KEVOS® MAKEOS · Threads
Single-Point Thread Cutting Tool Relief and Nose Angles (Leading and Trailing Flanks)
For a single-point tool to cut a thread of a given lead, major and minor diameter and thread angle, what side relief angles must I grind below the leading and trailing cutting edges (parallel to the axis and perpendicular to the edges) to keep the effective relief I want, and what is the angle where the two flanks meet?
Relief angles of single-point thread cutting tools by the handbook formulas: the helix angles of the thread at the minor diameter, tan ψ = lead ÷ (π K), and at the major diameter, tan φ = lead ÷ (π D); the side relief angles parallel to the thread axis a = ae + ψ at the leading edge and a′ = ae − φ at the trailing edge for an effective relief ae; the relief angles actually ground perpendicular to the side cutting edges, tan b = tan a cos(½ thread angle) and tan b′ = tan a′ cos(½ thread angle); and the nose angle where the flanks meet, tan n = (tan a − tan a′) ÷ (2 tan(½ thread angle)).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Lead of the thread (pitch × number of starts) | mm | Axial advance per turn: the pitch for a single-start thread, pitch × starts for a multiple-start thread. |
| Major diameter D | mm | Major (outside) diameter of the thread. |
| Minor diameter K | mm | Minor (root) diameter of the thread. |
| Included angle of the thread (and tool) | ° | Included angle of the thread form: 60° for Unified and metric, 29° for Acme, 30° for metric trapezoidal. |
| Effective relief angle ae wanted | ° | Effective relief angle wanted below every cutting edge, measured parallel to the thread axis; the handbook recommends 8 to 14° for high-speed steel and 5 to 10° for carbide. |
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: Lead of the thread (pitch × number of starts)
- What it is
- Axial advance of the thread in one turn: pitch times the number of starts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.16 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger lead raises both helix angles and the leading relief.
- Get it right
- A 5 tpi double-start thread has a lead of 0.4 in (10.16 mm).
What this means: Major diameter D
- What it is
- Major (outside) diameter of the thread being cut.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25.4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the helix angle that reduces the trailing relief.
- Get it right
- Use the basic major diameter of the thread.
What this means: Minor diameter K
- What it is
- Minor (root) diameter of the thread being cut.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 19.812 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the helix angle added to the leading relief.
- Get it right
- Use the basic minor diameter from the thread standard.
What this means: Included angle of the thread (and tool)
- What it is
- Included angle of the thread form, which the tool point must match.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 120°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 29° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the relief ground perpendicular to the edges and the nose angle.
- Get it right
- 60° Unified and metric, 29° Acme, 30° trapezoidal.
What this means: Effective relief angle ae wanted
- What it is
- Effective relief angle wanted below every cutting edge, measured parallel to the thread axis.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.000001° to 30°. 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
- Adds directly to both side relief angles.
- Get it right
- 8 to 14° for high-speed steel and 5 to 10° for carbide; more for soft, gummy metals.
Method and formulas
- tan ψ = lead ÷ (π K) (helix angle at the minor diameter); tan φ = lead ÷ (π D) (at the major diameter).
- Leading edge: a = ae + ψ; trailing edge: a′ = ae − φ (parallel to the thread axis).
- Ground relief perpendicular to the edges: tan b = tan a cos(½ thread angle); tan b′ = tan a′ cos(½ thread angle).
- Nose angle: tan n = (tan a − tan a′) ÷ (2 tan(½ thread angle)).
- Example: a 10.16 mm lead on 25.4 mm major and 19.812 mm minor diameters with 10° effective relief needs 18.7° below the leading edge and 2.6566° below the trailing edge.
Limitations
- For right- or left-hand threads the leading edge is the one facing the direction of tool travel.
- The effective relief at the nose is ae; grind it without further correction.
- The nose angle is the angle of a sharp point; the actual nose carries the flat or radius of the thread form.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Grind a single-point tool for a coarse, multiple-start or high-helix thread
- Check that the trailing flank will not rub
- Set the angles on a tool and cutter grinder
Who it is for
- Toolroom machinists
- Lathe operators
- Tool grinders
What you get
- Helix angles at the minor and major diameters
- Side relief parallel to the axis at the leading and trailing edges
- Relief angles to grind perpendicular to the leading and trailing edges
- Nose angle where the flanks meet
Interpreting the result
- When the trailing relief comes out small or negative, the trailing flank rubs: increase the effective relief or reduce the trailing-side helix effect with a smaller lead per pass.
- High helix (multiple-start or coarse) threads need much more leading relief than standard threads.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2040–2041. Topic reference; no source tables or recommended settings are reproduced.
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