BIZOMAT MAKEOS · Manufacturing
Form Tool Profile Plan (Step Depths and Angles on a Flat or Circular Tool)
For a form tool cutting a stepped or angled profile, what depths and angles must be ground on the tool for each step, and does the profile fit the tool?
Plan of a form tool profile with up to four steps measured from the largest diameter of the work: for a flat tool with front clearance, the depth and angle of each step on the tool (as the forming tool depth tool, flat mode); for a circular tool with its face below centre, the radius of the tool at each step (as the same tool, circular mode), against the usable depth of the flat tool or the smallest radius the circular tool can have.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tool | choice | Flat (dovetail) form tool or circular form tool. |
| Front clearance angle (flat) | ° | Front clearance angle of the flat tool. |
| Largest radius of the circular tool | mm | Radius of the circular tool at the largest work diameter. |
| Face offset below centre (circular) | mm | How far the cutting face is below the tool centre (gives the circular tool its clearance). |
| Step 1 | ||
| Radial depth from the largest work diameter (0 = unused) | mm | Radial depth of step 1 below the largest diameter of the work. |
| Flank angle on the work (flat) | ° | Angle of the step 1 flank on the work (flat tool). |
| Step 2 | ||
| Radial depth from the largest work diameter (0 = unused) | mm | Radial depth of step 2. |
| Flank angle on the work (flat) | ° | Angle of the step 2 flank. |
| Step 3 | ||
| Radial depth from the largest work diameter (0 = unused) | mm | Radial depth of step 3. |
| Flank angle on the work (flat) | ° | Angle of the step 3 flank. |
| Step 4 | ||
| Radial depth from the largest work diameter (0 = unused) | mm | Radial depth of step 4 (0 if unused). |
| Flank angle on the work (flat) | ° | Angle of the step 4 flank. |
| Limits | ||
| Usable profile depth of the flat tool | mm | Deepest profile the flat tool blank allows. |
| Smallest radius allowed on the circular tool | mm | Smallest radius the circular tool may have (bore and wall). |
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: Tool
- What it is
- Whether the profile is for a flat (dovetail) form tool with front clearance or a circular form tool whose cutting face is set below its centre.
- Units and format
- Choose one of 2 options from the list: Flat tool with clearance; Circular tool (face below centre).
- Example
- The form opens with “Flat tool with clearance” selected as a worked example. Choose the option that matches your case.
- Get it right
- Clearance angle and usable depth apply only to the flat tool; tool radius, face offset and smallest radius only to the circular tool.
What this means: Front clearance angle (flat)
- What it is
- The front clearance angle of the flat form tool, the angle at which its front face is tilted back from the vertical so it does not rub. Depths on the tool are shorter than on the work by its cosine.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.000001° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger clearance angle makes the depths and angles on the tool smaller.
- Get it right
- Used only for the flat tool; take it from the tool drawing or your tool holder.
What this means: Largest radius of the circular tool
- What it is
- The radius of the circular form tool at the point that cuts the largest diameter of the work, from the tool centre to that cutting edge.
- 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 38.1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the radius, not the diameter; used only for the circular tool.
What this means: Face offset below centre (circular)
- What it is
- How far the cutting face of the circular tool is set below its centre line, which gives the tool its clearance. It is measured at right angles to the face.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6.35 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only for the circular tool; it must be smaller than the tool radius.
Step 1
What this means: Radial depth from the largest work diameter (0…
- What it is
- The radial depth of step 1 of the work profile, measured from the largest diameter of the work inward (half the difference in diameters). 0 leaves the step out.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deeper steps give deeper profiles on the tool and smaller radii on a circular tool.
- Get it right
- Enter radial depth, not diameter difference: halve the difference between the largest diameter and the step diameter.
What this means: Flank angle on the work (flat)
- What it is
- The angle of the step 1 flank on the work, which the tool converts into the corresponding angle ground on the flat tool.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 89°. 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.
- Get it right
- Used only for the flat tool. Measure it the same way for every step, from the same reference on the drawing.
Step 2
What this means: Radial depth from the largest work diameter (0…
- What it is
- The radial depth of step 2 of the work profile, measured inward from the largest work diameter. 0 leaves the step out.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter radial depth: halve the difference in diameters.
What this means: Flank angle on the work (flat)
- What it is
- The angle of the step 2 flank on the work, converted to the angle ground on the flat tool.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only for the flat tool.
Step 3
What this means: Radial depth from the largest work diameter (0…
- What it is
- The radial depth of step 3 of the work profile, measured inward from the largest work diameter. 0 leaves the step out.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter radial depth: halve the difference in diameters.
What this means: Flank angle on the work (flat)
- What it is
- The angle of the step 3 flank on the work, converted to the angle ground on the flat tool.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only for the flat tool.
Step 4
What this means: Radial depth from the largest work diameter (0…
- What it is
- The radial depth of step 4 of the work profile, measured inward from the largest work diameter. 0 leaves the step out.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter radial depth: halve the difference in diameters.
What this means: Flank angle on the work (flat)
- What it is
- The angle of the step 4 flank on the work, converted to the angle ground on the flat tool.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only for the flat tool, and ignored while the step 4 depth is 0.
Limits
What this means: Usable profile depth of the flat tool
- What it is
- The deepest profile that can be ground on the flat tool blank while leaving enough body to hold it, compared with the deepest step on the tool.
- 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 15 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only for the flat tool; take it from the blank size and holder.
What this means: Smallest radius allowed on the circular tool
- What it is
- The smallest radius the circular tool may have at any step, set by its bore and the wall it needs around the bore.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only for the circular tool; take it from the tool’s bore size and your wall requirement.
Method and formulas
- Flat tool: depth on the tool = depth on the work × cos C; angle on the tool = atan (tan A × cos C) (as the forming tool depth tool).
- Circular tool: k = √(R_t² − offset²); radius at a step = √((k − depth)² + offset²) (as the same tool).
- Deepest tool depth or smallest tool radius against the limit.
- Example: the deepest step is 7.7274 mm on the tool.
Limitations
- Steps measured radially from the largest work diameter; axial positions are unchanged on the tool.
- Zero top rake; a raked tool changes the depths (use the rake mode of the forming tool depth tool).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Grind a flat form tool for a stepped part
- Lay out a circular form tool profile
- Check a profile is not too deep for the tool
Who it is for
- Toolmakers
- Machinists
- Screw machine setters
What you get
- Depth and angle of each step on the tool
- Deepest step or smallest radius
- Against the tool limits
Interpreting the result
- Clearance shortens every depth on the tool by the same factor, so a profile ground to work depths cuts too deep.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 797–801. Topic reference; no source tables or recommended settings are reproduced.
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Open the Form Tool Profile Plan (Step Depths and Angles on a Flat or Circular Tool) calculator