KEVOS® 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. |
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
