3 = Machining Cost/ piece R4 = Tool changing Cost/ piece R5 = Tool regrinding Cost/ pieceλ 1= Cost/ min of labour and overheadsλ 2= Cost of setting a tool for regrindingλ3 = Cost/mm of tool groundts = Set-up tme and idel time/ piece, min,tm = Machining time/piece, min,tct = Tool changing time, min
24. 24. Set- up and idle time cost R2 = λ1tsMachining cost π LD L = Length R3 = λ1t3 = λ1 D =Diameter 1000 fv f = feedTool Changing cost V = speed tm R4 = λ1 tct T k T = 1/ n 1/ m T = Tool life v f π LD R4 = λ1tct v1/ n −1 f 1/ m −1 1000 fv
25. 25. Tool regrinding cost δ = h f tan vs , hf = flank wear δ = Minimum length of tool to be reground λ2 + λ3 = λ2 + λ3h f tanν s tm R5 = (λ2 + λ3 h f tan vs ) T Vs = Clearance angle π LD = (λ2 + λ3 h f tan vs ) v1/ n −1 f 1/ m −1 1000k If tool cost of new tool is A and the total length that can be reground is B mm , then cost per mm of the tool A λ3 = ⎛ B ⎞ 1 + ⎜ h f ⎟ ⎝ ta n v s ⎠
26. 26. Total cost per piece π LD π LD π LD R = R1 + λ1ts + λ1 + λ1tct v1/ n −1 f 1/ m −1 + (λ2 + λ3 h f tan vs ) v1/ n −1 f 1/ m −1 1000 fv 1000 fv 1000 fvOptimum speed for a given feed∂R π LD −2 ⎛ 1 ⎞ π LD 1/ n − 2 1/ m −1 = −λ1 v + (λ1tct + λ2 + λ3h f tan vs ) × ⎜ − 1⎟ v f =0∂v vopt 1000 f ⎝ n ⎠ 1000k v = vopt or n ⎡ nk λ1 ⎤vopt =⎢ ⎥ ⎢ (1 − n) f (λ1tct + λ2 + λ3 h f tanν s ) ⎥ 1/ m ⎣ ⎦
27. 27. Optimum speed for minimum cost n ⎡ nk λ1 ⎤ vopt =⎢ ⎥ ⎣ (1 − n) f (λ1tct + λ4 ) ⎦ 1/ mOptimum feed for minimum cost m ⎡ mk λ1 ⎤ f opt =⎢ ⎥ ⎣ (1 − m)v (λ1tct + λ4 ) ⎦ 1/ n f max = 8rH max lim H maxlim= Limiting value of unevenness
28. 28. Machining force Fc = 1000U 0 wt10.6 Fc = k1 f 0.6 Power consumption Variation of machining cost with v and f W = k1vf 0.6Maximum available power in the machine then limiting cutting speed-feed Wlim vf 0.6 = k1 Selection of optimum feed
29. 29. Variation of various costs with cutting speed.
30. 30. Optimum cutting parameters for maximum production tm tt = ts + tm + tct min T π LD π LD = ts + + v1/ n −1 f 1/ m −1tct min 1000 fv 1000kFor optimum speed to minimize t1∂tt π LD −2⎛ 1 ⎞ π LD 1/ n − 2 1/ m −1 = v + ⎜ − 1⎟ v f tct =0∂v v = vopt 1000 f ⎝ n ⎠ 1000k v = vopt n ⎡ nk ⎤ vopt =⎢ ⎣ (1 − n) f 1/ mtct ⎥ ⎦
31. 31. Optimum cutting seed for maximum efficiency Profit rate S−R S = Amount received per piece pr = tt R and tt can be expressed in terms of v as before, then ∂pr =0 ∂v v = vopt