Why Cutting Force Analysis is Important ?
Most of the time cutting force acting on a tool is measured
experimentally. But it is also important to predict quantity of cutting
force and how different cutting parameters are affecting cutting force
even before setting up the machining operation due to following reasons.
- In order to design of mechanical structure of cutting machine which will withstand cutting force and thrust force effectively.
- To determine power consumption during machining process. This will help in selecting suitable motor drive.
- To predict tool life.
- To increase productivity
Cutting Terminology
The following figure describes important terminologies used in cutting force analysis.
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Fig.1 A tool under orthogonal cutting operation |
The figure shows a case where tool velocity (V) and cutting edge are
perpendicular to each other,this is known as orthogonal cutting. Here we
are analyzing cutting force for an orthogonal cutting operation.
Cutting force (Fc) is the force parallel to cutting tool velocity. Rake
angle of cutting tool is represented by 'alpha'
Forces Acting on the chip
If you make a free body analysis of the chip, forces acting on the chip would be as follows.
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Fig.2 Forces acting on the chip on tool side and shear plane side |
At cutting tool side due to motion of chip against tool there will be a
frictional force and a normal force to support that. At material side
thickness of the metal increases while it flows from uncut to cut
portion. This thickness increase is due to inter planar slip between
different metal layers. There should be a shear force (Fs) to support
this phenomenon. According to
shear plane theory this metal layer
slip happens at single plane called shear plane. So shear force acts on
shear plane. Angle of shear plane can approximately determined using
shear plane theory analysis.It is as follows
Shear force on shear plane can be determined using shear strain rate and
properties of material. A normal force (Fn) is also present
perpendicular to shear plane. The resultant force (R) at cutting tool
side and metal side should balance each other in order to make the chip
in equilibrium. Direction of resultant force, R is determined as shown
in Figure 2.
Merchant's Circle Analysis
Steps involved in Merchant's circle analysis is as follows. Since we
know angle of resultant force at tool side, draw a line parallel to
this. On one end of this line draw shear force(Fs), magnitude and
direction of which is known. Now draw a line perpendicular to shear
force line, it will meet resultant force line at one point. You can draw
a circle assuming the intersected line as diameter of the circle, this
is known as Merchant's circle. It is shown in figure below.
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Fig.3 Construction of Merchant's circle |
In order to determine cutting force (Fc) one can draw a line parallel to
tool motion in Merchant's circle, starting from end of diameter. The
chord so obtained will give magnitude of cutting force. If you draw a
line perpendicular to Fc that will give thrust force acting on the tool
(Ft). So resultant force, R at tool side also can be considered as a
summation of cutting force and and thrust force. The diagram so obtained
is shown in following figure.
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Fig.4 Determination of cutting force and thrust force using Merchant's circle diagram |
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