Face Milling Formulas Calculator
This interactive page provides all key face milling formulas with built-in calculators. Formulas use MathJax for rendering. Each section includes a description, formula, variables, and a JavaScript-based calculator with a sample input.
1. Spindle Speed (n or RPM)
This determines the rotational speed of the cutter.
| Formula | Description | Variables |
|---|---|---|
| \[ n = \frac{1000 \times v_c}{\pi \times D_c} \] (metric) | Spindle speed from cutting speed | \( n \): Spindle speed (rev/min) \( v_c \): Cutting speed (m/min) \( D_c \): Cutter diameter (mm) \( \pi \): 3.14 |
| \[ \text{RPM} = \frac{3.82 \times \text{SFM}}{D} \] (imperial) | Spindle speed from surface feet per minute | \( \text{SFM} \): Surface feet per minute (ft/min) \( D \): Cutter diameter (in) |
Metric Spindle Speed Calculator
Result: 798 rev/min
Sample: For \( v_c = 200 \) m/min and \( D_c = 80 \) mm: \( n \approx 798 \) rev/min.
2. Cutting Speed (v_c or SFM)
The peripheral speed at the cutter's edge.
| Formula | Description | Variables |
|---|---|---|
| \[ v_c = \frac{\pi \times D_c \times n}{1000} \] (metric) | Cutting speed from spindle speed | Same as above |
| \[ \text{SFM} = \frac{\pi \times D \times \text{RPM}}{12} \] (imperial) | Surface feet per minute from spindle speed | Same as above (imperial units) |
Metric Cutting Speed Calculator
Result: 200 m/min
Sample: For \( D_c = 80 \) mm and \( n = 798 \) rev/min: \( v_c = 200 \) m/min.
3. Feed per Tooth (f_z or IPT/FPT)
The distance the tool advances per tooth/insert.
| Formula | Description | Variables |
|---|---|---|
| \[ f_z = \frac{v_f}{z \times n} \] (metric) | Feed per tooth from table feed | \( f_z \): Feed per tooth (mm/tooth) \( v_f \): Table feed (mm/min) \( z \): Number of inserts/teeth |
| \[ \text{IPT} = \frac{\text{IPM}}{\text{RPM} \times z} \] (imperial) | Inches per tooth | \( \text{IPM} \): Inches per minute \( \text{RPM} \): Spindle speed (rev/min) |
| \[ \text{AFPT} = \text{IPT} \times \sqrt{\frac{D}{WOC}} \] (imperial, chip thinning) | Adjusted feed per tooth | \( WOC \): Width of cut (in) |
Metric Feed per Tooth Calculator
Result: 0.1 mm/tooth
Sample: For \( v_f = 500 \) mm/min, \( z = 10 \), \( n = 500 \) rev/min: \( f_z = 0.1 \) mm/tooth.
4. Table Feed (v_f or IPM)
The linear speed of the workpiece relative to the tool.
| Formula | Description | Variables |
|---|---|---|
| \[ v_f = f_z \times z \times n \] (metric) | Table feed from feed per tooth | Same as above |
| \[ \text{IPM} = \text{RPM} \times \text{IPT} \times z \] (imperial) | Inches per minute | Same as above (imperial) |
Metric Table Feed Calculator
Result: 500 mm/min
Sample: For \( f_z = 0.1 \) mm/tooth, \( z = 10 \), \( n = 500 \) rev/min: \( v_f = 500 \) mm/min.
5. Machining Time (T_c or T_m)
Time required to complete the cut.
| Formula | Description | Variables |
|---|---|---|
| \[ T_c = \frac{L}{v_f} \] (metric, basic) | Machining time (no approach/overlap) | \( T_c \): Machining time (min) \( L \): Length of cut (mm) |
| \[ T_m = \frac{L + A + O}{v_f} \] (metric, with approach and overlap) | Machining time for face milling | \( A \): Approach = \( D_c / 2 \) (mm) \( O \): Overlap (mm) |
Basic Machining Time Calculator
Result: 0.4 min
Sample: For \( L = 200 \) mm, \( v_f = 500 \) mm/min: \( T_c = 0.4 \) min (24 seconds).
6. Material Removal Rate (MRR or Q)
Volume of material removed per unit time.
| Formula | Description | Variables |
|---|---|---|
| \[ Q = a_p \times a_e \times v_f \] (metric) | Metal removal rate | \( Q \): cm³/min \( a_p \): Axial depth (mm) \( a_e \): Radial width (mm) |
| \[ \text{MRR} = \text{IPM} \times \text{DOC} \times \text{WOC} \] (imperial) | Cubic inches per minute | \( \text{DOC} \): Depth of cut (in) \( \text{WOC} \): Width of cut (in) |
Metric MRR Calculator
Result: 4000 cm³/min
Sample: For \( a_p = 2 \) mm, \( a_e = 40 \) mm, \( v_f = 500 \) mm/min: \( Q = 4000 \) cm³/min.
7. Power Consumption (P_c or HP)
Power required by the machine.
| Formula | Description | Variables |
|---|---|---|
| \[ P_c = \frac{a_p \times a_e \times v_f \times k_c}{60 \times 10^6 \times \eta} \] (metric) | Net power | \( P_c \): Power (kW) \( k_c \): Specific cutting force (MPa, e.g., 2200 for steel) \( \eta \): Efficiency (e.g., 0.8) |
| \[ \text{HP} = \text{MRR} \times m_f \] (imperial) | Horsepower | \( m_f \): Material factor (e.g., 1 for steel) |
Metric Power Calculator
Result: 1.22 kW
Sample: For \( a_p = 2 \), \( a_e = 40 \), \( v_f = 500 \), \( k_c = 2200 \), \( \eta = 0.8 \): \( P_c \approx 1.22 \) kW.
8. Other Specific Formulas
| Formula | Description | Variables |
|---|---|---|
| \[ A = \frac{D_c}{2} \] (mm) | Approach Distance | \( A \): Approach distance |
| \[ M_c = \frac{P_c \times 30 \times 60}{2 \pi n} \] (Nm) | Torque | \( M_c \): Torque (Nm) |
| \[ h_m = f_z \times \sin(\kappa_r) \] (mm) | Average Chip Thickness | \( h_m \): Chip thickness \( \kappa_r \): Approach angle (often 90°) |
Approach Distance Calculator
Result: 40 mm
Sample: For \( D_c = 80 \) mm: \( A = 40 \) mm.
Note: These calculators use JavaScript and default to metric units. Adjust inputs for your needs. For imperial, convert units accordingly. Always verify with manufacturer data.
