## What is Merchant circle theory?

2. Merchant’s Circle Diagram is constructed to ease the analysis of cutting forces acting during orthogonal (Two Dimensional) cutting of work piece.

**How do you draw a Merchant circle?**

How to draw Merchant’s circle diagram?

- Determine the value of thrust force .
- As the rake angle of the tool is known, draw the chip and tool in the orthogonal plane.
- Draw the force as a horizontal component and the other force as a vertical component.
- For the forces, and draw their resultant force .

### What is Ernst merchant theory?

Ernst and Merchant developed the first reasonable theory in metal cutting. This assumed that the shear angle would take up a value to make the work done in cutting a minimum. For given cutting conditions, The work done is proportional to Fc. An expression has been developed for Fc in terms of the shear angle.

**What is a cutting force?**

Cutting force is the resistance of the material against the intrusion of the cutting tool. The force directions and amplitudes differ in different cutting processes such as turning, milling, drilling, etc. performed in manufacturing machines –often CNC (See Fig. 1-3 below for an example on turning).

## What is Lee and Shaffer theory?

Lee and Shaffer’s relationship between and is derived on the assumption that: A. The material being cut behaves like an ideal plastic which does not strain harden. As the tip of the tool approaches the stress builds up till it reaches a value high energy to cause plastic deformation.

**What is Taylor’s tool life equation?**

5. With the slope, n and intercept, c, Taylor derived the simple equation as VTn = C where, n is called, Taylor’s tool life exponent. The values of both ‘n’ and ‘c’ depend mainly upon the tool-work materials and the cutting environment (cutting fluid application).

### What is meant by built up edge?

In single point cutting of metals, a built up edge (BUE) is an accumulation of material against the rake face, that seizes to the tool tip, separating it from the chip.

**How built up edge is formed?**

## How do you calculate cutting force?

cutting speed Tangential velocity on the surface of the tool or workpiece at the cutting interface. The formula for cutting speed (sfm) is tool diameter 5 0.26 5 spindle speed (rpm). The formula for feed per tooth (fpt) is table feed (ipm)/number of flutes/spindle speed (rpm).

**How do you calculate specific cutting force?**

If you want, you can make an experimental test to calculate the specific cutting force. The idea is to measure the force than results by machining the aluminum and the cutting speed. Then you divide the cutting force over the cutting area.

### What are the assumptions made in Lee and Shaffer’s theory?

In metal cutting, Lee and Shaffer’s theory is based on slip line field theory. It is based on the assumption that: The material being cut behaves like an ideal plastic with no strain hardening. The shear plane represents a direction of maximum shear stress.

**How do you find the value of F in Merchant circle diagram?**

By trignometric relations, the value of F s and F n is obtained from the merchant circle diagram. F s = F z c o s β − F x s i n β F n = F z sin A dynamometer is used directly to measure cutting force and its thrust force in this special case. How to draw Merchant’s circle diagram?

## How do you calculate merchant equation?

Take derivative of the shear stress with respect to the shear angle and setting the derivative to zero, then we get Merchant Equation: f = 45 + a /2 – b /2 � (10) Assumption: shear strength of material is a constant unaffected by strain rate, temperature, and other factors.

**What are the force components of Merchant circle diagram?**

From the above merchant circle diagram, the following force components are mentioned below. The diameter of the circle and the resultant force is denoted by F. The cutting force is denoted by F z. The thrust force is denoted by F x.

### What is meritmerchant circle diagram?

Merchant circle diagram is used to analyze the forces acting in metal cutting. The analysis of three forces system, which balance each other for cutting to occur. Each system is a triangle of forces. Shear surface is a plane extending upwards from the cutting edge.