University of Nevada Las Vegas

MEG426/626 Manufacturing Processes

Department of Mechanical Engineering

Fall Semester 2000


Cutting Mechanics (I)



Orthogonal Cutting Model:

Orthogonal cutting uses a wedge-shaped tool in which the cutting edge is perpendicular to the direction of cutting speed.


Shear plane:

As the tool is forced into the material, the chip is formed by shear deformation along a plane called the shear plane, which is oriented at an angle f with the surface of the work.


Chip thickness ratio (or chip ratio):

r = t0/tc (1)

r = ls sin f /ls cos (f - a )

tan f = r cos a /[1 - r sin a ] (2)



Primary deformation zone shear in the work material

Secondary deformation zone friction between chip and rake face

Tertiary deformation zone friction between machined surface and flank face

Discontinuous chip: when machining relatively brittle materials at low cutting speeds, the chips often form into separated segments.

Disadvantage: vibration, surface roughness, irregular surface texture, tool life.

Trend: large feed, large depth of cut, and high tool-chip friction promote the formation of this chip type.

Segmented chip:

Powdered chip:

Continuous chip: when machining ductile materials at high speeds and relatively small feeds and depths, long continuous chips are formed.

Disadvantage: damage machined surface.

Trend: high speeds and relatively small feeds and depths, and low tool-chip friction.

Build-up edge: when machining ductile materials at low to medium cutting speeds, friction between tool and chip tends to cause portions of the work material to adhere to the rake face of the tool near the cutting edge. This formation is called a build-up edge (BUE).

Characteristic: cyclical in nature, it forms, grows, and breaks off. Unstable.

Disadvantage: change tool geometry, cutting forces, cutting temperature and machined surface quality.


Forces in metal cutting

Forces in the secondary deformation zone:

  1. Friction force F:

The force between the tool and chip, which resisting the flow of the chip along the rake face of the tool.

  1. Normal force to friction N:

The force which is normal to the friction force.

Friction coefficient: m = F/N

Friction angle: b

Resultant force: R


Forces in the first deformation zone:

  1. Shear force Fs:

The force which causes shear deformation to occur in the shear plane.

  1. Normal force to shear Fn:

The force which is normal to the shear force.


Forces on the cutting tool:

  1. Cutting force Fc:

The force in the direction of cutting, the same direction as the cutting speed v.

  1. Thrust force Ft:

The force which is perpendicular to the cutting force.


Trigonometric relationships:

F = Fc sin a + Ft cos a (3)

N = Fc cos a - Ft sin a (4)

Fs = Fc cos f - Ft sin f (5)

Fn = Fc sin f + Ft cos f (6)


Shear stress:

t = Fs/ As (7)

where: As = t0 w/ sin f (8)


The Merchant Equation

t = Fs/ As (7)

As = t0 w/ sin f (8)

Fs = Fc cos f - Ft sin f (5)


Combine Eqs. (7), (8), and (5):


t = ( Fc cos f - Ft sin f ) / (t0 w/ sin f ) (9)

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.


Value: The Merchant equation defines the general relationship between rake angle, tool-chip friction, and shear plane angle.


Conclusions: (1) rake angle increases, shear angle increases;

        1. friction decreases, shear angle increases.


Importance of increasing shear angle:

If all other factors remain the same, a higher shear angle results in a smaller shear plane area. Since the shear strength is applied across this area, the shear force required to form the chip will decrease when the shear plane area is decreased. This tends to make machining easier to perform, and also lower cutting energy and cutting temperature.

Created by Dr. Wang