Merchant Circle Diagram (What is it? and How to Draw it?)

What is Merchant Force Circle Diagram?
Merchant Force circle is a method which is used for calculating the various forces involved in the cutting process.


Merchant’s circle diagram is a graphical representation of the forces acting on the workpiece during a metal cutting operation.

Now, let me give you a whole procedure for constructing a Merchant circle diagram, step-by-step.

How to draw Merchant Circle Diagram?

merchant circle diagram for cutting forces

Step 1: Draw the horizontal x-axis and vertical y-axis with the origin at the center of the paper. The scale should be enough that the measured force can fit on the page.

Draw the cutting force (Fc) in the horizontal direction and tangential force (Ft) in the vertical direction.

(The tool is exerting the force from the first quadrant, hence both the forces will be in the fourth quadrant.)

Step 2: Draw the resultant force of Fc and Fr. Denote that force as R.

Step 3: Find out the center point of R and draw the circle from that center which covers the entire vector R.

If you have done this correctly, then you can see that the heads and tails of the three vectors will lie on the circle.

Step 4: Draw the cutting tool in the first quadrant such that it makes the angle of α degrees with the vertical axis.

Step 5: Extend the line from the face of the tool and name that vector as F. (F is a friction vector).

Step 6: Now, a new vector can be drawn starting from the head of the friction vector (F) to the head of the resultant vector R.

This is a normal vector and name that vector as N.

The angle between R and F is known as a friction angle (τ).

Mathematically, R = Fc + Ft = F + N

Step 7: Now we use the chip thickness to determine the shear force acting on the tool. For this purpose, the chip is drawn as shown in the above diagram.

Before drawing the chip thickness, you should select some magnification factor (like 100 times) to multiply the values.

So now draw the feed thickness line (t1) which is parallel to the horizontal axis.

Also draw the chip thickness line parallel to the surface of the cutting tool.

Name this thickness as t2.

Step 8: Now, draw the vector from the origin point of the tool to the intersection point of both chip lines, stopping at the circle.

This vector is a shear force vector which is denoted as Fs.

Measure the shear force angle between Fs and Fc.

Step 9: Finally, draw the shear force normal (Fn) from the head of Fs to the head of R.

Step 10: Use the scale and protractor to measure all the forces (distances) and angles.

In this way, Merchant circle diagram for cutting forces is drawn.

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