BIZOMAT MAKEOS · Gears
Gear Tooth Caliper Setting for Backlash (Chordal Thickness Limits)
What chordal tooth thickness and depth setting should my gear tooth vernier use for the backlash I want, and does the measured tooth pass?
Gear tooth vernier (caliper) settings for a spur gear thinned for backlash: arc tooth thickness reduced for this gear’s share of the normal backlash range, chordal thickness and chordal addendum at both limits (as the chordal tooth tool), the depth setting corrected for the measured tip diameter, and accept or reject of the measured chordal thickness.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module. |
| Number of teeth | Number of teeth. | |
| Pressure angle | ° | Pressure angle. |
| Smallest normal backlash wanted (pair) | mm | Smallest normal backlash the pair must have. |
| Largest normal backlash wanted (pair) | mm | Largest normal backlash the pair may have. |
| Share of the backlash taken by this gear | % | How much of the backlash comes from thinning this gear. |
| Measured tip diameter (0 = nominal) | mm | Measured outside diameter of the gear (the caliper depth is set from the tip); 0 uses the nominal tip diameter. |
| Measured chordal thickness | mm | Chordal thickness read on the vernier. |
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 tooth size of the spur gear: the pitch diameter divided by the number of teeth, as on the gear drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.3 mm to 50 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
- Do not confuse module with diametral pitch (teeth per inch of pitch diameter).
What this means: Number of teeth
- What it is
- The number of teeth on the gear being measured. With the module it sets the pitch diameter used for the chordal thickness.
- Units and format
- Enter a plain number with no unit. The form accepts 6 to 500. Use a whole number. 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.
What this means: Pressure angle
- What it is
- The pressure angle of the gear’s involute, set by the cutting tool. The tool uses it to turn normal backlash into tooth thinning.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 14.5° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Smallest normal backlash wanted (pair)
- What it is
- The smallest backlash the gear pair must have, measured along the line of action, normal to the tooth flanks. It sets the thickest allowed tooth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.08 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More minimum backlash thins the tooth and lowers the upper chordal thickness limit.
- Get it right
- Use normal backlash, not circumferential backlash measured at the pitch circle.
What this means: Largest normal backlash wanted (pair)
- What it is
- The largest backlash the gear pair may have, measured normal to the tooth flanks. It sets the thinnest allowed tooth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.16 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More maximum backlash lowers the lower chordal thickness limit.
- Get it right
- It must not be below the smallest backlash.
What this means: Share of the backlash taken by this gear
- What it is
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger share thins this gear more and lowers both chordal thickness limits.
- Get it right
- The shares of the two gears together should make up the whole backlash.
What this means: Measured tip diameter (0 = nominal)
- What it is
- The measured outside (tip) diameter of the gear. The caliper depth is set from the tip, so a tip off nominal moves the depth setting. Type 0 to use the nominal tip.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5000 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 depth setting changes by half the difference between measured and nominal tip diameter.
- Get it right
- Measure the tip at the same teeth used for the reading.
What this means: Measured chordal thickness
- What it is
- The chordal tooth thickness read on the gear tooth vernier, with its depth slide set to the chordal addendum the tool gives.
- 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 4.65 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set the depth slide before reading; a wrong depth gives a wrong thickness.
Method and formulas
- Thinning Δs = share × j_n ÷ cos α; arc thickness s = π m ÷ 2 − Δs at each backlash limit.
- Chordal thickness t_c = D sin(s ÷ D); chordal addendum a_c = m + D ÷ 2 [1 − cos(s ÷ D)] with D = m z (as the chordal tooth tool).
- Depth setting = chordal addendum + (measured tip − nominal tip) ÷ 2.
- Example: set the depth to 3.06 mm; the chordal thickness should read 4.6252–4.6677 mm.
Limitations
- Spur gears; for helical gears use the normal module and virtual tooth count.
- Vernier readings are less accurate than span or over-pins measurement.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set a gear tooth vernier for a cut gear
- Convert a backlash requirement into tooth thickness limits
- Inspect a gear on the machine
Who it is for
- Gear cutters
- Inspectors
- Machinists
What you get
- Arc tooth thickness limits
- Chordal thickness and depth settings
- Accept or reject
Interpreting the result
- Always correct the depth setting for the actual tip diameter: a large tip error changes the thickness read.
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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Open the Gear Tooth Caliper Setting for Backlash (Chordal Thickness Limits) calculator