BIZOMAT MAKEOS · Manufacturing
Equivalent Chip Thickness (ECT) and Cutting Forces
What equivalent chip thickness, removal rate, cutting force and power does this turning cut give?
Equivalent chip thickness from feed, depth of cut and cutting edge length (Woxén–Colding), the metal removal rate, the main cutting force from a specific cutting force, the feed-plane force and its axial and radial components from the chip flow angle, and the power.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Feed per revolution | mm/rev | Feed per revolution. |
| Depth of cut | mm | Depth of cut. |
| Engaged cutting edge length | mm | Length of cutting edge in contact (depends on depth, lead angle and nose radius). |
| Cutting speed | m/min | Cutting speed. |
| Specific cutting force at this ECT | N/mm² | Specific cutting force for the material at the ECT (from tests or tooling data). |
| Feed-plane force ÷ cutting force (F_H ÷ F_C) | Ratio of the feed-plane force to the cutting force (about 0.3–0.4 roughing, 0.5–0.6 finishing per the handbook). | |
| Chip flow angle | ° | Chip flow angle (about 30° roughing, 60° finishing at 15° lead angle). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Feed per revolution
- What it is
- How far the tool advances along the work for each revolution of the spindle in this turning cut.
- Units and format
- Enter a number in mm/rev: millimetres per revolution. The form accepts 0.000001 mm/rev to 10 mm/rev. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.8 mm/rev as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Chip area, ECT, forces, removal rate and power all rise in proportion.
- Get it right
- This is per revolution, not per minute; it multiplies the depth of cut to give the chip area.
What this means: Depth of cut
- What it is
- The radial depth of cut: how far the tool cuts into the work measured square to the machined surface.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Chip area, ECT, forces, removal rate and power all rise in proportion.
- Get it right
- Give the depth on one side (radius), not the reduction in diameter.
What this means: Engaged cutting edge length
- What it is
- The length of the cutting edge actually engaged with the work, which depends on the depth of cut, lead angle and nose radius.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer engaged edge lowers the ECT; the forces here do not change.
- Get it right
- It is longer than the depth of cut when the lead angle or nose radius spreads the cut; work it out from the insert geometry.
What this means: Cutting speed
- What it is
- The surface speed of the work past the cutting edge, from the tooling supplier’s data or your process sheet.
- Units and format
- Enter a number in m/min: metres per minute. The form accepts 0.000001 m/min to 5000 m/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 m/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Removal rate and power are directly proportional to cutting speed.
- Get it right
- This is metres per minute at the cut diameter, not spindle rpm.
What this means: Specific cutting force at this ECT
- What it is
- The specific cutting force: the cutting force needed per square millimetre of chip area for this material at this chip thickness, from tests or tooling data.
- Units and format
- Enter a number in N/mm²: newtons per square millimetre (equal to MPa). The form accepts 0.000001 N/mm² to 20000 N/mm². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 N/mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All forces and the power are directly proportional to it.
- Get it right
- It varies with ECT; use the value for your chip thickness, not a single catalogue figure for all cuts.
What this means: Feed-plane force ÷ cutting force (F_H ÷ F_C)
- What it is
- The force in the feed plane divided by the main tangential cutting force. It sets the combined axial and radial force on the tool.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The feed-plane, axial and radial forces are proportional to it.
- Get it right
- Type it as a ratio; the guide notes the handbook’s roughing and finishing bands.
What this means: Chip flow angle
- What it is
- The chip flow angle: the direction in the feed plane in which the chip leaves, which splits the feed-plane force into axial and radial parts.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 90°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger angle shifts force from axial to radial.
- Get it right
- It depends on lead angle, nose radius and depth; the guide gives the handbook’s roughing and finishing values.
Method and formulas
- ECT = area ÷ CEL ≈ feed × depth ÷ CEL (handbook example: 0.8 × 3 ÷ 4 = 0.6 mm).
- MRR = 1000 V × ECT × CEL mm³/min.
- F_C = area × K_c; F_H = ratio × F_C; F_A = F_H cos(CFA), F_R = F_H sin(CFA).
- Power = F_C × V ÷ 60,000 kW.
- Example: 0.8 mm/rev × 3 mm over a 4 mm edge gives ECT = 0.6 mm.
Limitations
- Area approximated as feed × depth; K_c and the force ratio vary with ECT and speed.
- Nose radius and lead angle enter through the cutting edge length.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate turning forces and power for a new cut
- Compare roughing and finishing conditions on one basis
- Estimate radial force for deflection checks
Who it is for
- Machinists
- CNC programmers
- Manufacturing engineers
What you get
- Equivalent chip thickness
- Metal removal rate
- Cutting, axial and radial forces and power
Interpreting the result
- When the product of feed and depth is held constant, tool life stays about constant at the same speed and edge length.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1132–1141. Topic reference; no source tables or recommended settings are reproduced.
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