BIZOMAT MAKEOS · Manufacturing
Forming Tool Step Depths and Angles
What depth and angle must I grind on a flat or circular forming tool to produce these steps on the work?
Forming tool dimensions by the handbook methods: step depth and angle on a flat tool with front clearance, step depth on a tool with both rake and clearance from the work radii, and the radius of each step on a circular forming tool whose cutting face sits below centre.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tool | choice | Type of forming tool. |
| Radial step depth on the work (flat, circular) | mm | Difference in radius between two steps on the work. |
| Front clearance angle (flat) | ° | Front clearance angle of the flat tool. |
| Angle on the work (flat) | ° | Angle of a flank on the work (for its reduced angle on the tool). |
| Larger work radius (rake) | mm | Larger radius on the work. |
| Smaller work radius (rake) | mm | Smaller radius on the work. |
| Rake angle (rake) | ° | Top rake angle of the tool. |
| Clearance angle (rake) | ° | Front clearance angle of the tool. |
| Largest radius of the circular tool | mm | Radius of the circular tool at its largest step. |
| Cutting face below centre (circular) | mm | Distance of the cutting face below the tool’s horizontal centre line (set by the machine). |
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
- The kind of forming tool being ground: a flat (dovetail) tool with front clearance only, a flat tool with both top rake and clearance, or a circular tool whose cutting face sits below its centre.
- Units and format
- Choose one of 3 options from the list: Flat tool with clearance; Tool with rake and 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
- Each tool uses only the inputs marked for it in brackets; the others are ignored, so fill in the right group.
What this means: Radial step depth on the work (flat, circular)
- What it is
- The difference in radius between two adjacent steps of the profile on the finished work, measured square to the work axis. The flat and circular tools use it.
- 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 12.7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- On the flat tool the step depth is D × cos C, so it scales directly with D.
- Get it right
- This is a radial step: half the difference between the two diameters, not the diameter difference itself.
What this means: Front clearance angle (flat)
- What it is
- The front clearance angle ground on the flat tool, which tilts its front face back and makes the depth measured on the tool smaller than the step on the work.
- 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 reduces both the step depth and the angle ground on the tool.
- Get it right
- Used by the flat tool only; the tool with rake and clearance has its own clearance angle input.
What this means: Angle on the work (flat)
- What it is
- The angle of a sloping flank of the profile as it appears on the work. The tool converts it to the smaller angle that must be ground on the flat tool, measured in plane x-x.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.000001° 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 by the flat tool only; it changes the angle on the tool, not the step depth.
What this means: Larger work radius (rake)
- What it is
- The larger of the two work radii that form the step, from the work axis to the outer surface of that step, for the tool with rake and clearance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Radius, not diameter: halve the diameter shown on the drawing.
What this means: Smaller work radius (rake)
- What it is
- The smaller of the two work radii that form the step, from the work axis to the deeper surface; the radial step on the work is R − r.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Radius, not diameter, and it must be less than the larger radius.
What this means: Rake angle (rake)
- What it is
- The top rake angle on the cutting face of the tool with rake and clearance, which tilts the face so the edge cuts more freely.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. 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.
- Get it right
- It must be above zero in this mode; for a tool with no top rake use the flat tool option.
What this means: Clearance angle (rake)
- What it is
- The front clearance angle of the tool with rake and clearance, on the face below the cutting edge, used with the rake to find tool angle D.
- 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 reduces tool angle D = 90° − (E + F) and so the step depth on the tool.
- Get it right
- Rake plus clearance must be less than 90°, or the construction cannot be solved.
What this means: Largest radius of the circular tool
- What it is
- The radius of the circular forming tool at its largest step, from the tool’s centre of rotation out to the 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
- Radius, not the diameter of the tool blank.
What this means: Cutting face below centre (circular)
- What it is
- How far the cutting face of the circular tool sits below the tool’s horizontal centre line, set by the machine or tool holder so the edge cuts on the work centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 200 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
- It must be less than the tool radius; take it from the machine maker for that holder.
Method and formulas
- Flat tool: depth d = D cos C; angle in plane x-x: tan A′ = tan A × cos C.
- Rake and clearance: A = 180° − F; sin B = r sin A ÷ R; C = 180° − (A + B); y = R sin C ÷ sin A; tool angle D = 90° − (E + F); depth x = y sin D (handbook example: 16 and 10 mm radii, 10° rake, 15° clearance → 5.490 mm).
- Circular tool: r = √[(√(R² − C²) − D)² + C²], with C the offset of the cutting face.
- Example: a 12.7 mm step with 15° clearance is 12.267 mm deep on a flat tool.
Limitations
- Straight radial steps; curved profiles need point-by-point correction.
- Machine-specific tool radius and offset come from the machine maker.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Grind a dovetail or circular form tool for a profile
- Correct form depths for rake and clearance
- Check a supplier’s form tool drawing
Who it is for
- Machinists
- Toolmakers
- Manufacturing engineers
What you get
- Step depth on the tool
- Angle or radius on the tool
- Correction from the work dimension
Interpreting the result
- Without correction, a raked or offset tool cuts steps shallower than intended.
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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