# Machining Metal Removal

Written by Jerry Ratzlaff on . Posted in Welding Engineering

## Cutting Speed formula

 $$\large{ v_c = \pi \; d_o \; N }$$

### Where:

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

$$\large{ d_o }$$ = origional diameter of workpiece

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

$$\large{ N }$$ = rotation speed of workpiece

## Cutting Time formula

 $$\large{ t_c = \frac{ l }{ f \; N } }$$

### Where:

$$\large{ t_c }$$ = cutting time

$$\large{ f }$$ = feed

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

$$\large{ N }$$ = rotation speed of workpiece

## Cubic Inch Per Minute Metal Removal Rate formula

 $$\large{ CIP = SFM \; 12 \;\; IPR \; d_o }$$

### Where:

$$\large{ CIP }$$ = cubic inch per minute metal removal rate

$$\large{ IPR }$$ = inches per revolutions feed rate

$$\large{ d_o }$$ = origional diameter of workpiece

$$\large{ SFM }$$ = surface feet per minute

## 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 Rate formulas

 $$\large{ fr = \frac{ HP }{ MMF \; c_d \; c_w } }$$ $$\large{ fr = RPM \; N \; CL }$$

### Where:

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

$$\large{ CL }$$ = clip load per tooth

$$\large{ c_d }$$ = cut depth

$$\large{ c_w }$$ = cut width

$$\large{ HP }$$ = horsepower

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

$$\large{ N }$$ = number of teeth on the cutter

## Horsepower formulas

 $$\large{ HP = MRR \; MMF }$$ $$\large{ HP = MMF \; c_d \; c_w \; fr }$$

### Where:

$$\large{ HP }$$ = horsepower

$$\large{ c_d }$$ = cut depth

$$\large{ c_w }$$ = cut width

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

$$\large{ MMF }$$ = material machining factor

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

## Inches per Minute Feed Rate formula

 $$\large{ IPM = RPM \; IPR }$$

### Where:

$$\large{ IPM }$$ = inches per minute feed rate

$$\large{ IPR }$$ = inches per revolutions feed rate

$$\large{ RPM }$$ = revolutions per minute

## Inches per revolutions Feed Rate formula

 $$\large{ IPR = \frac{ IPM }{ RPM } }$$

### Where:

$$\large{ IPR }$$ = inches per revolutions feed rate

$$\large{ IPM }$$ = inches per minute feed rate

$$\large{ RPM }$$ = revolutions per minute

## Material Machining Factor Table

MaterialMMF
Aluminum 0.12
Brass 0.4
Low-carbon Steel 1.25
High-carbon & Low-alloy Steel 1.5 - 1.9
Stainless and Tool Steels 1.8 - 2.2
Super Alloys 2.5 - 5.0

## Material Removial Rate formula

 $$\large{ MRR = c_d \; c_w \; fr }$$

### Where:

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

$$\large{ c_d }$$ = cut depth

$$\large{ c_w }$$ = cut width

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

## revolutions Per Minute formula

 $$\large{ RPM = \frac{ SFM \; \frac{12}{ \pi } }{ d_o } }$$

### Where:

$$\large{ RPM }$$ = revolutions per minute

$$\large{ d_o }$$ = origional diameter of workpiece

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

$$\large{ SFM }$$ = surface feet per minute

## Surface Feet Per Minute formula

 $$\large{ SFM = \frac{ RPM \; d_o \; \pi }{ 12 } }$$

### Where:

$$\large{ SFM }$$ = surface feet per minute

$$\large{ d_o }$$ = origional diameter of workpiece

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

$$\large{ RPM }$$ = revolutions per minute