KEVOS® MAKEOS · Gears
Gear Tooth Measurement for Backlash (Span and Over Pins)
What span measurement and measurement over pins should this gear show once the teeth are thinned for the backlash I want?
Inspection dimensions for an external involute gear cut thin for backlash: the tooth thickness reduction for this gear’s share of the normal backlash range, the number of teeth spanned and the base tangent length (span) at nominal and at both backlash limits (as the span measurement tool), the face width the anvils need on a helical gear, and for spur gears the measurement over pins at nominal and at both limits (as the gear over pins tool).
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal module | mm | Normal module. |
| Number of teeth | Number of teeth. | |
| Normal pressure angle | ° | Normal pressure angle. |
| Helix angle (0 = spur) | ° | Helix angle; 0 for a spur gear (over-pins values are given for spur gears). |
| Profile shift coefficient | Profile shift coefficient of this gear. | |
| Face width | mm | Face width (for the span anvils on a helical gear). |
| 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 (50% for equal sharing). |
| Pin diameter (0 = 1.728 × module) | mm | Pin or ball diameter for the over-pins check. |
Method and formulas
- Normal backlash j_n = (Δs₁ + Δs₂) cos α_n, so this gear’s thinning Δs = share × j_n ÷ cos α_n; the span falls by share × j_n.
- Span W = m_n cos α_n [π(k − 0.5) + z inv α_t] + 2x m_n sin α_n with k from the usual rule (as the span measurement tool); anvils need a face width of W sin β cos α_n.
- Over pins (spur): solve inv φ = s ÷ d + inv α + d_p ÷ d_b − π ÷ z with the thinned tooth thickness s; M = d_b ÷ cos φ + d_p (even teeth) (as the gear over pins tool).
- Example: span over 4 teeth should read 32.178–32.218 mm (nominal 32.258 mm).
Limitations
- External gears; internal gears need a different method.
- Over-pins values are for spur gears; helical gears need the helical over-balls formula.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set the inspection limits for a gear drawing
- Convert a backlash requirement into a span measurement
- Check a gear on the shop floor with a micrometer
Who it is for
- Gear engineers
- Inspectors
- Machinists
What you get
- Tooth thinning for the backlash limits
- Teeth spanned and span measurement limits
- Measurement over pins limits (spur gears)
Interpreting the result
- The span is easier to measure on the machine and does not depend on the outside diameter.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2236–2248. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Gear Tooth Measurement for Backlash (Span and Over Pins) calculator
