Question

Suppose in the previous example (from Machining 1 lecture) that cutting force and thrust force are measured during an orthogonal cutting operation: Fc = 1559 N and Ft = 1271 N. The width of the orthogonal cutting operation w = 3.0 mm. Based on these data, determine the shear strength of the work material.

Answer 1

Complete Question

Suppose in the previous example (from Machining 1 lecture) that cutting force and thrust force are measured during an orthogonal cutting operation: Fc = 1559 N and Ft = 1271 N. The chip thickness before the cut =0.5mm and the width of the orthogonal cutting operation is 3.0mm . Rake angle is equal to 10 and shear plane angle is 25.4. Based on these data, determine the shear strength of the work material.

Answer:

The shear strength of the work material is
`\sigma = 245.09 N/mm^2`

Step-by-step explanation:

From the question we are told that the

The the cutting force is
`F_c = 1559N`

The thrust force is
`F_t = 1271\ N`

The width of the octagonal cutting operation is
`w = 3.0\ mm`

The thickness is
`t = 0.5mm`

The shear plane angle is
`\theta = 25.4^o`

The shear strength of the work materiel is mathematically represented as

`\sigma = (F_s)/(A)`

Where
`F_s` is the shear force which is mathematically evaluated as

`F_s = F_c cos\ \theta -F_t sin\ \theta`

Substituting values we have

`F_s = 1559 cos (25.4) - 1271sin(25.4)`

`= 857.841N`

While A is the area which is mathematically evaluated as

`A = (t* w)/(sin \theta )`

Substituting values

`A = (0.5 *3)/(sin (25.4))`

`= 3.50`

Substituting this into the equation for shear strength

`\sigma = (857.8)/(3.5)`

`\sigma = 245.09 N/mm^2`