# Machining Metal Removal

Written by Jerry Ratzlaff on . Posted in Welding Engineering

## Cutting Speed formula

 $$\large{ v_c = \frac{ \pi \; d \; v }{ 1000 } }$$

### Where:

$$\large{ v_c }$$ = cutting speed

$$\large{ d }$$ = diameter of workpiece

$$\large{ \pi }$$ = Pi

$$\large{ v }$$ = spindle speed

## Feed formulas

 $$\large{ f = \frac{ l_m }{ v } }$$ $$\large{ f = v \; f_t \; Z }$$

### Where:

$$\large{ f }$$ = feed

$$\large{ f_t }$$ = feed per tooth

$$\large{ l_m }$$ = machined length per minute

$$\large{ Z }$$ = number of flutes

$$\large{ v }$$ = spindle speed

## Feed per Tooth formula

 $$\large{ f_t = \frac{ f }{ v \; Z } }$$

### Where:

$$\large{ f_t }$$ = feed per tooth

$$\large{ f }$$ = feed

$$\large{ Z }$$ = number of flutes

$$\large{ v }$$ = spindle speed

## Machining time formula

 $$\large{ f = \frac{ l }{ l_m } }$$

### Where:

$$\large{ Tc }$$ = machining time

$$\large{ l }$$ = length of workpiece

$$\large{ l_m }$$ = machined length per minute

## Metal Removal Rate formulas

 $$\large{ MRR = \frac{ A \; d }{ t } \; 60 }$$ $$\large{ MRR = s \; f \; d }$$ $$\large{ MRR = \frac{s \; f \; d }{ 1000 } }$$

### Where:

$$\large{ MRR }$$ = metal removal rate

$$\large{ A }$$ = area of cut

$$\large{ d }$$ = depth of cut

$$\large{ s }$$ = speed of cut

$$\large{ t }$$ = cut time

$$\large{ f }$$ = feed rate

## Net Power formula

 $$\large{ P_n = \frac{ z \; f \; v_c \; F_c }{ 60 \; 10^3 \; n_m } \; KW }$$

### Where:

$$\large{ P_n }$$ = net power

$$\large{ z }$$ = depth of cut

$$\large{ f }$$ = feed per revolution

$$\large{ v_c }$$ = cutting speed

$$\large{ F_c }$$ = specific cutting force

$$\large{ n_m }$$ = machine efficiency

## Spindle Speed formula

 $$\large{ v = \frac{ \frac{ v_c }{ \pi } }{ d_d } \; 1000 }$$

### Where:

$$\large{ v }$$ = spindle speed

$$\large{ v_c }$$ = cutting speed

$$\large{ d_d }$$ = diameter of drill

$$\large{ \pi }$$ = Pi

## theoretical Finished Surface Toughness formula

 $$\large{ h = \frac{ f^2 }{ 8 \; Re } \;1000 }$$

### Where:

$$\large{ h }$$ = feed

$$\large{ f }$$ = feed per revolution

$$\large{ r_c }$$ = insert's corner radius