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Grinding
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Common Grinding Processes
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Details of Surface grinding
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Mechanics of Grinding
1ft mmZN
=
Where Z = Number of active grains
N = rpm of the wheel
Uncut Chip thickness per grit
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'Z DCbπ=
1g
ftDNCrπ
=
'1/gr b t=
Where
D = Diameter of the wheel
C = Surface density of active grains (mm-2)
b’ = Average grain width of cut (mm)
60cAfUW =
' 100060,000 cfUWF c N NDACN DCNπ π
= =
Where A cross sectional area of the job
Uc = Specific energy
Force per single grit
Power
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Chip Formation during surface grinding
2Dl β≈
2( ) / 12 2D D dCos d
Dβ = − = −
2
12
Cos ββ ≈ −
l Dd≈
'max 1max
1( )6
NDBC b t l fdBπ × =
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0.8 0.4 0.2'
0.8 1.2 0.8
369 o gc
U f d r NF
N D C=
' 60,000c
WF NNDCB Ddπ
=
100060,000 cc
BfdUWFND NDπ π
= =
1max6
g
f dtNDr C Dπ
=
60cBfdUW W=
Average force per grit
Components of Grinding Force
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1maxg c
vtUk C
θρ
= Θ
0.9 0.3 0.2 0.2
0.2sd D C N
fθ α
1 1max12avt t=0.4
1( )c o avU U t −=s cdUθ α
csF NDBfπθ α
Thermal aspects Energy spent per unit surface area ground
Grain chip interface temperature
Since
and and
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Residual stress in workpiece after surface grinding
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Growth of power requirement of different wheel grades
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Grinding Wheel Specification
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Grinding Wheel Wear
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Types of grinding operations
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Honing Operation
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Lapping
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Abrasive Flow Machining (AFM)
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Magnetic Abrasive Finishing (MAF)
Sintered ferromagnetic abrasive particle
Magnetic Abrasive Finishing
Ferromagnetic abrasive particle in action
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MAF
External Finishing by MAF Internal Finishing by MAF
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Ideal roughness in turning
2
max 8fHr
=
max 'tan cotfH
ψ γ=
+
Maximum height of unevenness
Maximum height of unevenness, when nose radius (r) is used
where
ψ side cutting edge angle
γ end cutting edge angle
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Generation of Ideal roughness in slab milling
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Verification of surface roughness with cutting Speed during turning mild steel bar
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Economics of Machining Operation
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Optimizing cutting parameters for Minimum cost
1 2 3 4 5R R R R R R= + + + +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/ piece
λ 1= Cost/ min of labour and overheads
λ 2= Cost of setting a tool for regrinding
λ3 = Cost/mm of tool ground
ts = Set-up tme and idel time/ piece, min,
tm = Machining time/piece, min,
tct = Tool changing time, min
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1/ 1 1/ 14 1 1000
n mLDR tct v ffv
πλ − −=
2 1 sR tλ=
3 1 3 1 1000LDR tfv
πλ λ= =
4 1mtR tctT
λ=
Set- up and idle time cost
Machining cost
Tool Changing cost
T = Tool life
L = Length
D =Diameter
f = feed
V = speed
1/ 1/n m
kTv f
=
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Tool regrinding cost
tan ,f sh vδ =
2 3 2 3 tanf shλ λ λ λ ν+ = +
5 2 3( tan ) mf s
tR h vT
λ λ= +
1/ 1 1/ 12 3( tan )
1000n m
f sLDh v v fk
πλ λ − −= +
hf = flank wear
δ = Minimum length of tool to be reground
Vs = Clearance angle
3
1t a nf
s
ABhv
λ =⎛ ⎞
+ ⎜ ⎟⎝ ⎠
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
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1/ 1 1/ 1 1/ 1 1/ 11 1 1 1 2 3( tan )
1000 1000 1000n m n m
s f sLD LD LDR R t tct v f h v v ffv fv fv
π π πλ λ λ λ λ− − − −= + + + + +
2 1/ 2 1/ 11 1 2 3
1( tan ) 1 01000 1000
opt opt
n mf s
v v v
R LD LDv tct h v v fv f n k
π πλ λ λ λ− − −
=
∂ ⎛ ⎞= − + + + × − =⎜ ⎟∂ ⎝ ⎠
11/
1 2 3(1 ) ( tan )
n
opt mf s
nkvn f tct h
λλ λ λ ν
⎡ ⎤= ⎢ ⎥
− + +⎢ ⎥⎣ ⎦
Total cost per piece
Optimum speed for a given feed
or
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11/
1 4(1 ) ( )
m
opt n
mkfm v tct
λλ λ
⎡ ⎤= ⎢ ⎥− +⎣ ⎦
11/
1 4(1 ) ( )
n
opt m
nkvn f tct
λλ λ
⎡ ⎤= ⎢ ⎥− +⎣ ⎦
Optimum speed for minimum cost
Optimum feed for minimum cost
limmax max8f rH=
limmaxH = Limiting value of unevenness
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Machining force
0.60 11000cF U wt=
0.61cF k f=
Power consumption
0.61W k vf=
0.6 lim
1
Wvfk
=
Maximum available power in the machine then limiting cutting speed-feed
Variation of machining cost with v and f
Selection of optimum feed
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Variation of various costs with cutting speed.
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Optimum cutting parameters for maximum production
minmt s m
tt t t tctT
= + +
1/ 1 1/ 1 min1000 1000
n ms
LD LDt v f tctfv k
π π − −= + +
2 1/ 2 1/ 11 1 01000 1000
opt opt
n mt
v v v v
t LD LDv v f tctv f n k
π π− − −
= =
∂ ⎛ ⎞= + − =⎜ ⎟∂ ⎝ ⎠
1/(1 )
n
opt m
nkvn f tct
⎡ ⎤= ⎢ ⎥−⎣ ⎦
For optimum speed to minimize t1
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rt
S Rpt−
=
0opt
r
v v
pv =
∂=
∂
Optimum cutting seed for maximum efficiency
Profit rate
S = Amount received per piece
R and tt can be expressed in terms of v as before, then