BIZOMAT MAKEOS · Manufacturing
Chip Thickness and Specific Cutting Force
What mean chip thickness does this cut produce, and what specific cutting force results?
Mean chip thickness for milling (from feed per tooth, radial engagement and lead angle) or turning, and the specific cutting force kc from the material’s kc1.1 and exponent mc, for use in power calculations.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Operation | choice | Milling or turning. |
| Feed per tooth (milling) or per rev (turning) | mm | Feed per tooth (milling) or per revolution (turning). |
| Radial engagement (milling) | mm | Width of cut across the cutter (milling). |
| Cutter diameter (milling) | mm | Cutter diameter (milling). |
| Lead (entering) angle κr | ° | Lead or entering angle of the cutting edge (90° for a square shoulder cutter). |
| kc1.1 (specific force at 1 mm chip) | N/mm² | Specific cutting force at 1 mm chip thickness and 0° rake for the material, from tooling data (steel about 1500–2100, aluminium 500–800 N/mm²). |
| Exponent mc | Chip thickness exponent from the same data (about 0.2–0.3). | |
| Effective rake angle | ° | Effective rake angle of the insert (positive rake lowers the force by about 1% per degree). |
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: Operation
- What it is
- Whether the cut is milling, where the chip thickness varies around the cutter’s engagement, or turning, where it is steady. It changes which inputs are used.
- Units and format
- Choose one of 2 options from the list: Milling; Turning.
- Example
- The form opens with “Milling” selected as a worked example. Choose the option that matches your case.
What this means: Feed per tooth (milling) or per rev (turning)
- What it is
- How far the tool advances into the material for each cutting edge (milling) or each spindle revolution (turning), as programmed.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.15 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Chip thickness rises in direct proportion; kc falls as the chip gets thicker.
- Get it right
- For milling, use feed per tooth, not per revolution: divide the feed per revolution by the number of teeth.
What this means: Radial engagement (milling)
- What it is
- The width of material the milling cutter engages, measured across the cutter at right angles to the feed direction. Used for milling only.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not confuse it with axial depth of cut ap along the cutter axis.
What this means: Cutter diameter (milling)
- What it is
- The cutting diameter of the milling cutter, used with the radial engagement to find the engagement angle. Used for milling only.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the effective cutting diameter, which differs from the body diameter for some insert cutters.
What this means: Lead (entering) angle κr
- What it is
- The angle between the main cutting edge and the feed direction, as given in the tool or insert catalogue. A square shoulder cutter has 90°.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 90°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Chip thickness rises with the sine of the entering angle.
- Get it right
- Some catalogues give the lead angle measured from the other side; this tool needs the entering angle κr.
What this means: kc1.1 (specific force at 1 mm chip)
- What it is
- The material’s specific cutting force for a chip one millimetre thick at zero rake: the cutting force per square millimetre of chip section, from 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 10000 N/mm². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1700 N/mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- kc rises in direct proportion to kc1.1.
- Get it right
- Use the value for the actual grade and condition (annealed, hardened) from the tool maker’s material tables.
What this means: Exponent mc
- What it is
- The exponent describing how fast specific cutting force rises as the chip gets thinner, from the same tooling data as kc1.1.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.25 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger exponent makes kc rise faster as chips get thinner.
- Get it right
- Take kc1.1 and mc from the same source; they are fitted together.
What this means: Effective rake angle
- What it is
- The effective rake angle of the cutting edge as mounted, from the insert and holder data. Positive rake makes the edge sharper and lowers the force.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -30° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each degree of positive rake lowers kc by one per cent in this tool; negative rake raises it.
- Get it right
- Use the effective rake of the insert in its holder, not the insert’s own rake alone.
Method and formulas
- Milling: hm = (360 × fz × sin κr × ae) ÷ (π D φ), with engagement angle φ = arccos(1 − 2ae/D) in degrees (for ae ≤ D/2).
- Turning: h = f sin κr.
- kc = kc1.1 × h^(−mc) × (1 − rake/100).
- Example: 0.15 mm/tooth with 20 mm of a 50 mm cutter gives hm = 0.087627 mm and kc ≈ 3,124.6 N/mm².
Limitations
- Engagement angle formula assumes the cutter centre outside the material (ae up to D); slotting uses full engagement.
- Material data vary; use the tool maker’s kc1.1 and mc for the actual grade.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Get the right kc for the milling and turning power tools
- See how light radial engagement thins the chip
- Compare feeds for efficient cutting
Who it is for
- Machinists
- CNC programmers
- Manufacturing engineers
What you get
- Mean chip thickness
- Engagement angle (milling)
- Specific cutting force kc
Interpreting the result
- Thin chips raise kc; keeping hm near the tool maker’s recommendation improves tool life and efficiency.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1084–1101. Topic reference; no source tables or recommended settings are reproduced.
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