BIZOMAT MAKEOS · Manufacturing
Tool Life from the Force Ratio FH ÷ FC (Colding)
From the ratio of the feed-plane force to the cutting force that I measure or estimate, what tool life does the Colding relation give, and at what force ratio should I change the tool for a target life?
The handbook’s relation between tool life and the force ratio from machining econometrics: T = (FH ÷ (a FC))^(LF/L), with the rake angle constant a (about 0.25 to 0.5 in turning) and the ratio LF ÷ L of the force ratio and tool life equation constants (10 to 20), both entered by you, giving the tool life for a measured or estimated force ratio and, the other way round, the force ratio that corresponds to a target tool life, FH ÷ FC = a T^(L/LF).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Force ratio from | choice | Whether to take the ratio from two measured forces or enter it directly. |
| Feed-plane force FH | N | Resultant force in the feed plane (axial and radial combined). |
| Cutting force FC | N | Tangential cutting force. |
| Force ratio FH ÷ FC | Ratio of the feed-plane force to the cutting force. | |
| Rake angle constant a | Constant that depends on the rake angle; the handbook gives about 0.25 to 0.5 for turning. | |
| Constant ratio LF ÷ L | Ratio of the force-ratio constant LF to the tool-life constant L, from your tests; the handbook gives 10 to 20. | |
| Target tool life (0 = none) | min | Tool life you want, to find the matching force ratio. |
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: Force ratio from
- What it is
- Whether the force ratio comes from two measured forces or is entered.
- Units and format
- Choose one of 2 options from the list: Measured forces FH and FC; A force ratio you enter.
- Example
- The form opens with “Measured forces FH and FC” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Chooses how FH ÷ FC is found.
- Get it right
- Use measured forces from a dynamometer when you have them.
What this means: Feed-plane force FH
- What it is
- Resultant of the axial and radial forces in the feed plane.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger feed-plane force raises the ratio and the life.
- Get it right
- Combine the feed and radial dynamometer readings into one resultant.
What this means: Cutting force FC
- What it is
- Tangential force in the direction of the cutting speed.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger cutting force lowers the ratio.
- Get it right
- Read it from the dynamometer or estimate it as Kc × chip area.
What this means: Force ratio FH ÷ FC
- What it is
- Ratio of the feed-plane force to the tangential cutting force.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The tool life rises steeply with it.
- Get it right
- The handbook gives about 0.3 to 0.4 in roughing and 0.5 to 0.6 in finishing turning.
What this means: Rake angle constant a
- What it is
- Constant of the force ratio relation that depends on the rake angle.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 5. 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
- A larger a shortens the life for the same ratio.
- Get it right
- The handbook gives about 0.25 to 0.5 in turning; take it from your tests.
What this means: Constant ratio LF ÷ L
- What it is
- Ratio of the force-ratio constant LF to the tool-life constant L.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 100. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets how steeply life rises with the force ratio.
- Get it right
- The handbook gives 10 to 20; take it from your tests.
What this means: Target tool life (0 = none)
- What it is
- Tool life you want between tool changes.
- Units and format
- Enter a number in min: minutes. The form accepts 0 min to 100000 min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Gives the force ratio at which to change the tool.
- Get it right
- Enter 0 to skip the check and the matching force ratio.
Method and formulas
- FH ÷ FC from the measured forces, or as entered.
- T = (FH ÷ (a FC))^(LF ÷ L) minutes.
- For a target life: FH ÷ FC = a × T^(L ÷ LF).
- Example: a force ratio of 0.5 gives a tool life of 1 min.
Limitations
- The constants a, L and LF come from tests on your tool and work material; the relation holds along the tool-life curve described in the handbook.
- The force ratio also varies with ECT and cutting speed; compare ratios at the same conditions.
- Use the result to set monitoring limits and confirm them with tool-life tests.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate tool life from measured cutting forces
- Set a force ratio limit for tool-change monitoring
- See how sensitive tool life is to the force ratio
Who it is for
- Manufacturing engineers
- Process developers
- Tooling engineers
What you get
- Force ratio FH ÷ FC
- Tool life from the relation
- Force ratio for the target tool life
- Whether the present ratio meets the target life
Interpreting the result
- With the handbook’s a = 0.5, a force ratio of 0.5 gives a life of 1 minute whatever LF ÷ L is.
- A larger LF ÷ L makes the tool life rise very steeply with the force ratio.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1140–1143. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Useful alongside · BIZOMAT original book
Tool life and the Taylor equation
What it covers: Define tool life, fit Taylor's speed and tool-life relationship to two or more tests, predict life at other speeds and understand why feed is usually a cheaper lever than speed.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Tool Life from the Force Ratio FH ÷ FC (Colding) calculator