This article is about the merchant circle equation along with its diagram, assumptions, derivation, applications, advantages, limitations, and procedures on how to draw a merchant’s circle diagram.

Implication of Merchant’s Eq. An increase in rake angle causes the shear plane angle to increase. A decrease in friction angle cause the shear plane angle to increase. The analysis from orthogonal cutting can be used in a typical turning if the feed is small relative to depth of cut. Effect of shear plane angle φ :

Feb 1, 2008 · The Merchant's shear angle is obtained by minimization of the cutting energy: φ M = π 4 + α-λ 2, where α is the rake angle and λ is the friction angle defined by μ=tg(λ).

What does the Merchant relation indicate? If we increase the shear angle, we decrease the tool force and power requirements! Effect of shear plane angleφ : (a) higher φ with a resulting lower shear plane area; (b) smaller φ with a corresponding larger shear plane area.

The circle(s) drawn taking R or R1 as diameter is called Merchant’s circle which contains all the force components concerned as intercepts. The two circles with their forces are combined into one circle having all the forces contained in that as shown by the diagram called

Sep 19, 2016 · Merchant’s Theory can be represented by Equation 1, and it sp ecifies the relationship between the shear, rake and friction angles. These angles can be used further to determine the forces ...

Merchant's Force Circle is a method for calculating the various forces involved in the cutting process. This will first be explained with vector diagrams, these in turn will be followed by a few formulas.

There are two ways to derive Merchant ́s Relationship: find the minimum of the cutting force or the maximum of the shear stress. We will have a look at both. With σs as the shear stress and As the shear area; t0 is the thickness of the uncut chip, called the depth of cut, w is the width of the work.

Eugene Merchant’s model for orthogonal cutting Video on plastic deformation in machining 10. Basic Machining Mechanism Shear takes place in ... The Merchant Equation 17. Ref. Groover The Merchant Equation 18. Ref. Kalpakjian & Schmid The Thrust Force 19. Specific energy, u S For comparison see Table 26.2 for grinding 20.

This document provides the solution to a homework problem on metal cutting and injection molding. For the metal cutting problem, it derives the Merchant relationship between shear angle, rake angle, and friction angle.