BIZOMAT MAKEOS · Gears
Gear Chordal Thickness and Addendum
What chordal thickness and chordal addendum should a gear tooth caliper read?
Chordal tooth thickness and corrected (chordal) addendum for measuring spur gear teeth with a gear tooth vernier caliper.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module of the gear. |
| Number of teeth | teeth | Number of teeth. |
| Addendum (0 = one module) | mm | Addendum; 0 uses the standard one module (enter the actual value for shifted or stub teeth). |
| Arc tooth thickness at pitch circle (0 = standard π m ÷ 2) | mm | Circular tooth thickness at the pitch circle; 0 uses the standard π m ÷ 2 (enter a thinned value to include backlash allowance). |
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: Module
- What it is
- The module of the gear: pitch diameter divided by the number of teeth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a helical gear checked in the normal plane, use consistent normal values throughout.
What this means: Number of teeth
- What it is
- The number of teeth on the gear being measured.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Count all teeth on the gear, not only those spanned by the caliper.
What this means: Addendum (0 = one module)
- What it is
- The radial height of the tooth from the pitch circle to the tip. 0 uses the standard addendum of one module.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100 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.
- Effect on the result
- The chordal addendum, the caliper depth setting, changes one for one with it.
- Get it right
- Enter the actual addendum for shifted or stub teeth; the standard value would set the caliper depth wrongly.
What this means: Arc tooth thickness at pitch circle (0 = standa…
- What it is
- The tooth thickness measured along the pitch circle arc. 0 uses the standard thickness, half the circular pitch.
- 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.
- Effect on the result
- A larger arc thickness gives a larger chordal thickness.
- Get it right
- Enter a thinned value to include the backlash allowance from the drawing.
Method and formulas
- Pitch diameter D = m z; half-angle θ = t ÷ D (radians).
- Chordal thickness tc = D sin θ (= D sin(90°/z) for standard teeth).
- Chordal addendum ac = a + (D ÷ 2)(1 − cos θ).
- Example: module 3, 30 teeth: set the caliper depth to 3.0617 mm and expect 4.7102 mm across the tooth.
Limitations
- Measures from the tip, so tip diameter errors affect the reading; span or over-pins methods are more accurate.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect cut gears with a gear tooth vernier
- Set up gear cutting depth
- Check worn teeth
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Chordal tooth thickness
- Chordal addendum (caliper depth setting)
- Pitch diameter
Interpreting the result
- Correct the depth setting by half the difference between measured and nominal tip diameters.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2145, 2238–2240. Topic reference; no source tables or recommended settings are reproduced.
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