Question

A face milling operation is used to machine 6.0 mm from the top surface of a rectangular piece of aluminum 300 mm long by 125 mm wide in a single pass. The cutter follows a path that is centered over the workpiece. It has four teeth and is 150 mm in diameter. Cutting speed

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The  machining time is $T_m = 0.866minutes$

b

The maximum metal removal rate is $R_{mr} =4812.75mm^3 /sec$

Explanation:

From the question we are told that

            The length of the work piece is  $L =300mm$

            The width of the work piece is $W = 125mm$

           The cut Depth is  $D = 6mm$

             The chip load is  $f = 0.27 mm/tooth$

             The number of teeth is  $n = 4$

              The cutting speed is $v = 2.8m/s = 2800mm/s$

Now in  order to obtain the actual machining time to make the pass across the surface

We first obtain the speed of rotation of the machine

The cutting velocity is  mathematically represented as

                    $v = \pi d N$

 Where d is the diameter given as 150mm

              N is the speed of rotation

Making N the subject of the formula

               $N =\frac{v}{\pi *d}$

                    $= \frac{2800}{\pi *150 }$

                    $= 5.941rev/sec$

Next we need to obtain the feed rate this is mathematically represented as

                $f_r = N nf$

Substituting the values accordingly  

              $= 5.94 * 4 * 0.27$

              $= 6.417 mm/s$

The displacement  of the milling operation  is mathematically represented as

                  $A = 0.5(d - \sqrt{d^2 - W^2} )$

                      $= 0.5(150 - \sqrt{150^2 - 125^2} )$

                      $= 0.5 * (150 - 82.9)$

                      $= 33.5mm$

The  machining time is mathematically represented as  

                   $T_m = \frac{(L + A)}{f_r}$

                         $= \frac{(300 +33.5)}{6.417}$

                        $=\frac{51.97}{60} = 0.866min$

The maximum metal removal rate is mathematically represented as

                     $R_{mr} = W D f_r$

Substituting values accordingly

                            $= 125 * 6* 6.417$

                            $= 4812.75 mm^3/sec$