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