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  $\sigma = 245.09 N/mm^2$

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

                       $\sigma = \frac{F_s}{A}$

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

                        $A = \frac{t* w}{sin \theta }$

Substituting values

                      $A = \frac{0.5 *3}{sin (25.4)}$

                         $= 3.50$

Substituting this into the equation for shear strength

               $\sigma = \frac{857.8}{3.5}$

                  $\sigma = 245.09 N/mm^2$