Known
as
Merchant’s
circle
diagram,
which
is
convenient
to
determine the relation between the
various forces and angles.
In the diagram two force triangles
have been combined and R and
R’
together have been replaced by R.
the force R can be resolved into two
components F
c
and F
t
.
Fc and Ft can be determined by
force dynamometers.
t
c
F
F
R
The rake angle
(α)
can be measured from the tool, and forces F and N can
then be determined. The shear angle (
) can be obtained from
it’s
relation
with chip reduction coefficient. Now Fs & Fn can also be determined.
Merchant’s Circle Diagram
∅
Work
Tool
Chip
Clearance Angle
F
t
F
c
F
N
F
n
F
s
α
α
β
(
β

α
)
R
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The procedure to construct a Merchant’s circle diagram
∅
Work
Tool
Chip
Clearance
Angle
F
t
F
c
F
N
F
n
F
s
α
α
β
(
β

α
)
R
Set up xy axis
labeled
with
forces, and the
origin
in
the
centre
of
the
page.
The
cutting
force
(Fc) is drawn
horizontally,
and
the
tangential
force
(Ft)
is
drawn
vertically.
(Draw
in
the
resultant
(R)
of Fc and Ft.