Merchant's circle

Merchant’s Circle
prepared by: Deepak Juneja, Geeta Engineering College, Panipat

Merchant’s Circle / Mechanics of
Orthogonal Metal Cutting
• Two thoughts of plastic deformation – Thin
Zone & Thick zone
• Thin zone is simple so good for analysis
purpose
• This model is applicable to general production
where high speed cutting is done
prepared by: Deepak Juneja, Geeta
Engineering College, Panipat

Assumptions
• Tool is perfectly sharp
• No contact between workpiece and tool flank
• Surface where shear is occurring is a plane
• Chip doesn’t move either side /sideways.
• Width of tool is greater than work
• Continuous chip is produced without BUE
• Work moves with uniform velocity
• Stress on shear plane is uniformly distributed

In figure shown above we will consider the chip as rigid body which is moving at a
constant velocity
Now if Chip is moving with constant velocity, then its acceleration is zero which stands
for that the sum of all forces working on chip shall be zero. Or if chip velocity is
constant and its acceleration is zero, then we may say that two equal and opposite
forces are working on it. These equal and opposite forces are R & R’ where R is force
exerted by Tool on the chip and R’ is the force exerted by tool on the chip

Tool is exerting a force R on chip which may be resolved in 2 components i.e N & F where N is
normal force perpendicular to rake face and F is frictional force along the rake face.
The same way R’ is also resolved in 2 components, Fs & Fn where Fs is working along the shear
plane whereas Fn is working normal to shear plane.
Tool is also facing a force which may be resolved in 2 components, one may be in direction of
Cutting Motion which is marked as Fc=Cutting Force (Horizontal) and other component us Ft=
Thrust Force (Vertical)

Merchant's circle

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Merchant's circle