Post on 14-Jun-2015
Grinding
Common Grinding Processes
Details of Surface grinding
Mechanics of Grinding
1ft mmZN
=
Where Z = Number of active grains
N = rpm of the wheel
Uncut Chip thickness per grit
'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
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 × =
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
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
Residual stress in workpiece after surface grinding
Growth of power requirement of different wheel grades
Grinding Wheel Specification
Grinding Wheel Wear
Types of grinding operations
Honing Operation
Lapping
Abrasive Flow Machining (AFM)
Magnetic Abrasive Finishing (MAF)
Sintered ferromagnetic abrasive particle
Magnetic Abrasive Finishing
Ferromagnetic abrasive particle in action
MAF
External Finishing by MAF Internal Finishing by MAF
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
Generation of Ideal roughness in slab milling
Verification of surface roughness with cutting Speed during turning mild steel bar
Economics of Machining Operation
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
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
=
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
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
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
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
Variation of various costs with cutting speed.
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
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