Determination of Friction angle and Shear Stress in Machining Process

Determination of  Friction angle and Shear Stress  in Machining Process

In this blog, we are going to learn how to determine the shear stress or shear strength of the material and friction angle during the machining operation.


  • Material is homogeneous
  • The cutting operation is orthogonal
  • The cutting edge of the tool remains sharp and straight throughout the machining operation.
  • The shear zone presents in a very narrow zone and can be considered as a straight line.
  • There is no Ploughing Forces present during machining operation (Every material exhibits produce some ploughing force during operation but in this derivation, we assume its nill).

Let shear plane angle is denoted by `\phi `

Let Rake angle is denoted by  `\alpha `

Let thickness of chip before cutting is `t_{1} `

Let thickness of chip after cutting is `t_{2} `

Let chip thickness ratio (chip thickness before cutting /chip thickness after cutting) =`r_{c} `

Let width of the workpiece remove by tool during cutting operation is w.

Let Shear Force `F_{s} `

Let Thrust Force Ft

Friction Force is represented by FLet Cutting Force Fc

Normal Friction Force is represented by N

Area of shear plane  = `\frac{w  t_{1} }{sin \phi } `    ............(1)

`t_{2} ` is perpendicular to rake face and `t_{1} ` is perpendicular to cutting

We know that shear Stress is (Shear force/ Area) 

\tau = \frac{ F_{s} }{ \frac{w t_{1} }{sin \phi } }

From the diagram CG = CH + HG = CH + BE

CH = ` F_{t} cos \alpha `

BE = ` F_{c} sin\alpha `

`  F = F_{t} sin\alpha +F_{c} sin\alpha `

N  = CD = AG


AE = `F_{c} cos\alpha `

BH = `F_{t} cos\alpha`

N = `F_{c} cos\alpha - F_{t} sin\alpha`

`tan \beta  =  \frac{F}{N} = \mu `

` \frac{F_{t} sin\alpha +F_{c} sin\alpha}{F_{c} cos\alpha - F_{t} sin\alpha}  =  \mu  = tan \beta `

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